[ { "schema_version": "1.1", "record_id": "arr:record:9560497d-7e9a-41c0-8ad5-4a173a3b420c", "version_id": "arr:version:7e22618f-16b4-4b2a-a1d9-ffcb03e517ab", "id": "ARR-2026-4NC14QTZMT8708NN", "version": "v1", "record_type": "research_paper", "title": "A complete one-state error–delay law for asymmetric three-node routing", "abstract": "We determine the complete minimax error versus peak angular delay law for rational-inner passive routing of degree at most one at three asymmetric boundary nodes, with one exceptional orthogonal target and two repeated targets. The result supplies both exact branches, the positivity transition, positive lower certificates, and an attaining two-port construction. We then invert the law: a prescribed chordal error determines the minimum delay through one uniquely isolated cubic root with an explicit positivity constraint, or an elementary expression in the active regime. Constant and degree-one branches, the jump at unit peak delay, the transition target and the unattainability of zero error at finite delay are included. Exact rational and symbolic certificates distinguish the continuum proof from supplementary numerical constructions. The result concerns a dimensionless one-state, three-node model and does not claim general circuit-component synthesis or higher-degree optimality.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-09-05", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "*.py", "spdx": "Apache-2.0" }, { "path": "typeset/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "passive spectral routing", "rational inner functions", "peak delay", "minimax error", "positivity transition", "inverse design" ], "subjects": [ "Approximation theory", "Systems and control", "Operator theory" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-1.4" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e82792511520f394d2f67eb603b3b97e89e61911c7ed588436855f1fe416f51a", "canonical_bytes": 3664690 }, "ai_assistance": { "used": true, "systems": [ "OpenAI Codex (gpt-6-astra)" ], "statement": "OpenAI Codex assisted with derivation, exact replay, literature comparison, typesetting and separate internal critical review. Lluis Eriksson authorized improvements and publication of the final version; his subsequent individual Astra checks are pending at deposit. The producing model family participated in the internal review. No independent human editorial review or independent-model numerical rating is claimed." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-09-05", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-6-astra", "outcome": "pass", "report": "screening/final-internal-review.md", "runtime_provenance": "screening/runtime.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "source_integrity": "pass", "bibliography": "partial", "reproducibility": "pass", "lean4": "not_applicable", "report": "VERIFICATION.json" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-directed founder-pilot deposit implementing the current instruction to improve and publish this paper. The author and editorial signer are the same person. DEPOSIT_DECISION.json records a new exception scoped to this exact record/version/PDF; the ordinary independent-human-editor requirement is not fulfilled. Authorization to prepare and publish does not claim that the author already inspected the new final bytes. No independent editorial acceptance or peer review is claimed." }, "related_records": [ { "id": "ARR-2026-6M3VGTXZ6W8JW9C9", "relationship": "extends", "note": "Closes the one-state three-frequency error–delay law and adds exact error-to-minimum-delay inversion within the stated model." } ], "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-4NC14QTZMT8708NN-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:1c7663c2-7a94-4be0-874c-cb938dba17b2", "version_id": "arr:version:18495a50-3753-4e64-a103-0e60c75af85e", "id": "ARR-2026-0WESHW4YMM9FG8EK", "version": "v1", "record_type": "research_paper", "title": "Three-term Weyl operators: central multiplicities, rank laws, and exact list decoding", "abstract": "We classify the ranks of nonzero operators with at most three terms in a fixed cyclic Weyl basis in every prime-power dimension. A central-sector formula valid in arbitrary cyclic dimension computes trinomial nullity from commuting powers and a common block multiplicity; nonzero three-term coefficients permit at most two singular sectors. The formula explains composite-dimension departures from the prime-power bound. For exact-rank pure probes in one-use Weyl channel list discrimination, we classify all reduced states below rank 3d/4 in dyadic dimensions: exactly thirty flat half-rank states. Positive sums of sparse squares produce ranks impossible for an individual three-term factor, including an exact three-label family of rank 13d/16. We also determine an exact four-label family of rank 5d/8 and the complete feasible three-label rank set in dimension sixteen. Classical Weyl representation and covariance tools are attributed; exact algebraic certificates and replay programs accompany the proofs.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-09-05", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "*.py", "spdx": "Apache-2.0" }, { "path": "typeset/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "Weyl operators", "sparse rank", "prime-power dimension", "central sectors", "quantum list discrimination", "positive sparse squares" ], "subjects": [ "Quantum information", "Linear algebra", "Operator theory" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-1.4" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f777ae1be0bce53d34394c3cc823b4d21779156f43e2414a28cae7324cfcdd2f", "canonical_bytes": 2660508 }, "ai_assistance": { "used": true, "systems": [ "OpenAI Codex (gpt-6-astra)" ], "statement": "OpenAI Codex assisted with derivation, exact replay, literature comparison, typesetting and separate internal critical review. Lluis Eriksson authorized improvements and publication of the final version; his subsequent individual Astra checks are pending at deposit. The producing model family participated in the internal review. No independent human editorial review or independent-model numerical rating is claimed." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-09-05", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-6-astra", "outcome": "pass", "report": "screening/final-internal-review.md", "runtime_provenance": "screening/runtime.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "source_integrity": "pass", "bibliography": "partial", "reproducibility": "pass", "lean4": "not_applicable", "report": "VERIFICATION.json" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-directed founder-pilot deposit implementing the current instruction to improve and publish this paper. The author and editorial signer are the same person. DEPOSIT_DECISION.json records a new exception scoped to this exact record/version/PDF; the ordinary independent-human-editor requirement is not fulfilled. Authorization to prepare and publish does not claim that the author already inspected the new final bytes. No independent editorial acceptance or peer review is claimed." }, "related_records": [], "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-0WESHW4YMM9FG8EK-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:a4b8e347-c81f-433e-b26a-4bef1d5cb1c4", "version_id": "arr:version:f5ec2e3d-2bf4-4d0e-ba17-ae20057088d9", "id": "ARR-2026-54Q3HMFJ0Z8CZB4T", "version": "v1", "record_type": "research_paper", "title": "Polynomial vertex reduction and optimal stability at balanced inertia (4,4)", "abstract": "For every balanced sign multiplicity N and fixed ambient dimension, we reduce the optimal forward stability coefficient for inverse self-commutator cost to a rational list of O(N^5) spectral pairs. This counts Horn linear programs, not their size or total running time. At inertia (4,4), exact rational certificates for 89 ordered vertices establish the optimal coefficient 4/7 in every fixed ambient dimension at least eight. An ambient-independent Horn obstruction and a boundary perturbation prove sharpness. We classify the full equality set on the compact spectral closure and show strictness throughout the exact inertia stratum. Together with the previously sharp reverse coefficient 3/2, this completes both stability constants at multiplicity four. Constants for N at least five remain unevaluated. All finite certificates and replay programs are supplied; classical Horn sufficiency and written polyhedral arguments are explicit dependencies.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-09-05", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "*.py", "spdx": "Apache-2.0" }, { "path": "typeset/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "inverse self-commutator", "balanced inertia", "sharp stability", "Horn inequalities", "equality cases", "rational certificate" ], "subjects": [ "Matrix analysis", "Operator theory", "Exact computational mathematics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-1.4" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c4e21f587ecaafe4aa01e7b638e3f23b90263bfe77970a924b48625afbc52901", "canonical_bytes": 1845547 }, "ai_assistance": { "used": true, "systems": [ "OpenAI Codex (gpt-6-astra)" ], "statement": "OpenAI Codex assisted with derivation, exact replay, literature comparison, typesetting and separate internal critical review. Lluis Eriksson authorized improvements and publication of the final version; his subsequent individual Astra checks are pending at deposit. The producing model family participated in the internal review. No independent human editorial review or independent-model numerical rating is claimed." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-09-05", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-6-astra", "outcome": "pass", "report": "screening/final-internal-review.md", "runtime_provenance": "screening/runtime.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "source_integrity": "pass", "bibliography": "partial", "reproducibility": "pass", "lean4": "not_applicable", "report": "VERIFICATION.json" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-directed founder-pilot deposit implementing the current instruction to improve and publish this paper. The author and editorial signer are the same person. DEPOSIT_DECISION.json records a new exception scoped to this exact record/version/PDF; the ordinary independent-human-editor requirement is not fulfilled. Authorization to prepare and publish does not claim that the author already inspected the new final bytes. No independent editorial acceptance or peer review is claimed." }, "related_records": [ { "id": "ARR-2026-24M24KDPZK8HDBQ9", "relationship": "extends", "note": "Evaluates the previously open balanced multiplicity-four forward constant, proves a general finite vertex reduction and classifies the multiplicity-four equality cases." } ], "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-54Q3HMFJ0Z8CZB4T-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:44a08936-dbf3-445a-bba5-9e9dd2901e79", "version_id": "arr:version:9206c9f4-49d8-46f6-b5e6-4af5f804cc4a", "id": "ARR-2026-24M24KDPZK8HDBQ9", "version": "v1", "record_type": "research_paper", "title": "Sharp inertia ceilings and optimal stability for inverse self-commutators", "abstract": "We determine the sharp worst inverse self-commutator cost for every prescribed inertia, including arbitrary ambient zeros, and quantify its extremal geometry. For unequal sign multiplicities we obtain both optimal constants relating the normalized cost deficit to distance from the one-spike, opposite-flat boundary. The reverse coefficient is also optimal for every balanced inertia. For three positive and three negative eigenvalues we close the other direction as well: the optimal forward coefficient is 17/36. Its proof reduces a piecewise-affine distance to 22 rational vertices and supplies exact Horn witnesses; a boundary spectrum gives ambient-independent sharpness. Thus every nearly extremal sequence is classified. A transportation refinement gives computable primal-dual upper certificates, while an exact example shows a 12.5% gap from the actual matrix cost. A sharp deficit threshold also reduces rank-ceiling stability to the known one-spike case. Classical Horn sufficiency is imported; all finite certificates are supplied for replay. The optimal balanced forward coefficient for multiplicity at least four and the general interior cost remain open here.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-09-05", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "replay/*.py", "spdx": "Apache-2.0" }, { "path": "typeset/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "certificates/*.json", "spdx": "CC0-1.0" }, { "path": "replay/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "inverse self-commutator", "Hilbert--Schmidt norm", "inertia", "Horn inequalities", "sharp bound", "spectral stability", "optimal transport", "rational certificate" ], "subjects": [ "Matrix analysis", "Operator theory", "Exact computational mathematics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-1.4" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "15b54435c01a4972af77db0277c7f99fc21afb43be3bbc56b1884b76bb53bf30", "canonical_bytes": 3339311 }, "ai_assistance": { "used": true, "systems": [ "OpenAI Codex (gpt-6-astra)" ], "statement": "OpenAI Codex assisted with proof development, exact replay, literature comparison, typesetting and separate internal critical review. The author reviewed and approved this exact manuscript. The producing model family also supplied the declared ARR assessment, marked involved_in_manuscript and excluded from independent-model headline aggregation. No independent human editorial review is claimed." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-09-05", "evaluators": [ { "model_id": "gpt-6-astra", "reasoning_effort": "max", "outcome": "pass", "report": "screening/model-response.json", "runtime_provenance": "screening/runtime.json", "provider": "OpenAI" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "source_integrity": "pass", "bibliography": "partial", "reproducibility": "pass", "lean4": "not_applicable", "report": "VERIFICATION.json" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-directed founder-pilot deposit. Lluis Eriksson approved the reviewed manuscript and explicitly instructed publication after the independent-editor requirement had been disclosed. This is a record-specific exception to the ordinary founder-conflict rule in docs/GOVERNANCE.md and docs/EDITORIAL_POLICY.md. The sign-off is the conflicted author-editor's approval, not independent editorial acceptance or peer review. See DEPOSIT_DECISION.json for the exact version, evidence and scope." }, "related_records": [ { "id": "ARR-2026-1D2QV1RP1292JREW", "relationship": "extends", "note": "Improves the rank-only ceiling to the sharp fixed-inertia ceiling and resolves the stated local arbitrary-sign upper-endpoint stability problem." }, { "id": "ARR-2026-7NPRNBW4488HG90K", "relationship": "related_work", "note": "Supplies the one-spike cost formula and Gini constants recalled with proof; these are attributed antecedents." }, { "id": "ARR-2026-5QQF95VHTC9GABH8", "relationship": "related_work", "note": "Supplies the prior Horn spectral formulation, norm-optimal rank obstructions and examples refuting general zero-padding invariance." }, { "id": "ARR-2026-3M1EEG1T689ADSMW", "relationship": "related_work", "note": "Prior four-level cost formula; balanced multiplicity-two identity is attributed." }, { "id": "ARR-2026-37B8R0QTA894GTFF", "relationship": "related_work", "note": "Prior five-level cost theory underlying the transport separation benchmark." } ], "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-24M24KDPZK8HDBQ9-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:22e20904-af6c-42ee-a75f-73786281243d", "version_id": "arr:version:6ec382e4-810c-4e27-b826-2072d9a14d64", "id": "ARR-2026-12W84G9BVC8BQAEQ", "version": "v1", "record_type": "research_paper", "title": "Exact Rank Transitions through p=32 and a Half-Integral Optimum at p=53", "abstract": "For F_(p,q)=diag(q repeated p times, -p repeated q times), this paper studies the least rank among factors minimizing one half of the squared Hilbert--Schmidt norm subject to CC^*-C^*C=2F. On q=2p+1, exact rational hive primal-dual certificates determine the complete finite cost-and-rank frontier for 4<=p<=32: the rank excess above q is 0 on p=4..7, 1 on p=8..14, 2 on p=15..26, 3 at p=27, and 4 on p=28..32. The resulting consecutive rank transitions at p=27 and p=28 are followed by a distinct cost-slope transition at p=29. Separately, exact certificates prove kappa(F_(53,107))=8847 with minimum attaining rank 115; its optimum is half-integral, while an earlier integer candidate of trace 8843 is refuted by an integral Farkas certificate. The conclusions are finite and conditional on the classical Horn--Klyachko/hive theorem; no all-parameter recurrence, classification of all minimizers, exhaustive priority result, proof-assistant formalization, or independent peer review is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-09-02", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/**/*.py", "spdx": "AGPL-3.0-only" } ], "data": [ { "path": "src/repro/**/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "inverse self-commutator", "Hilbert--Schmidt norm", "minimum rank", "Horn inequalities", "hive polytope", "rank transition", "Farkas certificate", "half-integral optimum" ], "subjects": [ "Matrix analysis", "Operator theory", "Algebraic combinatorics", "Exact computational mathematics" ], "related_records": [ { "id": "ARR-2026-5QQF95VHTC9GABH8", "relationship": "extends", "note": "The related record supplies the earlier exact low-dimensional and amplification results. This paper extends the finite two-ray frontier through p=32 and adds the independent p=53 theorem and exact refutation." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3fe985b56fb83278d16fbbf55975a77d4964b87311ef4490c74fea8766b7fe1a", "canonical_bytes": 21272 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with corpus triage, mathematical exploration, exact certificate reconstruction, adversarial verification, manuscript revision, typesetting, visual QA, reproducibility hardening, and ARR record preparation. The author selected the claims, authorized publication, and remains responsible for the work.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "bibliography": "partial", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person; no independent editorial review is claimed." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:b7bbd25d-c74c-4c14-b8a1-fd0689e94154", "version_id": "arr:version:5b0e260a-0da2-4bb7-87ff-8247660c333d", "id": "ARR-2026-5QQF95VHTC9GABH8", "version": "v1", "record_type": "research_paper", "title": "Sharp Onset and Unbounded Growth of Norm-Optimal Self-Commutator Rank", "abstract": "For a traceless Hermitian target F, this paper studies the least rank r_*(F) among factors C minimizing one half of the squared Hilbert--Schmidt norm subject to CC^*-C^*C=2F. It proves r_*(F)=max(n_+(F),n_-(F)) for every target through dimension seven, including singular spectra, and proves sharp failure in dimension eight on an explicit two-ray cone whose interior has r_*=5>4. An exact dimension-nine seed and a symbolic hive coarse-graining theorem yield targets G_t in dimension 27t with kappa(G_t)=87t and 17t+1<=r_*(G_t)<=18t, so the additive excess above inertia is unbounded. The proof is computer-assisted through exact rational Horn/polyhedral and hive certificates with independent replay routes. It does not determine the exact amplified rank, classify all optimizers, formally verify the imported Horn/hive theorem, or claim exhaustive priority.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-30", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/**/*.py", "spdx": "AGPL-3.0-only" }, { "path": "src/repro/**/*.ps1", "spdx": "AGPL-3.0-only" }, { "path": "src/repro/tools/linux/**", "spdx": "GPL-2.0-or-later" } ], "data": [ { "path": "src/repro/**/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "self-commutator", "inverse commutator", "Hilbert--Schmidt norm", "minimum rank", "Horn inequalities", "hive polytope", "Farkas certificate", "coarse-graining" ], "subjects": [ "Matrix analysis", "Operator theory", "Algebraic combinatorics" ], "related_records": [ { "id": "ARR-2026-1D2QV1RP1292JREW", "relationship": "related_work", "note": "Provides general rank-adaptive cost bounds and equality classifications; it does not contain the complete threshold through dimension seven, the sharp dimension-eight onset, or unbounded optimal-rank excess." }, { "id": "ARR-2026-7NPRNBW4488HG90K", "relationship": "related_work", "note": "Provides the complete one-spike inverse-cost formula and exact kick-synthesis laws; it does not contain the threshold or amplification theorem proved here." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "17b2361721027649b8ef5b98440032b91b5b04e89e2a9535fcbe7a27954ac1c5", "canonical_bytes": 477088 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with corpus and literature triage, mathematical exploration, adversarial proof review, exact-arithmetic replay, manuscript revision, typesetting, visual QA, reproducibility hardening, independent model-assessment coordination, and ARR record preparation. The author selected the claims, reviewed the manuscript, authorized publication, and remains responsible for the work.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-08-30", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-5.6-sol", "reasoning_effort": "high", "outcome": "pass", "report": "screening/final-assessment.json", "runtime_provenance": "screening/runtime-provenance.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: the author and ARR founder-editor are the same person. 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On the complete one-spike spectral cone with nonzero spectrum (P,-b_1,...,-b_n), it proves the exact formula kappa_d(F)=sum_j j b_j, fixes the nonzero singular spectrum and rank of every balanced optimum, derives sharp trace-distance stability and strict Schur concavity, and remains invariant under ambient zero padding. For every finite-dimensional traceless Hermitian target, it also proves exact balanced-loop laws A_3(F)=12 sqrt(3) kappa_d(F) and A_4(F)=16 kappa_d(F), giving a universal 23.02 percent fourth-kick reduction. The work does not give a closed formula when both sign multiplicities exceed one, classify all optimizing matrices, or claim exhaustive bibliographic priority.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-30", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "AGPL-3.0-only" }, { "path": "src/repro/*.ps1", "spdx": "AGPL-3.0-only" } ], "data": [ { "path": "src/repro/results/*.json", "spdx": "CC0-1.0" }, { "path": "src/repro/manifest.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "self-commutator", "inverse commutator", "Hilbert--Schmidt norm", "Horn inequalities", "singular-value rigidity", "matrix polygon", "curvature synthesis", "Schur concavity" ], "subjects": [ "Matrix analysis", "Operator theory", "Mathematical physics" ], "related_records": [ { "id": "ARR-2026-1D2QV1RP1292JREW", "relationship": "related_work", "note": "Provides complementary rank-adaptive bounds and equality classifications for arbitrary sign patterns; it does not contain the complete one-spike formula or the all-target kick laws." }, { "id": "ARR-2026-1PT4297HNX9T4RBD", "relationship": "related_work", "note": "Contains the earlier qutrit specialization and associated quantum applications." }, { "id": "ARR-2026-3M1EEG1T689ADSMW", "relationship": "related_work", "note": "Contains the earlier complete four-level inverse-cost formula and triangular-loop specialization." }, { "id": "ARR-2026-37B8R0QTA894GTFF", "relationship": "related_work", "note": "Contains the earlier complete five-level inverse-cost formula." }, { "id": "ARR-2026-0FF03PQCTD89KBTM", "relationship": "related_work", "note": "Contains earlier balanced-kick mechanisms in an operational-curvature setting." }, { "id": "ARR-2026-2JJFS9HNTT87DAGC", "relationship": "related_work", "note": "Contains the earlier sign-paired matrix-polygon equality face extended here to arbitrary traceless Hermitian targets." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "0f45a998063e687cc689b8e43c2887194c0937c8587c34b783a1631f8974776d", "canonical_bytes": 341892 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with corpus and literature triage, algebraic exploration, adversarial proof review, exact-arithmetic replay, typesetting, visual QA, reproducibility hardening, and record preparation. The author selected the claims, reviewed the manuscript, authorized publication, and remains responsible for the work.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-08-30", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-5.6-sol", "reasoning_effort": "high", "outcome": "pass", "report": "screening/final-assessment.json", "runtime_provenance": "screening/runtime-provenance.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: the author and ARR founder-editor are the same person. Acceptance records a technically valid deposit after explicit audits; it is not independent peer review or a guarantee that the theorem is correct or novel." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7NPRNBW4488HG90K-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:2d15f61c-5822-48a5-8771-3ca8a3156a23", "version_id": "arr:version:9995fadc-8487-446c-b368-15ad54297648", "id": "ARR-2026-1D2QV1RP1292JREW", "version": "v1", "record_type": "research_paper", "title": "Sharp Rank-Adaptive Bounds for Inverse Self-Commutators", "abstract": "For a nonzero traceless Hermitian matrix F, this paper studies the least product of unnormalized Hilbert--Schmidt norms of Hermitian H and K satisfying -i[H,K]=F. Writing rho=rank(F) and P(F)=||F||_1/2, it proves the sharp dimension-free bounds P(F)<=kappa_d(F)<=rho P(F)/2. Both equality loci are classified: the lower endpoint is attained exactly by centrally paired nonzero spectra, while the upper endpoint is attained exactly, up to positive scale and sign, by the one-spike spectrum (rho-1,-1,...,-1), with arbitrary zero padding. An exact sign-cut leakage identity identifies the full tax above the trace-norm floor. The upper bound uses an exact weighted-shift permutation average, and rho-1 explicit Horn--Littlewood--Richardson inequalities certify upper-endpoint sharpness. The work does not claim a closed formula for general interior spectra or an upper-endpoint stability modulus.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-30", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "AGPL-3.0-only" } ], "data": [ { "path": "src/repro/verification.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "self-commutator", "inverse commutator", "Hilbert--Schmidt norm", "Horn inequalities", "weighted shift", "trace norm", "matrix analysis" ], "subjects": [ "Matrix analysis", "Operator theory", "Mathematical physics" ], "related_records": [ { "id": "ARR-2026-1PT4297HNX9T4RBD", "relationship": "related_work", "note": "Contains the earlier qutrit exact-cost specialization and associated quantum applications." }, { "id": "ARR-2026-3M1EEG1T689ADSMW", "relationship": "related_work", "note": "Gives the complete four-level Horn chamber formula, whereas this record resolves uniform extremal bounds." }, { "id": "ARR-2026-37B8R0QTA894GTFF", "relationship": "related_work", "note": "Gives the complete five-level interior formula; neither result subsumes the other." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "106e6011a9506b6f64ac04fdc6d991e11bae7db3b4bf7c76cad33825e2190337", "canonical_bytes": 455967 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with corpus and literature triage, algebraic exploration, hostile proof review, exact-arithmetic replay, typesetting, visual QA, and artifact preparation. The author selected the theorem, reviewed the claims, and remains responsible for the manuscript.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "pass", "critical_objections_unresolved": 0, "human_signoff": true, "completed_at": "2026-08-30", "evaluators": [ { "provider": "OpenAI", "model_id": "gpt-5.6-sol", "reasoning_effort": "high", "outcome": "pass", "report": "screening/model-gpt-5.6-sol.md", "runtime_provenance": "screening/runtime-provenance.json" } ] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: the author and ARR founder-editor are the same person. Acceptance records a technically valid deposit after explicit audits; it is not independent peer review or a guarantee that the theorem is correct or novel." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-1D2QV1RP1292JREW-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:a366b136-e6c6-416d-a287-00b745d4ccc2", "version_id": "arr:version:c0c14749-c916-4b96-b34c-d08145b25e9f", "id": "ARR-2026-53CTRKDSP685PT51", "version": "v5", "record_type": "research_paper", "title": "The Schwarzian Bridge in a Single Sigmoid Neuron: Oracle Gram Resolution, Joint Spectral Lexicography, and Spherical Saturation Phases", "abstract": "A sigmoid neuron induces two distinct spectral geometries: a population radial-tangential anisotropy controlled locally by the Schwarzian derivative, and an empirical extreme-saturation hierarchy controlled by samples nearest the transition hyperplane. For logistic powers h_p=sigma'^p, p>0, we prove exact saturation constants, sharp pointwise bilateral oracle-Gram complexity, and regularly varying spherical radius phases. We then make the empirical hierarchy quantitative. A deterministic exterior-power theorem resolves every leading eigenspace; an exact inverse-Gaussian angle law and a finite hierarchy perturbation lemma yield an explicit joint finite-radius, finite-sample guarantee for the bottom eigenspace and teacher direction. Finally, a two-dimensional tangent Gaussian process proves that uniform control over a full angular shell intrinsically incurs a square-root log-radius factor in the iterated high-probability limit. Deterministic replays, hostile proof, novelty, and reproducibility audits, and exact source provenance accompany the paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-30", "status": "corrected", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/**/*.py", "spdx": "AGPL-3.0-only" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "single neuron", "sigmoid activation", "Schwarzian derivative", "Loewner matrix", "matrix monotonicity", "Fisher information", "spherical design", "saturation anisotropy", "weighted sample covariance", "finite-sample concentration", "sharp empirical complexity", "spectral lexicography", "regular variation", "Gaussian inverse law", "angular concentration" ], "subjects": [ "Machine learning theory", "Matrix analysis", "Information geometry" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f90a308999b00697245dc87b0588efa162f8e380ed69f5c7454eff660b381e0d", "canonical_bytes": 660109 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with public-repository and primary-literature triage, theorem exploration, proof development, adversarial proof/algebra/priority audits, numerical replay, drafting, LaTeX production, visual QA, and deposit preparation. The retained AI audits are not human peer review, formal verification, independent reproduction, or a guarantee of priority; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable" }, "editorial": { "decision": "correction", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Version v5 supersedes v4. Declared major revision: Adds a joint finite-saturation bottom-eigenspace theorem, deterministic exterior-power spectral lexicography, an exact inverse-Gaussian angle law, and an intrinsic angular shell lower bound with the square-root log-radius factor; strengthens claim boundaries, hostile audits, and reproducibility. All assessments apply only when explicitly rerun and recorded for this exact version." }, "supersedes_version_id": "arr:version:1ec978e3-4d24-4bbe-b1e0-bd94e5a6d7ef", "revision": { "change_size": "major", "summary": "Adds a joint finite-saturation bottom-eigenspace theorem, deterministic exterior-power spectral lexicography, an exact inverse-Gaussian angle law, and an intrinsic angular shell lower bound with the square-root log-radius factor; strengthens claim boundaries, hostile audits, and reproducibility." }, "latest_version": "v5", "version_count": 5, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-53CTRKDSP685PT51-v1", "source_snapshot_available": true }, { "version": "v2", "publication_state": "published", "release_tag": "ARR-2026-53CTRKDSP685PT51-v2", "source_snapshot_available": true }, { "version": "v3", "publication_state": "published", "release_tag": "ARR-2026-53CTRKDSP685PT51-v3", "source_snapshot_available": true }, { "version": "v4", "publication_state": "published", "release_tag": "ARR-2026-53CTRKDSP685PT51-v4", "source_snapshot_available": true }, { "version": "v5", "publication_state": "published", "release_tag": "ARR-2026-53CTRKDSP685PT51-v5", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:8ff458b5-5c1a-43e3-85ea-65271ef4ee4e", "version_id": "arr:version:5dfd55c1-3e40-428a-a9c7-8e69d7db385d", "id": "ARR-2026-4FYHCBAQ0T8FHRBT", "version": "v1", "record_type": "research_paper", "title": "Prescribed Tjurina Algebras and Complete Spectra in Osculating-Absorbing Gauss Fibres", "abstract": "Given d >= 1, 1 <= s <= m, N = binom(d+m,d), and any N isolated complex hypersurface germs g_i of order at least s+1, we construct, for every D >= 1 + sum_i(tau(g_i)+2), a smooth integral degree-D hypersurface with a tangent hyperplane whose reduced Gauss fibre has exactly N points, is point-span order-s osculating-absorbing, and has the prescribed completed Tjurina algebras. The fibre length is sum_i tau(g_i), and the dual multiplicity is sum_i mu(g_i). For surfaces, the classical complete Tjurina spectrum of ordinary plane multiple points yields every integer fibre length between binom(m+2,2) floor((3s^2+4s-3)/4) and binom(m+2,2)s^2 at fixed dual multiplicity. We also give a direct strong-Lefschetz proof that x^(s+1)+y^(s+1)+z^(s+1)+(x+y+z)^(s+2) attains Wahl's classical three-variable value s(s+2)(2s-1)/3, producing sharp absorbed threefold fibres. All claims are over C; degree bounds are sufficient, not asserted minimal, and no exhaustive priority or human peer-review claim is made.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-25", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "Tjurina algebra", "Gauss fibre", "osculating absorption", "prescribed singularities", "strong Lefschetz property", "dual variety", "ordinary multiple point" ], "subjects": [ "Algebraic geometry", "Singularity theory", "Projective geometry", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-2MZWECWVEN97ARVQ", "relationship": "extends", "note": "Extends the earlier two-local-type separator and Bertini construction to heterogeneous lists of arbitrary isolated hypersurface germs." }, { "id": "ARR-2026-5XEX8EX0629R997Y", "relationship": "extends", "note": "Uses the Euler-reduced universal Tjurina floor and supplies a direct equality family in three variables plus new global realization consequences." }, { "id": "ARR-2026-66Q8M61AA196T8BC", "relationship": "related_work", "note": "Uses its minimal-support theorem for point-span higher-osculating absorption." }, { "id": "ARR-2026-0WAPCGQHNC82S8VJ", "relationship": "related_work", "note": "Shares the dual-multiplicity and Gauss-fibre framework." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d5f0bfaaa28e066c3d99fad9581b083ebb4ea16697931a1975089655b613c40c", "canonical_bytes": 24298 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with theorem development, adversarial proof repair, primary-literature and public-corpus triage, exact replay code, drafting, LaTeX production, visual QA, packaging, and deposit preparation. A separate Codex referee task audited an exact final source hash and reported no unresolved mathematical objections. These AI checks are not human peer review, formal verification, independent reproduction, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person. Deposit preserves a citable, reproducible research object but does not constitute independent editorial acceptance or scientific certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-4FYHCBAQ0T8FHRBT-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:bd7750ee-80c2-4e12-93fa-c4502aeb6598", "version_id": "arr:version:bd6b228a-9c77-4285-bc17-b18cdee37d3c", "id": "ARR-2026-5XEX8EX0629R997Y", "version": "v2", "record_type": "research_paper", "title": "Euler-Reduced Tjurina Floors for Osculating-Absorbing Gauss Fibres", "abstract": "Let h in C[[x_1,...,x_d]] have order at least s+1 and finite Tjurina algebra. Euler cancellation replaces h, without changing its Tjurina ideal, by a generator of order at least s+2. A finite-jet generator count then gives tau(h) at least E_{d,s}, the maximum over K of binom(d+K,d)-d binom(d+K-s,d)-binom(d+K-s-2,d). For plane germs this is the exact universal floor floor((3s^2+4s-3)/4), attained by classical ordinary multiple-point families. Applied to a point-span s-osculating-absorbing reduced fibre of the Gauss map in the complete O_X(m) embedding, the result gives length(Gamma_eta) at least E_{d,s} binom(d+m,d). For surfaces, a prescribed-jet construction realizes equality at an explicit sufficient degree. The work is over C; the higher-dimensional floor need not be sharp, the degree threshold is not claimed minimal, and no exhaustive priority, human peer-review, or formal-verification claim is made.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-25", "status": "corrected", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "Tjurina number", "Euler identity", "Gauss map", "osculating absorption", "scheme-theoretic fibre", "ordinary multiple point", "projective duality" ], "subjects": [ "Algebraic geometry", "Singularity theory", "Projective geometry", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-2MZWECWVEN97ARVQ", "relationship": "extends", "note": "Strengthens the predecessor's fat-point Tjurina floor by an Euler-reduced optimized local count and proves the exact surface floor." }, { "id": "ARR-2026-2MHNZRRJP49Y9SWP", "relationship": "related_work", "note": "Uses its exact point-span tangent-absorption support floor." }, { "id": "ARR-2026-0WAPCGQHNC82S8VJ", "relationship": "related_work", "note": "Shares the Gauss-fibre and dual-singularity framework." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "31d065fafafaff90b5449b8bc7243f3cfca8be40e0ac3d6fa824fd42c9cee37a", "canonical_bytes": 21734 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with theorem exploration, proof development, adversarial repair, primary-literature and public-corpus triage, exact replay code, drafting, LaTeX production, visual QA, packaging, and deposit preparation. Separate Codex referee tasks audited exact source snapshots. These AI checks are not human peer review, formal verification, independent reproduction, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "correction", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Version v2 supersedes v1. Declared minor revision: Corrects the canonical source hash after Git line-ending normalization and records the preserved LF byte stream; mathematical content is unchanged. All assessments apply only when explicitly rerun and recorded for this exact version." }, "supersedes_version_id": "arr:version:3c500b1c-50b2-47ed-b772-89dffdc0a718", "revision": { "change_size": "minor", "summary": "Corrects the canonical source hash after Git line-ending normalization and records the preserved LF byte stream; mathematical content is unchanged." }, "latest_version": "v2", "version_count": 2, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-5XEX8EX0629R997Y-v1", "source_snapshot_available": true }, { "version": "v2", "publication_state": "published", "release_tag": "ARR-2026-5XEX8EX0629R997Y-v2", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:54ff1cce-6dd5-49d5-8ddf-e9f45b289659", "version_id": "arr:version:6c745ad9-ca7b-4e2b-ad04-6e2ab157a127", "id": "ARR-2026-2MZWECWVEN97ARVQ", "version": "v1", "record_type": "research_paper", "title": "Fat Gauss Fibres and Tjurina–Milnor Defects Forced by Osculating Absorption", "abstract": "Let X be a smooth non-linear complex hypersurface and let Gamma_eta be the scheme-theoretic fibre of its Gauss normalization over a tangent hyperplane. The completed local fibre algebra is the Tjurina algebra of the tangent-section germ, while the classical dual multiplicity is the sum of its Milnor numbers; hence their difference is the total Tjurina–Milnor defect. Under point-span order-s osculating absorption in the complete O_X(m) embedding, the fibre contains the order-s fat point at every reduced support and has length at least binom(d+s-1,d) binom(d+m,d). When d(s-1)>s+1, prescribed jets realize every integral defect from 0 through the extremal support size while keeping all Milnor numbers fixed. The degree threshold is sufficient, not minimal; no positive-characteristic extension, exhaustive priority claim, human peer review, or formal verification is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-25", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "projective duality", "Gauss map", "Tjurina number", "Milnor number", "osculating absorption", "scheme-theoretic fibre", "ramification" ], "subjects": [ "Algebraic geometry", "Projective geometry", "Singularity theory", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-0WAPCGQHNC82S8VJ", "relationship": "extends", "note": "Refines the predecessor's dual-multiplicity floor by identifying the scheme-fibre length and constructing an exact Tjurina–Milnor defect ladder." }, { "id": "ARR-2026-66Q8M61AA196T8BC", "relationship": "related_work", "note": "Uses the predecessor's higher-osculating support floor and adapts its prescribed-jet architecture." }, { "id": "ARR-2026-2MHNZRRJP49Y9SWP", "relationship": "related_work", "note": "Uses the exact tangent-absorption support floor through the higher-osculating predecessor." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "36db52e07b299dedb47873c87fd8383261c4364a0e73b4eb41af1516b2be7c2c", "canonical_bytes": 26132 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with proof development, adversarial repair, primary-literature and public-corpus triage, exact replay code, drafting, LaTeX production, packaging, and deposit preparation. Separate read-only Codex referee tasks audited exact source hashes. These AI checks are not human peer review, formal verification, independent reproduction, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person. Deposit preserves a citable, reproducible research object but does not constitute independent editorial acceptance or scientific certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-2MZWECWVEN97ARVQ-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:1c55990b-c6ac-40b2-8dca-0a0e11d3f361", "version_id": "arr:version:147f2652-8dcb-4b05-9ca0-462f844e5288", "id": "ARR-2026-0WAPCGQHNC82S8VJ", "version": "v1", "record_type": "research_paper", "title": "Exact Multiplicity Floors for Dual Singularities from Absorbing Gauss Fibres", "abstract": "Let X be a smooth complex hypersurface and let Z be the complete reduced fibre of its Gauss map over a tangent hyperplane W. In the complete O_X(m) embedding, assume that the point span of Z contains the order-s osculating space at every support, with 1 <= s <= m. We prove the sharp floor mult_W(X^vee) >= s^d |Z| >= s^d binom(d+m,d). Absorption forces order-(s+1) contact; the classical multiplicity-Milnor formula and a local Milnor lower bound give the dual multiplicity estimate, while exact tangent absorption gives the branch floor. For every d,m,s we construct equality examples with proper point span, exact reduced Gauss fibre, ordinary section singularities, and the stated weighted tangent-cone cycle. The construction gives a sufficient nonminimal hypersurface degree. No equality classification, positive-characteristic extension, exhaustive priority claim, human peer review, or formal verification is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-24", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "projective duality", "Gauss map", "dual multiplicity", "Milnor number", "osculating spaces", "point-span absorption", "tangent cone" ], "subjects": [ "Algebraic geometry", "Projective geometry", "Singularity theory", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-66Q8M61AA196T8BC", "relationship": "extends", "note": "Adds exact reduced Gauss-fibre and complex dual-singularity geometry to the predecessor's higher-osculating floors and proper-span construction." }, { "id": "ARR-2026-2MHNZRRJP49Y9SWP", "relationship": "related_work", "note": "Uses version 3's exact tangent-absorption floor to obtain the binomial branch floor." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "1dcee79755257e0e4c46e63f259c3a2f3f9fc832c063d229057db3f383854770", "canonical_bytes": 25277 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with proof development, adversarial repair, primary-literature and public-corpus triage, exact replay code, drafting, LaTeX production, packaging, and deposit preparation. A separate read-only Codex referee audited exact source hashes. These AI checks are not human peer review, formal verification, independent reproduction, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person. Deposit preserves a citable, reproducible research object but does not constitute independent editorial acceptance or scientific certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-0WAPCGQHNC82S8VJ-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:c6ba2860-a941-49b4-85b2-4eaf110b556a", "version_id": "arr:version:a2e87f78-a6a8-4ea0-aec0-35765b7314f1", "id": "ARR-2026-66Q8M61AA196T8BC", "version": "v2", "record_type": "research_paper", "title": "Exact Floors and Proper-Span Extremizers for Higher Osculating Absorption", "abstract": "Let X be a smooth projective integral d-fold over an algebraically closed field, let H be very ample, and use the complete embedding defined by H^m. Fix 1 <= s <= m and suppose that the span of a nonempty finite reduced set Z contains the order-s affine osculating space at every support. We prove the exact characteristic-free floor dim(S_Z), |Z| >= binom(d+m,d), by reduction to exact tangent absorption. For every d, m, s and every characteristic, we construct a smooth integral hypersurface with a proper-span equality set whose normal coordinate vanishes to order s+1 at every support. If r_1(Z) is the degree-one evaluation rank and m >= 2s+1, we also prove the rank-sensitive term binom(d+s,d) r_1(Z); rational normal curves show the threshold is necessary for that uniform formula. The earlier mixed-jet certificate is retained for jet-ample polarizations but identified as numerically subordinate for tensor powers. No equality classification, minimal hypersurface degree, exhaustive priority claim, human peer review, or formal verification is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-24", "status": "corrected", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "osculating spaces", "jet ampleness", "fat points", "proper-span extremizers", "higher contact", "rank-sensitive bounds", "arbitrary characteristic", "fat points" ], "subjects": [ "Algebraic geometry", "Projective geometry", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-19BXX42GM38K6VZ3", "relationship": "extends", "note": "Uses an explicit higher-osculating hypothesis and retains the heterogeneous mixed-jet certificate; it is a separate record and does not supersede the earlier tangent/Gauss paper." }, { "id": "ARR-2026-2MHNZRRJP49Y9SWP", "relationship": "related_work", "note": "Invokes version 3's exact tangent-absorption floor and proves higher-order sharpness plus a rank-sensitive refinement." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "source_sha256": "17810cc2c07029b913b50665bf72fa569762670cc836900bc3cbfa1bfea0a414", "source_bytes": 29998, "pdf_sha256": "bc38ace5861ded29f0bf943e8825dac5d785a59f1ffbbaa917a7a154d02f2d7d", "pdf_bytes": 411060, "pdf_pages": 10 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with adversarial mathematical review, proof development and repair, primary-literature triage, exact replay code, drafting, LaTeX production, packaging, and ARR deposit preparation. Separate Codex referee tasks audited the mathematical claims and exact-source repairs. These AI checks are not human peer review, formal verification, independent reproduction, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable" }, "editorial": { "decision": "correction", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Version v2 supersedes v1. Declared major revision: replaces the valid but nonoptimal mixed-jet floor by the exact binomial floor, adds rank-sensitive higher-jet blocks above a sharp uniform threshold, and constructs proper-span equality examples in every characteristic and osculating order. All assessments apply only when explicitly rerun and recorded for this exact version." }, "supersedes_version_id": "arr:version:b6687eb9-532b-40bb-a589-8457c319425e", "revision": { "change_size": "major", "summary": "Replaces the valid but nonoptimal mixed-jet floor by the exact binomial floor, adds rank-sensitive higher-jet blocks, and constructs proper-span equality examples in every characteristic and osculating order." }, "latest_version": "v2", "version_count": 2, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-66Q8M61AA196T8BC-v1", "source_snapshot_available": true }, { "version": "v2", "publication_state": "published", "release_tag": "ARR-2026-66Q8M61AA196T8BC-v2", "source_snapshot_available": true } ] }, { "schema_version": "1.2", "record_id": "arr:record:548d7f8c-4ac4-4f93-9e5b-5611cc168349", "version_id": "arr:version:54024fe5-750d-47d9-9982-79440e4a8647", "id": "ARR-2026-2MHNZRRJP49Y9SWP", "version": "v3", "record_type": "research_paper", "title": "The Exact Rank Floor for Point-Span Tangent Absorption in Arbitrary Characteristic", "abstract": "Let X be a smooth projective integral d-fold over an algebraically closed field of arbitrary characteristic, let L be very ample, let m be at least one, and let Z be a nonempty finite reduced set whose point span in the complete L^m-embedding contains every tangent space at its supports. We prove the exact codimension-free floor h_Z(m), |Z| >= binom(d+m,d). An adapted finite projection to P^d transfers absorption to equality between the degree-m pieces of the radical ideal of the projected points and its symbolic square. The standard perfect-field derivative/p-th-root gap forces that piece to vanish. Simplex-lattice interpolation and characteristic-zero Bertini yield proper-span equality examples over C in every dimension and degree. No imperfect-field, singular, nonreduced, or equality-classification result is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-24", "status": "corrected", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "fat points", "symbolic square", "arbitrary characteristic", "Frobenius", "finite projection", "tangent absorption", "multivariate interpolation", "Gauss map", "Terracini locus" ], "subjects": [ "Algebraic geometry", "Commutative algebra" ], "related_records": [], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "source_sha256": "1480283c47f0e25762353f3e032fb459f2091c036c5ce676dbe2ddd9fe70d0d4", "source_bytes": 32873, "pdf_sha256": "af66e99f36e74234a53fa0ff3ba6895a84d14323b934e0faba252060079997ac", "pdf_bytes": 429891, "pdf_pages": 9 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with proof discovery, adversarial proof auditing, primary-literature triage, exact replay code, drafting, PDF production, and ARR packaging. The author remains responsible for the mathematical claims. A separate read-only Codex audit found no P0, and focused re-review scored this version 8.4/10 with uncertainty 0.6 after corrections. This is not human peer review or priority certification.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable" }, "editorial": { "decision": "correction", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Version v3 supersedes v2. Declared minor revision: Makes exact replay JSON emission byte-stable across LF and CRLF platforms by forcing LF newlines; mathematical statements and proofs are unchanged. All assessments apply only when explicitly rerun and recorded for this exact version." }, "supersedes_version_id": "arr:version:df413052-d8ef-4a18-99e9-869d18e902eb", "revision": { "change_size": "minor", "summary": "Makes exact replay JSON emission byte-stable across LF and CRLF platforms by forcing LF newlines; mathematical statements and proofs are unchanged." }, "latest_version": "v3", "version_count": 3, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-2MHNZRRJP49Y9SWP-v1", "source_snapshot_available": true }, { "version": "v2", "publication_state": "published", "release_tag": "ARR-2026-2MHNZRRJP49Y9SWP-v2", "source_snapshot_available": true }, { "version": "v3", "publication_state": "published", "release_tag": "ARR-2026-2MHNZRRJP49Y9SWP-v3", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:295f7a41-4283-44cd-bf8e-0960d0329671", "version_id": "arr:version:fd4cf9c6-d6ee-4a79-b03d-92f658026bf1", "id": "ARR-2026-19BXX42GM38K6VZ3", "version": "v1", "record_type": "research_paper", "title": "Characteristic-Free Bounds and Sharp Gauss-Fiber Examples for Point-Span Tangent Absorption", "abstract": "Let X be a smooth projective integral d-fold over an algebraically closed field and use the complete embedding defined by H^m, m at least 3. For a nonempty finite reduced point-span tangent-absorbing set Z, this paper proves in arbitrary characteristic the lower bound dim(S_Z), |Z| at least max{J(d,m), min{(d+1)(d+2), binom(d+m,d)}}. The positive-characteristic Gauss-branch argument replaces the characteristic-zero derivative contradiction by Frobenius and radicality. The paper also proves injectivity of the original Gauss map for suitable complete factorized polarizations and, over the complex numbers, constructs smooth hypersurfaces attaining the binomial estimate inside the exceptional Gauss branch for every d at least 2 and m at least 3. The construction is existential; no positive-characteristic Bertini realization, equality classification, human peer review, or exhaustive priority claim is made. A related ARR paper proves a sharper exact global binomial floor in characteristic zero.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-24", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/repro/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.tex", "keywords": [ "Gauss map", "tangent absorption", "first jets", "fat points", "positive characteristic", "multivariate interpolation" ], "subjects": [ "Algebraic geometry", "Projective geometry", "Commutative algebra" ], "related_records": [ { "id": "ARR-2026-2MHNZRRJP49Y9SWP", "relationship": "extends", "note": "Extends the characteristic-zero framework to characteristic-free two-branch and growing bounds; it does not supersede the sharper exact characteristic-zero floor." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "1e8986b9a754ffb9f0ccaf500ed2c271790cf7caf4d989ca1b37cd91054f5c95", "canonical_bytes": 32904 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with adversarial mathematical review, proof repair, literature triage, exact replay code, drafting, LaTeX production, repository publication, and ARR deposit preparation. A separate Codex referee audited the publication source and reported no invalidating gap. These AI checks are not human peer review, formal verification, or priority certification; the author remains responsible for every claim.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person; no independent human editorial or scientific review is claimed." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-19BXX42GM38K6VZ3-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:7107e7c9-5221-4522-97f5-328da7018f43", "version_id": "arr:version:efdbfb10-5c8b-4e0f-a04f-709d6bb6dabf", "id": "ARR-2026-3H0ZKWJMH18MH9FX", "version": "v1", "record_type": "research_paper", "title": "Strictly Scalable Exterior Decoders for Quantum Lists: Exact Full-Spark Widths and Fixed-Probe Weyl Bayes Curves", "abstract": "A quantum list measurement succeeds when its output contains the prepared label. Building on the known equivalence between learning width and Gram-matrix factor width, this paper closes an exact realization-sensitive branch. Every full-spark ensemble of N pure-state rays spanning C^r that admits strictly positive tight representatives has minimum zero-error list size N-r+1. Weighted Hodge duals of all (r-1)-fold frame wedges give an explicit attaining POVM, and a physical-space annihilator-cone formulation gives constructive compression to at most r^2 outcomes. A smallest-eigenvalue functional supplies a positive and perturbatively stable Bayes-error floor below threshold. For a flat consecutive-support Schmidt-rank-r probe of the complete d-dimensional Weyl-channel ensemble, the fixed-probe threshold is d-r+1. When r divides d, an arithmetic-support construction and dimension converse close the optimization over all pure Schmidt-rank-r probes at d/r. For the consecutive rank-two probe, the complete one-shot Bayes list curve is determined exactly. The nondivisible probe optimum, adaptive or multiuse testers, asymptotic capacity, arbitrary mixed states, and non-scalable full-spark ensembles remain outside scope.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-24", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/results/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "quantum list discrimination", "learning width", "factor width", "full-spark frames", "scalable frames", "exterior algebra", "Weyl channels" ], "subjects": [ "Quantum information", "Mathematical physics", "Frame theory" ], "related_records": [ { "id": "ARR-2026-15SJ1ANHDN8D88Z1", "relationship": "extends", "note": "The related record develops support-matroid bounds for quantum list discrimination and contains the earlier (4,2,2) subthreshold fixture. This independent paper gives realization-sensitive full-spark/scalability thresholds, exact Weyl probe frontiers, and the full consecutive rank-two Bayes curve." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "bf67bc3c4ae3f0b191c375691c375b93f9fdb3b70ce7f16f031bcb905324e16f", "canonical_bytes": 447420 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with theorem exploration, literature triage, proof stress testing, exact verifier development, manuscript editing, reproducibility checks, visual PDF inspection, machine-readable extraction, and ARR deposit preparation. A separate Codex task supplied critical model feedback recorded as an informal audit, not as peer review or scientific validation. The author selected and reviewed the claims, assumptions, proofs, citations, and executable evidence and remains responsible for the work.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, novelty certification, or scientific certification is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-3H0ZKWJMH18MH9FX-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:ed12d6e6-2292-42e8-8066-0f264128b8fe", "version_id": "arr:version:4c7d2cb5-3497-444d-b7ee-8df1ea80a8a9", "id": "ARR-2026-7D2BBEC8MJ8BM80S", "version": "v1", "record_type": "research_paper", "title": "Cellulation-Independent Boundary Gauge Averaging and Sharp Class-Sector Gaps in Two-Dimensional Yang--Mills", "abstract": "Let G be a compact connected Lie group with a bi-invariant metric. For the two-dimensional heat-kernel Yang--Mills model, this paper gives an explicit finite chain from a boundary-conditioned edge integral on an arbitrary regular annular cellulation to the gauge-invariant class-function transfer kernel. Conditional Haar coordinates make the boundary constraints and boundary-edge subdivision precise. Edge and face subdivision invariance, an explicit PL radial-cut construction, and a primal-tree/dual-cotree disk-elimination schedule yield a cellulation-independent orbital heat-kernel integral. Peter--Weyl theory then diagonalizes the transfer operator with multipliers exp(-t c_lambda). The exact mean-zero norm is exp(-t c_*(G)), the gap of I-T_t is 1-exp(-t c_*(G)), and the equality sector consists of all irreducible characters with minimum positive Casimir. In the stated SU(2) normalization the sharp exponent is 3/4, while the induced SO(3) quotient removes the fundamental channel and raises it to 2. The work assembles and audits classical two-dimensional Yang--Mills ingredients; it does not claim a new character solution, four-dimensional mass gap, continuum reconstruction, or clustering for arbitrary bulk observables.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-15", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/", "spdx": "NOASSERTION" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "two-dimensional Yang--Mills", "compact Lie group", "heat kernel", "cellulation independence", "boundary gauge averaging", "transfer operator", "spectral gap", "Casimir eigenvalue", "Lean 4" ], "subjects": [ "Mathematical physics", "Representation theory", "Lattice gauge theory", "Formalized mathematics" ], "related_records": [], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "ee51663a977f1932da74670956aafe39e6f43ac355c6d27b472a4285a2b3fe34", "canonical_bytes": 483920 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with repository discovery, mathematical exploration, drafting, adversarial proof review, Lean and numerical replay, revision in response to external criticism, deposit preparation, machine-readable extraction, and visual release QA. The author assumes responsibility for the definitions, proofs, claims, citations, licenses, and deposited artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "L2", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, novelty assessment, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7D2BBEC8MJ8BM80S-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:25cc82aa-c5b5-4350-8f86-2dadee41ec97", "version_id": "arr:version:37b6a5da-ba4a-432a-b006-4bed7f35d331", "id": "ARR-2026-15SJ1ANHDN8D88Z1", "version": "v1", "title": "Bayesian Matroid-Union Bounds for Quantum List Discrimination: Support Congestion, Process Compression, and Exact Adaptive-Parallel Phases", "abstract": "In quantum list discrimination a measurement returns at most ell candidate labels and succeeds when the true hypothesis belongs to the returned list. We associate a Rado independent-transversal matroid to the support subspaces of a mixed quantum ensemble and prove that every true-label inclusion vector lies in the independence polytope of the ell-fold matroid union. This yields all-subset Bayesian bounds for arbitrary priors, soft rewards, an integer congestion deficit, equality audits, and canonical compression to quantum-process testers. Exact attainment and insufficiency examples separate support combinatorics from quantum geometry. We then solve two input-dependent process families. For binary laminar dephase-prepare channels with M=2^h, list size ell=2^s, and q uses, arbitrary entangled parallel probes and adaptive quantum memories obey P_parallel=min(1,ell(q+1)/M) and P_adaptive=min(1,ell 2^q/M). For complete unitary-error ensembles we translate the known approximate dense-coding spectrum law into a list cap, derive an exact serial/parallel/Bell multitime trichotomy, and give a fixed-probe example where the coarse list-rank cap is not attained. The matroid theorem is a support obstruction rather than a general POVM feasibility characterization; the laminar separation is a classical feedback tradeoff embedded quantumly, and no indefinite-causal-order advantage is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-15", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/python/*.py", "spdx": "Apache-2.0" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "quantum list discrimination", "state exclusion", "matroid union", "Rado matroid", "quantum process testers", "adaptive channel discrimination", "unitary error bases" ], "subjects": [ "Quantum information", "Mathematical physics", "Combinatorics" ], "related_records": [ { "id": "ARR-2026-7CCV86W3Y59VS8PN", "relationship": "extends", "note": "The related record proves the one-label Rado-matroid Bayes bound. This independent paper develops the full list hierarchy through matroid union and adds exact input-dependent channel architecture phases." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a955a5e4a05adbef081a8fbb0c8a76f46b2027eca35a0be0dbaf82a607fbb8a2", "canonical_bytes": 462877 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with theorem exploration, literature triage, proof stress testing, exact verifier development, manuscript editing, reproducibility checks, machine-readable extraction, and ARR deposit preparation. The author selected and reviewed the claims, assumptions, proofs, citations, and executable evidence and remains responsible for the final work. AI output is not treated as independent scientific evidence.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "partial", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-15SJ1ANHDN8D88Z1-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:461ac072-8d97-4c85-a190-0dddcc278b17", "version_id": "arr:version:4e850a11-34d8-4519-baaf-baf92ec9d0c5", "id": "ARR-2026-263B0753CQ9J2T34", "version": "v1", "record_type": "research_paper", "title": "Exact Branch Rigidity and Unique Crossing in Grassmann Matrix--Bingham Free Energies: Finite Certification, All-Field Gr_C(3,6) and Gr_C(4,8) Two-Block Order, and a Gr_C(2,5) Exchange Theorem", "abstract": "Let P be a Haar-distributed complex Grassmann projector and consider the matrix--Bingham normalizer Z_A(s)=E exp{s tr(AP)} on the trace-zero, Frobenius-unit external sphere. We prove exact complementary results for its canonical two-level branch geometry. On every half Grassmannian Gr_C(r,2r), the balanced rank-r field strictly maximizes the normalized two-block moments of degrees 4, 6, 8, and 10. Exact endpoint analysis gives balanced dominance at small and large field, while a finite certification theorem reduces coefficientwise all-field order at each fixed rank to a terminating block of rational Hankel signs plus an analytic tail. At Gr_C(3,6), a closed all-degree argument proves strict balanced order for every field. At Gr_C(4,8), exact rational arithmetic through degree 268 and the analytic tail give a second all-field theorem. On Gr_C(2,5), compact overlap densities, Sturm arithmetic over Q(sqrt(6)), and strict total positivity prove a unique simple exchange in the complete oriented two-level family. The results do not classify arbitrary multi-level external spectra and do not claim an unrestricted all-distortion rate--distortion function.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-15", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro", "spdx": "Apache-2.0" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "Grassmannian", "matrix--Bingham distribution", "orbital Laplace transform", "Hankel determinant", "total positivity", "Sturm theorem", "computer-assisted proof", "random matrix theory" ], "subjects": [ "Mathematical physics", "Random matrix theory", "Harmonic analysis", "Information theory" ], "related_records": [ { "id": "ARR-2026-6F8XRSBM0J9Q2R2B", "relationship": "extends", "note": "Extends the predecessor's local Morse--Bott and metastability analysis with exact two-level moment, all-field ordering, and crossing theorems; the predecessor remains independently citable." }, { "id": "ARR-2026-61Y0FFA39M8KMBJ5", "relationship": "related_work", "note": "The related record proves the exceptional global all-field solution on Gr_C(2,4); this paper treats broader canonical two-level branch geometry without claiming arbitrary-spectrum optimality." }, { "id": "ARR-2026-6FDEKPVJ0W8BHBMC", "relationship": "related_work", "note": "The related record derives an exact high-fidelity Grassmann/Born rate--distortion segment; the present paper supplies exact branch comparisons but does not derive an unrestricted all-distortion frontier." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "226e5ef238e87a5e2a6af6a9bda5ecbe84c60a9c49cd68a8f0296c5eafe1a3a2", "canonical_bytes": 461192 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with repository and literature discovery, theorem exploration, exact algebraic replay, drafting, adversarial proof checking, bibliography review, deposit preparation, machine-readable extraction, packaging, and visual release QA. The author assumes responsibility for all definitions, proofs, claims, citations, and release artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-263B0753CQ9J2T34-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:cf477195-d012-4dc5-812d-9cfec88dcb46", "version_id": "arr:version:c2f6c594-6f2a-4bee-97a0-017b13befbc3", "id": "ARR-2026-6F8XRSBM0J9Q2R2B", "version": "v1", "record_type": "research_paper", "title": "All-Field Morse--Bott Stability at Critical Homogeneous Orbits: Half-Grassmann No-Spinodal Rigidity and Exact Jacobi Metastability", "abstract": "Let a compact group act orthogonally on a sphere and let mu be the invariant law of a proper antipodal orbit. We study the exponential orbital potential. At a point of the source orbit, every spherical-harmonic coefficient of the orbit average is a squared norm, giving an exact negative spherical-Laplacian identity at every nonzero field. Provided the source orbit is critical--automatically so when the normal isotropy representation has no fixed vector--irreducibility, or a transitive symmetry of its irreducible normal blocks, upgrades this trace identity to strict Morse--Bott maximality for every field. An explicit torus-orbit counterexample shows why criticality cannot be omitted. Applied to centered projector embeddings of the real, complex, and quaternionic half-Grassmannians, the theorem proves all-field local rigidity of the balanced matrix--Bingham branch and excludes a radial spinodal. In the complex case, exact Jacobi-generator identities yield constrained-Hessian operators for every two-block external spectrum and a sharp weak-field metastability threshold at k=2r/3. A Stein inequality closes every sufficiently high Taylor degree at each fixed multiplicity. The results constrain unresolved intermediate phases but do not claim global spectral optimality, a complete finite-field phase diagram, or an all-distortion rate--distortion function.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-15", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/python/verify_orbital_metastability.py", "spdx": "Apache-2.0" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "Morse--Bott stability", "homogeneous orbital potential", "Grassmannian", "matrix--Bingham distribution", "Jacobi ensemble", "constrained Hessian", "metastability", "positive-definite zonal kernel" ], "subjects": [ "Mathematical physics", "Harmonic analysis", "Random matrix theory", "Differential geometry" ], "related_records": [ { "id": "ARR-2026-6FDEKPVJ0W8BHBMC", "relationship": "extends", "note": "Strengthens the local finite-field geometry underlying the earlier high-fidelity complex-Grassmann result by proving balanced all-field no-spinodal rigidity and exact two-block metastability; the predecessor remains independently citable." }, { "id": "ARR-2026-61Y0FFA39M8KMBJ5", "relationship": "related_work", "note": "The rank-two record gives the exceptional global all-field solution on Gr_C(2,4); this record develops local all-rank geometry without claiming the corresponding global theorem." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4d14c983c342a64c56f4f6620edbe4c2d84b1f9ef0d9bc0bf53c631fa7a27853", "canonical_bytes": 414801 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with repository and literature discovery, theorem exploration, algebraic replay, drafting, adversarial proof checking, bibliography correction, deposit preparation, machine-readable extraction, and visual release QA. A criticality counterexample identified during external evaluation was incorporated and the theorem was repaired before deposit. The author assumes responsibility for all definitions, proofs, claims, citations, and release artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-6F8XRSBM0J9Q2R2B-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:fd2f7a06-2dc1-4d3b-bcff-91a284c737ba", "version_id": "arr:version:00436226-d0be-483d-a620-7b1a468c697e", "id": "ARR-2026-7X5XX0CBE19MXVSZ", "version": "v1", "record_type": "research_paper", "title": "Finite-Sample-Valid Tests for Structured Matricial Hausdorff Moments: Joint Gaussian Grams, Strict Half-Time Separation, and Sharp Tangent-Cone Power", "abstract": "We give a finite-sample test for whether one joint Gaussian sketch covariance is compatible with a positive-semidefinite matrix-valued measure supported on a prescribed interval. The observed vector contains several exponent blocks, so its population covariance is one block-Hankel Gram matrix rather than a list of unrelated moment estimates. The classical truncated matricial Hausdorff theorem supplies the exact parity-dependent null. A single Gaussian singular-value event gives a simultaneous Loewner band for the whole covariance; intersecting that band with the structured moment cone yields a nonasymptotic level-alpha semidefinite test without sample splitting. The full joint Gram is strictly more informative than the integer-time localizer used in the preceding finite-sample method: an explicit two-atom family satisfies the old population condition but violates the half-time condition. We prove opposing finite-sample power guarantees above an explicit threshold on the same acquisition. At regular boundary points, the constrained likelihood ratio converges to squared Gaussian distance from an explicit spectrahedral tangent cone, giving pointwise local power and a matching root-n separation boundary. We also give auditable dual semantics and an exact rational certificate for the strict fixture. Classical moment, concentration, and constrained-likelihood ingredients are attributed explicitly; the contribution is their structured joint-sketch integration and strict same-data separation.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/python/verify_matricial_hausdorff.py", "spdx": "Apache-2.0" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "matricial Hausdorff moment problem", "matrix-valued spectral measure", "finite-sample hypothesis testing", "Gaussian covariance", "Loewner confidence band", "tangent cone", "constrained likelihood ratio", "semidefinite certificate" ], "subjects": [ "Mathematical physics", "Statistics theory", "Optimization and moment problems" ], "related_records": [ { "id": "ARR-2026-77QM18J2KG9679B7", "relationship": "extends", "note": "Retains the full half-time joint Gram, imposes the parity-complete matricial Hausdorff cone, and proves strict same-acquisition separation beyond the earlier finite-sample spectral-support framework; the earlier record remains independently citable." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "9db79aa3bbd6471e5eeb8e5d2b7387a013dbab9f5e5da65aa373a8599f51b42e", "canonical_bytes": 461948 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with repository and literature discovery, theorem exploration, algebraic replay, drafting, adversarial proof checking, bibliography correction, deposit preparation, machine-readable extraction, and visual release QA. The author assumes responsibility for all definitions, proofs, claims, citations, and release artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7X5XX0CBE19MXVSZ-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:ec66d06e-0fc5-4ef2-8b55-3404d0c40587", "version_id": "arr:version:f8326572-dbd0-48d3-9db7-e269d820a2a9", "id": "ARR-2026-7CCV86W3Y59VS8PN", "version": "v1", "title": "Matroidal Bayes Bounds for General Quantum Process Discrimination: Canonical Compression, Support Congestion, and Exact Qubit Phase Families", "abstract": "Minimum-error discrimination of quantum processes is normally optimized over testers whose normalization may encode parallel, sequential, or indefinite-order access. For a fixed physical deterministic normalization, Moore-Penrose compression maps the tester exactly to a POVM on normalized effective states and preserves every conditional probability. We associate to the support subspaces of arbitrary positive process operators a Rado matroid on the hypothesis labels and prove that every correct-label probability vector lies in its independence polytope. Consequently the Bayes success probability is at most the prior weight of a maximum-weight independent transversal. A robust extension replaces exact supports by arbitrary positive low-rank cores and charges only the prior-weighted worst-case discarded tester mass; valid full-rank process admixture of weight eta degrades the certificate by at most eta. We give an explicit reduction to linear matroid intersection, an equality audit at strict prior drops, a deterministic Gram criterion for perfect rank-one discrimination, and exactly solved qubit phase-gate families. In a five-channel instance the exact general-tester optimum is 0.80 while the total-dimension relaxation is 0.90. The result is a support-based upper bound and is not claimed to determine every mixed-process optimum.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/manuscript/figure/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/SUPPLIED_MANIFEST.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "quantum process discrimination", "quantum testers", "Rado matroid", "nonuniform priors", "Moore-Penrose compression", "spectral-tail robustness", "matroid intersection" ], "subjects": [ "Quantum information", "Mathematical physics", "Combinatorics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e7ee32ac72a58ed620deb2e5598e54acf33713616dbb57e5676efcd2c236c534", "canonical_bytes": 385441 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with exploratory algebra, literature triage, proof stress testing, code and figure drafting, manuscript editing, reproducibility checks, machine-readable extraction, and ARR deposit preparation. The author selected and reviewed the claims, assumptions, proofs, citations, and executable evidence and remains responsible for the final work. AI output is not treated as independent scientific evidence.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "related_records": [ { "id": "ARR-2026-6WX2JF38WE87GB2M", "relationship": "companion", "note": "The related record studies global Hilbert-function support of structured unitary-oracle families. This paper instead resolves label-specific support congestion through Rado matroids, arbitrary priors, mixed process supports, and a spectral-tail robust extension." } ], "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7CCV86W3Y59VS8PN-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_id": "arr:record:cd90c025-8603-46c9-98b7-804e9dedefc2", "version_id": "arr:version:3a29a7f0-c5bd-4de5-94ac-c1ddd7f923c0", "id": "ARR-2026-6DJ302B1G38V4SHD", "version": "v1", "record_type": "research_paper", "title": "Universal Semiclassical Coexistence in Classical Compression of Phase-Lifted Coherent States: Dimension-Normalized Contacts and a Matched High-Fidelity Boundary Layer", "abstract": "Fix a nonzero dominant weight lambda and let the highest weight grow along the ray N lambda. We study the exact classical Shannon rate-distortion function of the invariant phase-lifted coherent orbit in V_{N lambda} under squared ambient Hilbert-space loss. The finite-N scalar formula is known; the new problem is the coupled large-weight and distortion limit. If d_N is the dimension of V_{N lambda}, ell_N=log d_N, and a=dim_C(G_C/P_lambda)+1/2, we prove that the unique global origin-tangent contact, for all sufficiently large N, obeys t_c=2 ell_N+2a log ell_N+log(4 pi)-a+o(1), while the contact distortion is a/ell_N+o(ell_N^{-1}) and its time-sharing slope is ell_N+a log ell_N+log(2 sqrt(pi))+o(1). All root-system and Weyl leading constants cancel in these dimension variables. For fixed 0 1-D. On the noncommuting boundary scale D=x/ell_N, the centered rate converges locally uniformly to an explicit two-branch profile, with a curved high-fidelity branch tangent to a linear coexistence face at x=a. We also identify the soft-activation window and an exact fixed-radius Legendre expansion. The result is classical rate-distortion for an embedded coherent-amplitude source, not quantum rate-distortion or a derivation of Born's rule.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/manuscript/generate_semiclassical_figure.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.ps1", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.json", "spdx": "CC0-1.0" }, { "path": "src/replay/*.sha256", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "classical rate-distortion", "generalized coherent states", "semiclassical highest-weight limit", "phase coexistence", "Weyl dimension formula", "Bessel saddle", "convex envelope", "high-fidelity boundary layer" ], "subjects": [ "Mathematical physics", "Information theory", "Representation theory" ], "related_records": [ { "id": "ARR-2026-6XH6JAS5ZA934A6J", "relationship": "extends", "note": "Extends the exact finite-dimensional phase-lifted coherent-orbit rate-distortion theorem to the coupled semiclassical and distortion limit; the earlier record remains independently citable." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3848730dfd1e4883f8b9de9a63c5ae0c123cf389569829d671503e5cbfe642a6", "canonical_bytes": 468754 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with literature discovery, theorem development, algebraic replay, drafting, adversarial proof checking, bibliography correction, deposit preparation, machine-readable extraction, and visual inspection. The author assumes responsibility for all definitions, proofs, claims, citations, and release artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-6DJ302B1G38V4SHD-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:dce8a4f1-a38e-41e0-b152-ce6af5821e1b", "version_id": "arr:version:74669808-5eaf-4e2b-be6b-a0d8d7ce09c1", "id": "ARR-2026-6WX2JF38WE87GB2M", "version": "v1", "title": "Algebraic Query Support for Unitary Oracles: Exact Hilbert Laws, Harmonic Spectra, and General-Tester Bounds", "abstract": "The standard k-query dimension bound for an unknown d-dimensional unitary uses the entire degree-k symmetric tensor space and scales as k^(d^2-1). We refine that bound to the degree-k Hilbert function of the projective oracle variety and compute the resulting support exactly in two physically structured families. For a fixed-angle qubit rotation with unknown axis, the repeated-query span has dimension (k+1)^2 on the generic branch, binomial(k+2,2) on the traceless branch, and one on the central branch. A compact-orbit leverage argument inserts this exact support into the general-tester bound, applying to the parallel, sequential, and mathematically admissible indefinite-order strategies covered by the standard tester model. The associated spherical and planar-axis frames admit closed harmonic spectra, purity formulae, endpoint cascades, and a complete tightness classification. For d-level selective-phase oracles, the projective closure is a Segre variety and the exact support is binomial(k+d-1,d-1)^2, reducing the ambient exponent from d^2-1 to 2d-2. These results quantify geometry-dependent query support rather than physical memory or an achievable discrimination probability in every finite ensemble. The work excludes inverse-oracle access, controlled bypasses, noise, finite-sample estimation, and tester models beyond those explicitly stated.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/SUPPLIED_MANIFEST.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "quantum query complexity", "unitary channel discrimination", "Hilbert function", "oracle varieties", "Segre variety", "SU(2) conjugacy class", "general quantum testers" ], "subjects": [ "Quantum information", "Mathematical physics", "Algebraic geometry" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b88efdbc4f3cbd39c4160e0803c795c4a1e640b5dac919b95edc681a6f4e1cec", "canonical_bytes": 422028 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with symbolic exploration, literature triage, proof stress testing, code drafting, manuscript editing, release preparation, machine-readable extraction, and ARR deposit checks. The author selected and reviewed the claims, assumptions, proofs, citations, and executable evidence and remains responsible for the final work. AI output is not treated as independent scientific evidence.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-6WX2JF38WE87GB2M-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:dd89a4ac-97ea-48c8-a34b-96e356d3b901", "version_id": "arr:version:d9b5aeec-723c-43b1-9840-a3b329185ea2", "id": "ARR-2026-6XH6JAS5ZA934A6J", "version": "v1", "title": "Exact Classical Rate–Distortion for Phase-Lifted Generalized Coherent States: Cartan-Product Laplace Rigidity, Universal Radial Envelopes, and Slater-Determinant Transitions", "abstract": "Let V_lambda be a finite-dimensional irreducible unitary representation of a compact connected semisimple group, and let X be uniform on the phase-lifted orbit of a highest-weight vector. We determine the classical Shannon rate–distortion function under squared ambient loss for arbitrary standard-Borel descriptions and decoders unrestricted to the orbit. Sugita's known integer-moment coherent-state extremum, combined with positive phase–Bessel resummation, yields an all-field fixed-radius Laplace order and exact equality classification. The vector problem reduces to an exact scalar radial envelope. Covariant tilted channels attain exposed points and revealed binary flags attain nonexposed chords. A representation-dimensional criterion forces discontinuous directional-information onset, while Weyl dimensions give a sharp root-system high-fidelity constant. For exterior powers, the source is a phased fermionic Slater determinant: the normalizer is hypergeometric, squared Pluecker overlap is a beta product, and every interior family with n at least 6 has discontinuous first activation. A distinct projective corollary treats intrinsic Pluecker distortion with reproduction restricted to the coherent orbit. The results concern classical phase-sensitive amplitude reconstruction, not quantum rate–distortion, click-only Born statistics, or particle dynamics.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/manuscript/generate_coherent_orbit_figure.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.ps1", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.json", "spdx": "CC0-1.0" }, { "path": "src/replay/*.sha256", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "rate-distortion theory", "generalized coherent states", "Cartan product", "highest-weight representations", "Slater determinants", "Grassmannians", "phase coexistence" ], "subjects": [ "Mathematical physics", "Information theory", "Representation theory" ], "related_records": [ { "id": "ARR-2026-7H9FAPTBZA897AMJ", "relationship": "related_work", "note": "Earlier oriented-two-plane rate–distortion paper with a narrower source geometry and a different operational reconstruction problem." }, { "id": "ARR-2026-61Y0FFA39M8KMBJ5", "relationship": "related_work", "note": "Independent complex rank-two Grassmann companion using spectral matrix-Bingham geometry rather than phase-lifted coherent amplitudes." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "01678e31e1fc652a1d1b8c8b00023ad6bc192439bc27267a0abde4d4568ede51", "canonical_bytes": 374586 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with literature discovery, theorem development, algebraic replay, drafting, adversarial checking, bibliography correction, deposit preparation, machine-readable extraction, and visual inspection. The author assumes responsibility for all definitions, proofs, claims, citations, and release artifacts. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-6XH6JAS5ZA934A6J-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:b3c9c10d-9e73-4b7c-a324-e3314596d2ae", "version_id": "arr:version:e8da7444-ed35-4465-8928-7d94b28b2fda", "id": "ARR-2026-5KS70GV7KK9DYA69", "version": "v1", "title": "Two-Query Chirality in Tetrahedral Quantum Echoes: Exact Parallel Readout, a Nine-Dimensional Query Defect, and a Certified Adaptive Advantage", "abstract": "Four balanced Pauli kicks along the vertices of a regular tetrahedron, followed by their reverse echo, generate 24 order-labelled qubit unitary channels. The words share a trace and form two 12-element orbits of the proper tetrahedral group. One query sees only their common trace. At two queries, orbit-dependent quadratic energies yield closed formulas for the Bell-square and globally optimized parallel strategies. At the algebraic point q=1/2, every causally ordered two-query protocol has success at most 9/24 because the fixed trace removes one dimension from the universal quadratic query space. An explicit rational two-comb normalization, a six-Kraus realization, and an exact weighted-frame identity attain the cap, giving P_causal=3/8 and P_parallel=(5+sqrt(15))/24. A uniform Lipschitz estimate proves that the same causal tester remains strictly better on an explicit open pulse interval. The result is an analytic adaptive advantage for a concrete non-group ensemble. It does not address indefinite causal order, noise, finite statistics, or arbitrary qubit ensembles. The central causal certificate is replayed exactly in quotient-ring arithmetic; the supplied word/collision and representation scripts are mixed symbolic-numerical corroborating audits.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/package_release.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.sha256", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "quantum channel discrimination", "adaptive quantum strategies", "quantum combs", "tetrahedral symmetry", "unitary echoes", "minimum-error discrimination" ], "subjects": [ "Quantum information", "Mathematical physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "bb1e9ccc4176c73834a5d8dd6c91ac0cf91d20c7f4b5d74016d89cc82d108863", "canonical_bytes": 413708 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with symbolic exploration, literature triage, proof stress testing, code drafting, manuscript editing, release preparation, machine-readable extraction, and ARR deposit checks. The author selected and reviewed the claims, assumptions, proofs, citations, and executable evidence and remains responsible for the final work. AI output is not treated as independent scientific evidence.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, frontier-model screening, or scientific certification is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-5KS70GV7KK9DYA69-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.1", "record_type": "research_paper", "record_id": "arr:record:f14bd56d-2fea-424e-aa48-f0bf81c67d9a", "version_id": "arr:version:1f2d37b4-1269-45ac-b8d8-6f12c8bc237a", "supersedes_version_id": "arr:version:26cebded-ef67-454b-9922-75e69fc8b139", "id": "ARR-2026-7H9FAPTBZA897AMJ", "version": "v2", "title": "Complete Rate–Distortion Phase Diagram of Haar Oriented Two-Planes: One-Change Hypergeometric Coefficients, Unique Coexistence, and No Reentrance", "abstract": "Let W=x wedge y be the signed unit Pluecker coordinate of a Haar oriented two-plane in R^n, and let reproduction range over the full posterior-mean body under squared ambient loss. An all-field extremum theorem reduces its unrestricted Shannon rate–distortion function to a scalar radial free energy with q=n-2 and overlap normalizer L_q(kappa)=q! sum_{j>=0} kappa^(2j)/(q+2j)!. We solve the remaining global phase problem in every dimension. For the Turanian-like combination J_q=L_q L_q' - kappa L_q L_q'' + kappa(L_q')^2, every coefficient is expressed through the variance of a central parity-truncated binomial law. Likelihood-ratio ordering and an exact uniform tail bound prove one coefficient sign change for every q>=4. Consequently the stationary curve has exactly one fold, the zero and positive phases have exactly one coexistence contact, and no later exchange or radial reentrance is possible. The RDF is an explicit linear face followed by one covariant branch for every n>=6; together with the continuous cases n=3,4,5, this completes the all-dimensional phase diagram. We also derive sharp large-dimension expansions for the coexistence field, active radius, distortion, and information, including the logarithmic finite-size displacement. As operational corollaries, the same RDF equals the minimum worst-source channel capacity, arbitrary joint N-letter classical memories cost N R_n(D), and the iid Haar source has constant tilted information and zero dispersion. The N-letter identity is a mutual-information/capacity theorem, not an exact finite-codebook achievability result. The work concerns signed Pluecker-coordinate compression, not quantum rate–distortion or Born-probability prediction.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/*.ps1", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.json", "spdx": "CC0-1.0" }, { "path": "src/replay/*.sha256", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "oriented Grassmannian", "Pluecker embedding", "rate-distortion theory", "hypergeometric coefficient inequalities", "phase coexistence", "no reentrance", "worst-source channel capacity" ], "subjects": [ "Mathematical physics", "Information theory", "Convex geometry" ], "related_records": [ { "id": "ARR-2026-61Y0FFA39M8KMBJ5", "relationship": "related_work", "note": "Independent rank-two complex companion with a related geometric mechanism but a different source, loss function, and operational problem." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f8bd2e9ed5f8b166e014dd7b51578adc572dd603b37a82c1fde837b7d89488be", "canonical_bytes": 441916 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with manuscript development, literature searches, algebraic stress testing, editing, deposit preparation, machine-readable text extraction, visual inspection, and bounded replay/integrity checks. The author assumes responsibility for all definitions, proofs, claims, citations, and the final manuscript. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned versioned record: Lluis Eriksson is both the author and ARR's current founder-editor. Version 2 supersedes version 1 under the same permanent ARR identifier. No independent editorial review, peer review, or frontier-model screening is claimed. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "latest_version": "v2", "version_count": 2, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7H9FAPTBZA897AMJ-v1", "source_snapshot_available": false }, { "version": "v2", "publication_state": "published", "release_tag": "ARR-2026-7H9FAPTBZA897AMJ-v2", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:d41ee1ae-fcdc-44b8-9624-bc408f44fa53", "version_id": "arr:version:406e94c3-5779-4bca-bb60-830c341eb6fc", "id": "ARR-2026-6M3VGTXZ6W8JW9C9", "version": "v1", "title": "Projective Memory and Resonant Bottlenecks in Passive Spectral Routing", "abstract": "At distinct boundary frequencies, let a square rational-inner multiport route one fixed input ray to prescribed output rays. We prove that the minimum McMillan degree equals the least degree of a base-point-free projective curve through the ordered target rays, independently of ambient port count. For orthogonal target bands we solve line-to-subspace incidence constraints by full-support Lagrange kernels and derive a closed generic codimension law. Exact memory is the maximum shifted band cost, whereas border memory is the minimum and may be arbitrarily smaller. An intrinsic incidence matrix gives a calibrated singular-value error floor, a determinantal zero-error closure, and an all-data base-point deletion law with an incremental exact certificate. Finally, every zero-error sequence below exact memory has divergent peak dimensionless Wigner-Smith delay; any finite delay cap restores compactness, a positive attained error, and a three-phase operational classification. Explicit planar strata and exact rational certificates audit the results.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-14", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/manuscript/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/**/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/**/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "rational inner matrix", "projective interpolation", "McMillan degree", "passive spectral routing", "border memory", "Wigner-Smith delay", "determinantal variety" ], "subjects": [ "Mathematical physics", "Systems and control theory", "Algebraic geometry" ], "related_records": [ { "id": "ARR-2026-52B6MSS1W197W9T2", "relationship": "related_work", "note": "Earlier direct-sum occupancy theory for finite spectral routing tables; the present record develops a global projective degree law, border-memory geometry, and delay-capped closure theory." } ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c0a1b3811dfa50d5bb6872c8973687bc078262e5eda59220e8a6b3a86024c425", "canonical_bytes": 556578 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with mathematical drafting, literature organization, exact-certificate preparation, release assembly, visual inspection, and replay/integrity checks. The author reviewed the claims, proofs, references, and final artifacts and accepts responsibility for this version. No independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, or frontier-model screening is claimed for this version. Acceptance records a technically valid deposit, not a finding that the paper is correct." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-6M3VGTXZ6W8JW9C9-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:fdd1d4b4-7256-4ded-a86b-afae0537e9f2", "version_id": "arr:version:be31e049-b52f-42be-98c4-7dbfe022c71e", "id": "ARR-2026-7XT7AB8WJP9QPTGT", "version": "v1", "title": "Certified Localized Weil Positivity Through Support 0.72: Multiband Schur Complements and a Complete Stieltjes Hierarchy", "abstract": "Suzuki's localized Weil form is represented by a lower-bounded self-adjoint operator A_a on L2(-a,a); nonnegativity for every a > 0 is equivalent to the Riemann hypothesis, while positivity at one fixed support is an unconditional and strictly weaker problem. We give a source-level interval certificate proving A_0.72 >= 5.890 x 10^-17 I > 0. Nested-core monotonicity gives the same scalar lower bound for every 0 < a <= 0.72. The proof decomposes the exact prime-power translation graph through n = 4 into thirteen intervals and bounds its infinite complement by a mode-sensitive Schur estimate. It isolates degrees 12 through 23 before controlling [24,176) and [176,infinity); both parity Schur matrices have 78 certified positive directions and no unresolved direction at 512-bit Arb precision. We also prove an exact Gauss-Stieltjes hierarchy for the logarithmic boundary potential, complete for strict positivity at every fixed support, and a multiband Loewner majorant requiring only O_epsilon(log log M) bands through degree M. The revised manuscript prints a formula-level source-to-Gram specification. A separately written program importing neither project modules nor python-flint reconstructs the prime-power graph and parity maps and independently reassembles the exported Schur balls with positive Weyl margins in both sectors. This is a bounded-support theorem, not a proof of the Riemann hypothesis.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-13", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/repro/**/*.py", "spdx": "AGPL-3.0-only" } ], "data": [] }, "source_of_truth": "paper.pdf", "keywords": [ "Weil quadratic form", "Riemann zeta function", "localized operator", "interval arithmetic", "Schur complement", "Gaussian quadrature", "Stieltjes function", "Legendre expansion" ], "subjects": [ "Number theory", "Mathematical physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e4fd12894f2d15bd503370a016f259aa0e2f619810ba309108ca6a1150a02935", "canonical_bytes": 629879 }, "ai_assistance": { "used": true, "statement": "AI tools assisted with literature discovery, adversarial proof checking, software inspection, and manuscript preparation. The author selected the claims, reviewed the mathematical arguments and executable evidence, and is responsible for the final text and any remaining errors.", "systems": [ "AI tools (not otherwise identified in the manuscript)" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, or frontier-model screening is claimed for this version. Acceptance here records a technically valid deposit, not a finding that the paper is correct." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-7XT7AB8WJP9QPTGT-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:c1f01ef5-0d34-44e8-b916-a093deae2655", "version_id": "arr:version:8688da48-1cba-41d4-b66a-a943c5c81cf9", "id": "ARR-2026-61Y0FFA39M8KMBJ5", "version": "v1", "title": "Complete Rank-Two Born-Prediction Rate–Distortion on Gr_C(2,4): All-Field Matrix–Bingham Rigidity and a Unique Coexistence Transition", "abstract": "We solve a finite-dimensional external-spectrum optimization problem for the complex matrix–Bingham law and use it to determine an unrestricted Shannon rate–distortion function. If P is Haar on Gr_C(2,4) and A is traceless Hermitian with fixed Frobenius norm, then E exp[s tr(AP)] is, for every s>0, uniquely maximized, up to unitary conjugacy, by the balanced spectrum (R/2,R/2,-R/2,-R/2). The exceptional model Gr_C(2,4)=Gr_2^+(R^6) turns the orbital integral into a positive series whose coefficients share one simplex-vertex maximizer. For the Haar rank-two state source rho_P=P/2, conditional least squares places arbitrary reports in the full body {sigma: 0<=sigma<=I/2, tr sigma=1}. We obtain its exact classical rate–distortion function for every 0<=D<=1/4. Beyond a scalar dual representation, we prove the complete radial phase diagram: one fold, one positive coexistence contact, no reentrance, and an exact two-piece frontier consisting of one time-sharing segment and one matrix–Bingham branch. The proof reduces the fold derivative to a power series with exactly one negative coefficient followed by strictly positive coefficients. Covariant channels attain the frontier, and the same value is the source-universal worst-state capacity; arbitrary joint n-block memories cost exactly n times the one-letter frontier. The result concerns classical memory for calibrated Born-probability prediction, not quantum rate–distortion, click simulation, or a derivation of Born's rule.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-13", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "matrix Bingham distribution", "complex Grassmannian", "rate-distortion theory", "Born probabilities", "spectral optimization", "HCIZ integral", "phase coexistence" ], "subjects": [ "Mathematical physics", "Physics — Quantum Physics", "Information theory" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "55d29a31ae2b0a8e5296b38d3940b5cf0ac8e88cab21a59843dd4f26bbb37d97", "canonical_bytes": 488812 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with preparation of this ARR deposit, machine-readable text extraction, provenance assembly, and integrity checks. The supplied manuscript contains no model-specific authorship disclosure; no independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: Lluis Eriksson is both the author and ARR's current founder-editor. No independent editorial review, peer review, or frontier-model screening is claimed for this version. Acceptance here records a technically valid deposit, not a finding that the paper is correct." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-61Y0FFA39M8KMBJ5-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:e7bd0289-0a70-498e-959c-35f2340adc15", "version_id": "arr:version:42b0d96d-10c5-4a1c-acff-b9925ace7c08", "id": "ARR-2026-77QM18J2KG9679B7", "version": "v1", "title": "Finite-Sample Spectral-Gap Falsification: Exact Weighted Visibility Minimax, Hidden-Atom LAN, and Honest Dependent Tests", "abstract": "Finite Euclidean correlation matrices are routinely converted into spectral gaps by generalized eigenvalue, Prony, or Lanczos procedures. We determine a finite-sample boundary for what such data can falsify and what they cannot certify by non-rejection. Block Hankel pencils give monotone lower bounds on the visible transfer edge, while exact rank stabilization recovers the complete visible spectrum. An atom of weight w at any x*=exp(-g) changes every moment by at most w while forcing gap at most g; arbitrarily small strictly positive gaps therefore remain hidden even when an extra zero mode is forbidden. For a fixed nonsingular Gaussian experiment we compute the exact hidden-atom likelihood and derive its LAN information, sharp local power envelope, and powerless/local/consistent phase at the w sqrt(n) scale. Under a disclosed visibility floor, a fourth-kind Chebyshev filter solves the weighted localizer minimax exactly; a two-atom measure attains the bound, making the uniform sign threshold necessary and sufficient in the declared polynomial class. This margin feeds an exact-level two-coordinate Wishart test and a closed depth–sample resource law. A distribution-free companion uses paired differences and the exact quadratic range to handle bounded iid readouts with unknown mean and same-sample selection over a finite filter bank. A dependence-robust extension treats one stationary bounded beta-mixing trajectory: sparse pairing, Berbee coupling, and an explicit lag-covariance correction give finite-sample level, power, and total chain-horizon bounds under an externally certified mixing envelope. An interacting ANNNI-chain experiment through 2^16 states demonstrates exact symmetry blindness and multichannel recovery. Rejection falsifies an overstated gap; non-rejection alone is not a positive gap certificate.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-13", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/**/*.py", "spdx": "Apache-2.0" }, { "path": "src/replay/**/*.ipynb", "spdx": "Apache-2.0" }, { "path": "src/formal/**/*.lean", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/**/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "spectral-gap falsification", "Euclidean correlators", "truncated moment problem", "near-critical atom", "local asymptotic normality", "Wishart confidence band", "bounded readouts", "beta-mixing", "Berbee coupling", "fourth-kind Chebyshev filter", "weighted minimax", "Krylov termination", "visibility", "ANNNI chain" ], "subjects": [ "Mathematical Physics", "General Mathematics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "db6246f174d209eac2354b372af48649f1c55a9ced1d4ba9cdda59394aa8e668", "canonical_bytes": 557827 }, "ai_assistance": { "used": true, "statement": "AI tools assisted with literature discovery, adversarial proof checking, symbolic fixture verification, and manuscript editing. All theorem statements, scope decisions, computations, and the final text were reviewed by the author, who takes responsibility for the claims.", "systems": [ "AI tools (model identifiers not stated in the manuscript)" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person; no independent editorial review or scientific endorsement is claimed." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-77QM18J2KG9679B7-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:a259a99c-8781-49f8-9d0b-77e58bed40f9", "version_id": "arr:version:f8835d86-15ae-44b2-aef6-a0eb7e4fbe25", "id": "ARR-2026-52B6MSS1W197W9T2", "version": "v1", "title": "Exact Memory of Finite Spectral Routing Tables: The Direct-Sum Occupancy Law and Its Singular Strata", "abstract": "We give a single exact state-counting theory for finite passive spectral routing tables. Fix distinct boundary frequencies, one input k-plane, and a word whose symbol a requests a target k-plane Y_a exactly n_a times. If the used targets are in direct-sum position—they need not be orthogonal and may have arbitrarily small principal angles—then the minimum McMillan degree among square finite rational-inner interpolants is k(L - min_a n_a). Thus the rarest target fixes generic passive memory, independently of node spacing and word order. The lower bound uses block-dual detectors: direct-sum geometry supplies a constant compression that is invertible on one target and annihilates every other target. Its determinant has k forced zeros at every wrong node, while a Blaschke–Potapov minor has no more zeros than the network has states. The upper bound is a matrix spectral compiler. Target-weighted node polynomials form a full-rank polynomial column; matrix Fejér–Riesz factorization normalizes it to a rational-inner column of degree at most the lower bound, and a degree-preserving lossless completion closes the network. Beyond the direct-sum locus we prove a detector-rank hierarchy, a maximum weighted hyperplane-occupancy bound for lines, and the complete three-line phase diagram. We also give a span sandwich, open-dense genericity, fail-closed noisy certification, an exact collision discontinuity, and the optimal integrated Wigner–Smith delay. Producer and independent verifiers audit nonorthogonal scalar and block tables, collision openings, and singular-incidence fixtures.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-13", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/**/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/**/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "rational inner matrix", "McMillan degree", "detector-rank hierarchy", "subspace interpolation", "Fejér–Riesz factorization", "passive memory", "spectral routing", "Wigner–Smith delay", "collision strata" ], "subjects": [ "Mathematical Physics", "General Mathematics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b18ba2f0f56cc8934b95454f4e145b15b19b0b82b463e7de93fb55ac420e0c89", "canonical_bytes": 375083 }, "ai_assistance": { "used": true, "statement": "OpenAI Codex assisted with preparation of this ARR deposit, machine-readable text extraction, provenance assembly, and integrity checks. The supplied manuscript contains no model-specific authorship disclosure; no independent AI scientific assessment is claimed.", "systems": [ "OpenAI Codex" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person; no independent editorial review or scientific endorsement is claimed." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-52B6MSS1W197W9T2-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:2d15fddb-337e-4c4e-aaaf-6f17a7a0b046", "version_id": "arr:version:c7ee9fa9-0cef-4f4e-ab2f-ae67b488f340", "id": "ARR-2026-1D2QYXPCVY9H7ANB", "version": "v1", "title": "Exact Rate–Distortion Theory for Complex-Projective Born Prediction: Finite-Dimensional Bingham Frontiers, Thermodynamic Coexistence, and Worst-State Capacity", "abstract": "We give a unified exact rate–distortion theory for retaining the complete rank-one Born-probability field of a Haar-random pure state in complex projective space. A constrained root count, a sharp centered power-sum theorem, and Newton's expansion prove an all-degree spectral result: at fixed traceless Frobenius norm the projective Laplace transform is maximized by a one-positive-spike spectrum. This reduces the unrestricted Shannon rate–distortion function to an exact scalar complex-Bingham envelope in every dimension, with covariant channels and independently flagged coexistence mixtures attaining every distortion. For dimension at least three, directional information turns on discontinuously; the qubit curve and the all-dimensional high-fidelity constant are explicit. We then solve the full fixed-normalized-distortion limit. If y_* > 2 solves y_* - 1 = 2 log y_*, the limiting free energy has a unique coexistence point, and the information cost per dimension is a closed two-piece function with a nontrivial linear face. The finite-dimensional onset multiplier equals alpha_* d minus [alpha_*/(2 log y_*)] log d up to an O(1) remainder. Finally, a pointwise Hilbert projection converts every measurable scalar reporter into a physical density-matrix reporter without increasing risk for any pure input. Hence the exact worst-state channel capacity equals the Haar rate–distortion function, arbitrary joint n-state memories cost exactly n times the one-state frontier, and transitivity forces zero rate dispersion with an exponential finite-blocklength strong converse. These results concern reusable calibrated probability fields, not click-only simulation, state update, or intrinsic randomness.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-13", "status": "accepted", "licenses": { "manuscript": "CC-BY-4.0", "metadata": "CC0-1.0", "code": [ { "path": "src/replay/*.py", "spdx": "Apache-2.0" } ], "data": [ { "path": "src/replay/*.json", "spdx": "CC0-1.0" } ] }, "source_of_truth": "paper.pdf", "keywords": [ "Born probability", "rate–distortion theory", "complex projective space", "complex-Bingham distribution", "quantum information", "worst-state channel capacity", "Kummer asymptotics", "thermodynamic limit", "zero dispersion" ], "subjects": [ "Quantum Physics", "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": true, "terms_version": "ARR-DEPOSIT-0.1" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "48bd09c67edf1d1754941d3df211952449cf3f91534637a2ac2eb3f598a0ba15", "canonical_bytes": 499166 }, "ai_assistance": { "used": true, "statement": "AI tools assisted with literature search, algebraic stress testing, editing, and reproducibility checks. The author is responsible for the definitions, proofs, claims, citations, and final manuscript.", "systems": [ "AI tools (model identifiers not stated in the manuscript)" ] }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-VERIFY-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "partial", "lean4": "not_applicable", "report": "VERIFICATION.md" }, "editorial": { "decision": "founder_pilot", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Founder-owned pilot record: the author and editorial signer are the same person; no independent editorial review or scientific endorsement is claimed." }, "record_type": "research_paper", "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "published", "release_tag": "ARR-2026-1D2QYXPCVY9H7ANB-v1", "source_snapshot_available": true } ] }, { "schema_version": "1.0", "record_id": "arr:record:cf6ba76d-c81c-42e2-ba31-843ff9941d59", "version_id": "arr:version:48aa5664-2e5f-4ad5-a370-9a376f98bcec", "id": "ARR-2026-6FDEKPVJ0W8BHBMC", "version": "v1", "title": "A Finite-Dimensional Nonanalytic Spectral Transition and Exact High-Fidelity Rate–Distortion for Rank-r Born Prediction on Complex Grassmannians", "abstract": "Let P be Haar on the complex Grassmannian Gr(r,d) and set rho_P=P/r. We solve two coupled finite-dimensional problems. First, on the sphere of traceless Hermitian external fields with fixed Frobenius norm, we determine incompatible weak- and strong-field optimizers of the matrix-Bingham free energy log E exp{s tr(AP)}. For 1= Lk this maximal-memory locus is open and dense. The paper gives an explicit positive Pick completion, a realization- and inertia-based lower bound, a family of targets that collide while retaining maximal exact degree for every nonzero opening, an exact quadratic certification margin, and a fail-closed noisy projector test. For three scalar target lines it also proves the complete phase diagram: degree zero for one common line, degree one exactly for three distinct coplanar lines, and degree two otherwise. Deterministic certificates and an independent implementation accompany the proofs.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0045", "abstract_url": "https://www.ai.vixra.org/abs/2608.0045", "first_submitted_at": "2026-08-11T15:57:16+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-11T15:57:16+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0045-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-11T15:57:16+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0045v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7366328bce0f2de84667acc5e2363baa29a266dd29e859fbec87237a10cd15e1", "canonical_bytes": 356986 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:626baf2a-2385-4cbb-9be8-2e79bbe1e7d7", "version_id": "arr:version:2532f4ef-105d-45eb-b07a-cc59f5224293", "id": "ARR-2026-32DEQJM8W59JXSQT", "version": "v1", "record_type": "research_paper", "title": "Tetrahedral Echoes on the Fuzzy Sphere", "abstract": "Four balanced spin kicks along the vertices of a regular tetrahedron generatean order-dependent eight-pulse echo. We prove that all 24 echo orders have oneconjugacy class in SU(2). Haar randomization of only the global orientationtherefore gives an order-law-independent, self-adjoint random-unitary channelon every spin-j matrix algebra. Its exact eigenvalues are normalized SU(2)characters, lambda_l=U_{2l}(q)/(2l+1), with multiplicity 2l+1 and an explicitfinite-pulse architecture polynomial q=1-A/2. The maximal link-reflection-positive interval connected to zero is alpha<=pi/(4j+1), with an exact endpointequation and a finite OS Hamiltonian under strict inequality. In the doublescaling N=4j+1, y=xi/sqrt(N), the full tower converges uniformly tosinc(8xi^2u). This gives the sharp full-tower boundary xi_c=sqrt(pi/8), acritical boundary law N lambda_top -> 3pi/8-2s, an explicit scaled mass profile,and an ultraviolet heat-trace integral. The fixed-rank limit recovers the fuzzy-sphere Laplacian. Poissonization yields a genuine CPTP semigroup and an exactmany-body connected nuclear profile exp(3e^-c)-1. Symbolic and deterministicmatrix certificates accompany the manuscript.The Haar average also has explicit exact finite implementations. A classicalpositive Gauss--Legendre/trapezoidal cubature at bandlimit 4j needs(4j+1)(2j+1) order-conditioned frames, or (4j+1)^2(2j+1) frames when the sameframe list must be order oblivious.The common-class proof reduces the 24 orders to the even and odd A4 orbits.For finite implementations, a separate stability bound controls l1 weighterror, orientation displacement, and pulse perturbations; total variationagainst Haar is not used for discrete frames.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0046", "abstract_url": "https://www.ai.vixra.org/abs/2608.0046", "first_submitted_at": "2026-08-11T15:21:20+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-11T15:21:20+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0046-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-11T15:21:20+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0046v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "30de956fc19ed2bdc9ba60572164349a65558b9fd00959d5900a31c703028306", "canonical_bytes": 451539 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:3ceb37d4-9b26-4414-9dce-41b168128237", "version_id": "arr:version:ba807fd1-3bd5-4233-aebd-d6daebb7d762", "id": "ARR-2026-1WXCVX96S68GA9VK", "version": "v1", "record_type": "research_paper", "title": "Orthogonal Spectral Fan-Out Costs K(L-1) States: a Global Memory Law Beyond Pairwise Routing", "abstract": "A passive lossless network may route the same k-dimensional input channel to different output subspaces at different frequencies. Every two-frequency restriction can be cheap while the joint task is not. For L distinct boundary frequencies and mutually orthogonal prescribed output k-planes, we prove that the minimum McMillan degree among square finite rational-inner transfer matrices regular at the interpolation nodes is exactly k(L-1). Each pair alone requires degree k, so the largest two-node minimum underestimates the global memory by the unbounded factor L-1. The result is independent of node spacing. Necessity follows both from a zero budget for an analytic minor and from a Pick-Stein displacement identity whose negative inertia cannot exceed realization rank. Sufficiency follows from an explicit positive Pick completion. Beyond exact orthogonality, we derive a general cross-frequency inertia certificate, a gauge-independent span bound, an open robust region preserving the integer memory count, and a fail-closed noisy-eigenvalue certificate. Deterministic code tests arbitrary nodes, synthesizes minimal conservative realizations, and independently verifies the stated identities.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0047", "abstract_url": "https://www.ai.vixra.org/abs/2608.0047", "first_submitted_at": "2026-08-11T13:47:42+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-11T13:47:42+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0047-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-11T13:47:42+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0047v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "775c60c5f00f96f9cb84ebcdea5b4c9b49c9dc2d2d0ffec1b9a1c4350dc3b3b8", "canonical_bytes": 360616 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:0dfdc5ca-cedc-4419-ab2b-c02df90f4a57", "version_id": "arr:version:dc8706b0-b863-4b53-8b6e-f7c209efc775", "id": "ARR-2026-0DZQ2WNKPW8GCTPA", "version": "v1", "record_type": "research_paper", "title": "Orthogonal Measurements Maximize All-Degree Born Rigidity among Equal-Trace Rank-One POVM Orbits in Dimension Five and Above", "abstract": "Under an explicit noncontextual homogeneous-response ansatz for rank-one quantum effects, we study normalization on every unitary rotation of a fixed finite POVM. The orbit-normalization operator diagonalizes on the projective harmonics of complex projective space. We derive its weighted all-degree singular spectrum and show that the smallest non-Born spectral value is the sharp condition number controlling distance from the affine space of trace-one Hermitian quadratic responses. For dimensions at least three, the high-degree spectrum of a finite seed converges to the sum of squared aggregate ray weights; for an outcome-simple equal-trace seed with N outcomes, the limit is d squared divided by N. Combining this ceiling with the forced geometry of the two smallest tight frames solves the global equal-trace design problem in every dimension d at least five. An orthonormal-basis seed uniquely maximizes the all-degree Born-rigidity gap, with value d minus 6 divided by d plus 1, up to unitary equivalence and outcome relabeling. Every distinct-outcome overcomplete seed in the stated class is strictly worse. By contrast, every weighted complex projective 2-design has a degree-two nullspace and therefore zero rigidity gap. Thus measurements optimal for state tomography can be maximally non-rigid for this covariant normalization objective. The result concerns one-step response fields and does not derive state update, intrinsic randomness, or microscopic particle dynamics.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0048", "abstract_url": "https://www.ai.vixra.org/abs/2608.0048", "first_submitted_at": "2026-08-11T13:00:56+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-11T13:00:56+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0048-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-11T13:00:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0048v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e868dd2643eb5e36e31e51c729d6c703e4e5fb06bd69a1c075c084f5603ba914", "canonical_bytes": 311081 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:675a300b-e948-4921-a7bd-f2cd7e7a2e18", "version_id": "arr:version:5def0588-f41e-4328-a569-e6bb83f3f539", "id": "ARR-2026-37B8R0QTA894GTFF", "version": "v1", "record_type": "research_paper", "title": "The Exact Five-Level Inverse Commutator Cost: Twelve Horn Chambers, Optimal Rank, and the Sharp 5/2 Resource Tax", "abstract": "For a prescribed traceless Hermitian five-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. If g_i=lambda_i-lambda_{i+1} are the ordered spectral gaps, the answer is the maximum of six explicit rational linear forms and their reversals. Exact Littlewood-Richardson enumeration gives 142 Horn inequalities. Twelve sparse dual identities prove the lower facets, and twelve rational singular-spectrum maps attain them; exact cone certificates prove completeness without sampling. In contrast with the two qutrit facets and four four-level facets, dimension five has twelve exposed facets and open chambers that force rank four. For every nonzero target, the least rank of an optimal factor is max(n_+(F),n_-(F)). We also prove the sharp tax 1 <= kappa_5/(||F||_1/2) <= 5/2 with complete equality loci, and the exact balanced triangular perimeter S_2^2=12 sqrt(3) kappa_5. Two rational certificates and an independent deterministic LP campaign accompany the paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0049", "abstract_url": "https://www.ai.vixra.org/abs/2608.0049", "first_submitted_at": "2026-08-11T12:20:40+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-11T12:20:40+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0049-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-11T12:20:40+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0049v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "cf7d5a17a4c205f08b97acfead00e30a63292df38338504398d322651b27f39c", "canonical_bytes": 412601 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:740b9d00-e8c8-4a9b-9a70-ee51257abbe6", "version_id": "arr:version:fa3706d4-6787-4fcb-94e8-a33ec4792c98", "id": "ARR-2026-3M1EEG1T689ADSMW", "version": "v1", "record_type": "research_paper", "title": "The Exact Four-Level Inverse Commutator Cost: Horn-Littlewood-Richardson Facets, Rank Transitions, and Sharp Loop Synthesis", "abstract": "For a prescribed traceless Hermitian four-level target F, we determine exactly the least product of Hilbert-Schmidt norms of Hermitian A,B satisfying -i[A,B]=F. With ordered eigenvalues lambda_1 >= ... >= lambda_4, the answer is the maximum of four explicit linear spectral forms. The lower bounds are Horn-Littlewood-Richardson certificates and four closed constructions attain them. On every nonzero spectral stratum, the least optimal rank is exactly max(n_+(F),n_-(F)), closing all chamber walls and degenerations. We also prove a finite-dimensional Horn linear-program reduction, the sharp tax 1 <= kappa_4/(||F||_1/2) <= 2 with complete equality cases, and the exact balanced three-kick action S_2^2=12 sqrt(3) kappa_4. Exact symbolic and deterministic LP certificates accompany the manuscript.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0031", "abstract_url": "https://www.ai.vixra.org/abs/2608.0031", "first_submitted_at": "2026-08-10T21:34:32+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T21:34:32+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0031-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T21:34:32+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0031v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f40f39d3e839bb2b7a722d593a3435af9d3e0bb6963c6237ec1a14e48bfb59dd", "canonical_bytes": 484360 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:796c512c-cce3-488b-8ecc-60d3d1ee5492", "version_id": "arr:version:66098576-e501-4d39-a458-7f01f9684cd5", "id": "ARR-2026-3SDH8JSK73925RXK", "version": "v1", "record_type": "research_paper", "title": "Reflection Positivity and Exact Gap Certificates from Forgotten Quantum Order", "abstract": "A balanced sequence of short Hamiltonian kicks has no first-order drift, but its order-dependent commutator holonomy survives when the order record is discarded. We prove that a reversal-symmetric average of complete order/reverse echoes is a self-adjoint random-unitary transfer operator and obeys the nonperturbative bound cos(4|y|S) I <= T_y <= I for |y|S < pi/8. This yields site and link reflection positivity and a finite-dimensional Osterwalder-Schrader Hamiltonian. The physical transfer approaches the curvature-frame generator with an explicit sixth-order remainder, giving quantitative O(y^2) convergence of its mass gap. For the regular tetrahedral qubit loop, we derive the exact finite-pulse depolarizing eigenvalue, isolate its first positivity zero at y = 0.455698535295322..., and obtain the mass expansion. We then prove a complete finite-depth Hausdorff criterion for visible transfer edges, with uniformly sharp depth r-1, and give an exact rational four-kick certificate: the true frame gap 10/3 is certified while the false claim 4 has rational witness value -1/64. A Wishart-Loewner band supplies finite-sample type-I control for independent Gaussian correlator sketches, including adaptive witnesses. Exact symbolic and deterministic numerical certificates accompany the manuscript.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0032", "abstract_url": "https://www.ai.vixra.org/abs/2608.0032", "first_submitted_at": "2026-08-10T20:30:59+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T20:30:59+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0032-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T20:30:59+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0032v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d18422c9981769c4c36a7382e6831e200a94bcbb1fab447741ae240536e6b6d2", "canonical_bytes": 451563 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2cf3cbf5-0c7a-4a84-a699-6bf917628792", "version_id": "arr:version:80917f5e-fd6d-45b8-bc8f-24148ab793a9", "id": "ARR-2026-1CYF5ZA33T9A2AD6", "version": "v1", "record_type": "research_paper", "title": "The Action—Memory Diamond: Exact Resource Regions for Passive Matrix Networks Autor", "abstract": "A passive lossless network pays two different costs when it rotates a signal subspace over a frequency arc: a continuous Wigner—Smith action and an integer McMillan memory. Known Grassmannian length bounds and rational-inner degree identities constrain these resources separately. For the stated finite rational-inner class, we determine their joint attainable region exactly. Let two rank-k subspaces have principal angles βj, put B = Σj βj and let r be the number of nonzero angles. For a square finite rational inner transfer matrix of degree at most d, define the arc action A = ∫I tr Q(θ)dθ, where Q = −iS*∂θS is positive semidefinite. If B > 0, the exact feasible set is d ≥ r and 2B ≤ A ≤ 2πd − 2B. Both faces are attained. Equivalently, dmin(A) = max{r, ⌈(A + 2B)/(2π)⌉}. The upper face is a return cost: the complementary arc must rotate the subspace back, while the full-circle trace action is exactly 2π times the degree. We prove sufficiency by an explicit compiler of normalized rank-one Blaschke—Potapov gates; it realizes every interior point and both faces, including rank-deficient and orthogonal cases. When the endpoint subspaces coincide, the region changes discontinuously to A ∈ [0, 2πd), with the upper endpoint open. We derive fail-closed noisy degree certificates and give a multi-frequency warning using classical boundary Nevanlinna—Pick theory: three pairwise degree-one routing tasks can require degree two jointly. For orthogonal-line data the obstruction is a frame-independent cycle phase, exhibited by an exact positive semidefinite Pick completion with spectrum (2,1,0). Deterministic code compiles random points of the diamond, constructs the degree-two colligation, and is replayed by an independent verifier.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0033", "abstract_url": "https://www.ai.vixra.org/abs/2608.0033", "first_submitted_at": "2026-08-10T19:28:35+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T19:28:35+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0033-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T19:28:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0033v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4280e0e5b02f85331668d70f022baa124853980edabbd339fb6393df7e903d91", "canonical_bytes": 330946 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:36d10493-c6bd-4e89-85b4-1446341d461f", "version_id": "arr:version:e2d4b811-eb71-47a4-b2c6-f5760b4b7cd5", "id": "ARR-2026-1PT4297HNX9T4RBD", "version": "v1", "record_type": "research_paper", "title": "Sharp Costs and Exact Semigroups from Forgotten Quantum Order", "abstract": "A balanced sequence of short Hamiltonian kicks has zero first-order drift but retains an order-dependent commutator holonomy. For a traceless qutrit target with ordered eigenvalues, we solve the inverse Hermitian-commutator problem exactly: its minimum product Hilbert-Schmidt norm is the larger adjacent spectral gap, equivalently half the trace norm plus the absolute middle eigenvalue. This yields the exact minimum action of a balanced three-kick realization and identifies a middle-eigenvalue cost tax between 1 and 3/2. Among four equal-norm balanced qubit kicks, the forgotten-order curvature gap is at most `S^4/108`, with equality only for a regular tetrahedron. Its 24 orders generate exactly the six Pauli holonomies, so the finite twirl is depolarizing and an explicit inverse-cosine schedule realizes any depolarizing semigroup exactly at every finite step count. We then derive the diffusion limit from complete echoed, pinched physical words, obtaining an explicit `O(n^-1/2)` diamond-norm bound. Off-block pulses of size `y^(1+beta)` produce a sharp trichotomy: irrelevant for `beta>1`, additive at `beta=1`, and Zeno-projective for `0= 3`, a gauge-invariant operator action obeys a sharp, dimension-free polygonal bound on the spectral diameter of the geometric Hamiltonian; regular two-level polygons attain the constant in every dimension. A target-sensitive Hilbert--Schmidt companion bound is controlled by the trace norm and has equality exactly for sign-paired nonzero spectra. These laws yield exact diamond-norm ceilings with a physical state witness. For a uniformly forgotten order, we derive an exact `1/12` commutator-frame covariance. The resulting reversal-symmetric random-unitary product converges in diamond norm at rate `O(n^-1)` to a GKLS frame Laplacian whose fixed algebra is the joint commutant of the pair commutators. A tetrahedral Pauli architecture gives exact primitive depolarization with gap `64/3`. Finally, fixed laboratory time `T` and bounded kick amplitude `Lambda` impose a sharp curvature ceiling proportional to `T^2 Lambda^2/n`; maintaining nonzero holonomy requires `Lambda=Omega(sqrt(n))`. Exact symbolic and deterministic numerical certificates accompany the paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0035", "abstract_url": "https://www.ai.vixra.org/abs/2608.0035", "first_submitted_at": "2026-08-10T16:16:46+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T16:16:46+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0035-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T16:16:46+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0035v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "22bcbf520628de8471ab72c9f35dcb7c30d13ea0469c8db079d763b8f5694153", "canonical_bytes": 393920 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:b08450b2-c1aa-4271-88f5-c737d5e7ec96", "version_id": "arr:version:6e52f5fa-99b2-4008-bbe7-2b9cd9583b1d", "id": "ARR-2026-5GGH8B5GDA89RRHX", "version": "v1", "record_type": "research_paper", "title": "Complete Continuous Delay Regions, Quantized Passive Memory, and Pick Tomography for Quantum Networks", "abstract": "Lower bounds do not determine which resource profiles are physically attainable. We close the continuous inverse problem for passive subspace transport. Let two rank-k subspaces in C^N, N >= 2k, have ordered canonical angles beta, and let q_j be the integrated leading eigenvalues of a positive generator Q = -iS* dS/dt. We prove the exact equivalence: q is attainable if and only if 2 beta is weakly majorized by q. Every feasible profile has a compiler using at most k+1 mutually commuting positive generators of rank at most k, with constant ordered top spectrum. Analytic rationality adds an integer-valued resource: for two boundary frequencies, the least McMillan degree of an inner matrix sending a fixed input subspace to two prescribed output subspaces equals the number of nonzero canonical angles. We also give a fail-closed finite-error certificate for both resources from noisy projectors.At multiple frequencies, Wigner-Smith delay is only the block diagonal of a boundary de Branges-Rovnyak Pick matrix. This positive matrix is the Gram matrix of frequency-excited internal states and has rank bounded by the McMillan degree. Its spectrum yields robust degree certificates and unavoidable model-reduction tails. An exact example exhibits identical local proper delays for degree-one and degree-two devices while their Pick ranks distinguish them. Deterministic code reconstructs the compilers, tests 2,240 randomized theorem interfaces, checks the strict separation, and independently replays the certificate.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0036", "abstract_url": "https://www.ai.vixra.org/abs/2608.0036", "first_submitted_at": "2026-08-10T15:47:43+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T15:47:43+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0036-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T15:47:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0036v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4a44994295084a172518717c1a196e0968735bd2ceb7f502f169590be89beb10", "canonical_bytes": 294838 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:0f78076b-b34d-4266-bd51-24eb338ee7f9", "version_id": "arr:version:332f1fee-74e1-4ed1-9e77-e4de6a10c11d", "id": "ARR-2026-0FF03PQCTD89KBTM", "version": "v1", "record_type": "research_paper", "title": "Operational Curvature of the Heisenberg Cut: Exact Diamond Readout, a Discrete Stokes Law, and Sharp Action Bounds for Dissipative Zeno Holonomy", "abstract": "The order of short operations is normally a microscopic detail. We show that a fixed degenerate measurement turns it into an operational curvature with an exact macroscopic readout. Let E retain a block matrix algebra, and let two words apply the same short Hamiltonian kicks in different orders, with the same nonselective pinching after every kick. Their leading difference is `-i tau^2 ad(F) E`, where F is the sum of `i[h_j,h_k]` over pairwise inversions. This gives a discrete non-Abelian Stokes law. Its diamond-norm coefficient is exactly the largest spectral diameter of a block of F, and therefore fixes the leading optimal channel-discrimination advantage. Under first-order balance, all permutations have the same dissipator while their geometric Hamiltonians differ exactly by F, so local curvature integrates into distinct diffusive quantum Markov semigroups. We characterize contextual invisibility, the rank-one classical boundary, and inverse-success amplification under postselection. Every retained Hamiltonian modulo the block center is realizable by a balanced three-kick loop. For a qubit block we prove the sharp action law `kappa <= S^2/[m tan(pi/m)]`, attained by regular planar kick polygons. An integer-Pauli four-kick architecture saturates the bound and supports primitive dissipation. Symbolic, semidefinite, and convergence certificates accompany the paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0037", "abstract_url": "https://www.ai.vixra.org/abs/2608.0037", "first_submitted_at": "2026-08-10T15:20:28+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T15:20:28+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0037-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T15:20:28+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0037v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "16c1224fd17383f9f191fa69622961863c3925076f9a1669024d9335dc3c38b4", "canonical_bytes": 413414 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6a1fac26-3a27-4b49-8d80-1bf164f6b486", "version_id": "arr:version:6dab2e58-a577-44c2-a8c4-1a3143f4acdc", "id": "ARR-2026-3A3YP2CEH79D4RV0", "version": "v1", "record_type": "research_paper", "title": "Noncommuting Block Measurements Generate Quantum Diffusion: A Three-Obstruction Convergence Hierarchy, a Noncommutative Connectivity Gap, and Exact Algebraic Architectures", "abstract": "Repeated projective measurements are usually discussed either in the ballistic Zeno scaling or after reduction to classical outcome probabilities. We study a different regime in which each nonselective measurement retains a full matrix algebra inside every degenerate outcome block. Let E(X)=sum_a P_a X P_a, let E_tau be its rotation by exp(-i tau H), and close one cycle by Phi_tau=E E_tau E. We prove, uniformly on compact time intervals and in diamond norm, that Phi_{sqrt(t/n)}^n converges to exp(-tK)E, where K=E ad_H(1-E)ad_H E=C_H^* C_H. The limit is a genuinely quantum Markov semigroup on the direct sum of the block matrix algebras, with explicit jumps sqrt(2) P_b H P_a. Beyond upper bounds, we identify three exact local obstructions for the unprocessed physical product. The cubic map M_H produces a nonzero n^{-1/2} coefficient; after it vanishes, the quartic product obstruction J_H produces a nonzero n^{-1} coefficient; after both vanish, the quintic obstruction P_H produces a nonzero n^{-3/2} coefficient. If all three vanish, the error is O(n^{-2}). All three coefficient transforms are injective. An exact three-record algebraic example has M_H=J_H=0 but P_H nonzero, proving that the third branch is attained. The fixed algebra is A intersect {H_off}', and the least singular value of the commutator frame C_H defines a noncommutative connectivity gap. In the primitive case that gap is the exact exponential mixing exponent in diamond norm and is Lipschitz robust under Hamiltonian perturbations. Rank-one blocks reduce exactly to twice the squared-coupling graph Laplacian. An eight-dimensional rational architecture with four qubit blocks is certified irreducible; its gap is the unique root in (0.4545,0.4547) of an explicit quartic. Symbolic certificates, semidefinite diamond-norm replays, and convergence tests accompany the paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0038", "abstract_url": "https://www.ai.vixra.org/abs/2608.0038", "first_submitted_at": "2026-08-10T14:22:14+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T14:22:14+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0038-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T14:22:14+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0038v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "1ebd2390b9be9257e6d6772dea56b6acb90867674aa77c05cc53c5b3956a178f", "canonical_bytes": 460394 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:223f4d9c-4d5b-4ff3-b7d0-9a6ce9aab212", "version_id": "arr:version:930d3186-3947-4625-babb-aed191910611", "id": "ARR-2026-127X6SRKAV9ZSVFM", "version": "v1", "record_type": "research_paper", "title": "Proper-Delay Spectra Majorize Subspace Rotation: Exact Finsler Resource Laws for Passive Networks", "abstract": "A subspace quantum speed limit usually records only the largest canonical angle. Passive scattering theory usually records either the largest proper delay or their total trace. Both compressions discard how a rank-k routing event is distributed across modes. We derive the missing vector law: the integrated spectral-spread vector weakly majorizes twice the canonical-angle vector. More strongly, for every symmetric gauge Φ and every pair of k-subspaces in N ≥ 2k dimensions, we solve the variational problem exactly: the minimum spectral-spread action is 2Φ(β). The same value holds for the leading-proper-delay action under positive generators, and one constant coupled-mode path minimizes all gauges simultaneously. The Ky Fan members recover the bandwidth limit, strengthen the trace-action law, and expose every intermediate modal budget. An exact nonnegative slack decomposition separates common-mode delay, inefficient spectral coupling, and nongeodesic subspace motion. Robust corollaries convert heterogeneous pass/stop leakage spectra and finite tomography errors into certified Lorenz curves for delay and, for rational inner networks, McMillan-degree lower bounds. A deterministic artifact tests 8,192 random generators, 1,536 time-dependent paths, sharp equality families, and 2,048 noisy tomography instances.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0039", "abstract_url": "https://www.ai.vixra.org/abs/2608.0039", "first_submitted_at": "2026-08-10T12:58:55+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T12:58:55+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0039-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T12:58:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0039v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "cd5abe8bc1cb3766e25a7007d4d8cd68583634883fb7aab3eec28c70e3d0b1c8", "canonical_bytes": 314170 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:c3289f7e-144b-4aa0-b47f-94676f26a286", "version_id": "arr:version:ac5d3795-b7aa-42f8-923a-5f68197b658b", "id": "ARR-2026-6352FQW52B9AGB8Z", "version": "v1", "record_type": "research_paper", "title": "Every Spectral Switch Costs Memory: Sharp Robust Wigner—Smith Speed Limits for Passive Quantum Networks", "abstract": "Exact interpolation can force the internal degree of a passive network, but laboratory calibrations are approximate. We prove a sharp frequency-domain speed limit requiring neither exact zeros nor analytic continuation away from the measured frequency axis. Let (S(e^{itheta})) be an absolutely continuous unitary scattering path with positive Wigner—Smith generator (Q(theta)=-iS(e^{itheta})^astpartial_theta S(e^{itheta})succeq0). If a fixed (k)-dimensional input subspace is routed approximately between complementary output sectors with amplitude leakages (varepsilon_p,varepsilon_s), define (alpha=[pi/2-arcsinvarepsilon_p-arcsinvarepsilon_s]_+). Every transition then requires Wigner—Smith trace action at least (2kalpha) and largest-proper-delay action at least (2alpha). Costs add over disjoint frequency arcs. For a rational inner network of McMillan degree (n), (M) alternating pass/stop pairs imply (nge 2Mkalpha/pi), recovering (nge Mk) at zero error. An explicit (2k)-port interferometric family attains the bounds for every admissible error pair. A tomography-error corollary converts finite scattering measurements directly into certified degree and delay lower bounds. Reproducible certificates audit equality cases, positive-block inequalities and random Blaschke—Potapov products.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0040", "abstract_url": "https://www.ai.vixra.org/abs/2608.0040", "first_submitted_at": "2026-08-10T11:14:40+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T11:14:40+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0040-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T11:14:40+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0040v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "fc8ff261e056d5cc56603764d75ba44ef9772aff652d833762e1d8c82e47eaf5", "canonical_bytes": 305665 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:077446cf-e1a8-4f98-8954-2889d2578a14", "version_id": "arr:version:cffb7f7a-cacb-4d79-bfff-cce16fec2b87", "id": "ARR-2026-07EH3CZRD89YC8JN", "version": "v1", "record_type": "research_paper", "title": "Lossless Calibration Is Stored Memory: A Topological McMillan-Degree and Wigner—Smith Law for Passive Quantum Networks", "abstract": "How many internal passive modes are required to transmit prescribed quantum noise channels without loss while suppressing all signal directions elsewhere? We prove an architecture-independent answer for finite-dimensional rational networks. Let a causal rational inner scattering matrix S have McMillan degree n, signal block G, and complementary loss block C. At distinct regular boundary frequencies, suppose that G is isometric on input subspaces of dimensions k_j. If G is a strict contraction at one other frequency, then sum_j k_j ≤ n.Every lossless direction lies in the kernel of C; a nonzero maximal minor of C therefore has a zero of multiplicity at least k_j. Exterior powers of a minimal Blaschke—Potapov factorization show that no minor can have more than n zeros. The same factorization yields the exact topological delay identity(1/2π) ∫ tr Q(θ) dθ = deg_McM S = n,where Q = −i S* ∂θS is positive semidefinite. Thus lossless calibration multiplicity is bounded by integrated Wigner—Smith delay. The bound is sharp in every dimension. We establish robustness under analytic passive perturbations, prove why unstructured approximate samples cannot imply a degree bound, and show that a previously constructed six-port reservoir filter is universally optimal up to six internal states. Proofs and numerical certificates are reproduced by the linked public repository.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0041", "abstract_url": "https://www.ai.vixra.org/abs/2608.0041", "first_submitted_at": "2026-08-10T10:22:35+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T10:22:35+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0041-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T10:22:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0041v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "afd633aeb139c4dbb8daf714968b1d09032e1f6fa68b26cc7f906a634a8df16c", "canonical_bytes": 346829 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:8f3e5e87-f681-42aa-aec4-b7d11ea3d403", "version_id": "arr:version:017d1e23-38f4-4ec0-a2c8-2aa1876a7ebb", "id": "ARR-2026-4F7SF8FXM18ANAXH", "version": "v1", "record_type": "research_paper", "title": "Architecture-Dependent Decoherence Suppression in Passive Quantum Networks: Irreducible Channel Mixing, Squared Rate Gaps, and the Price in Dwell Time", "abstract": "We study whether passive reservoir filtering can suppress decoherence more effectively when its channel mixing is irreducible, even after fixing the passband responses and rational complexity. For every integer S ≥ 5, we construct an explicit causal inner six-port network with three signal and three vacuum-loss ports. Its signal block is a rational Schur transfer satisfying 3(S−1) delayed full-spark tangential calibrations and exhibiting exponentially small leakage on two stop arcs. In contrast, every transfer of the same bidegree possessing a constant nontrivial reducing channel and satisfying the same calibrations retains unit stopband norm.We strengthen this exact separation with a quantitative finite-error obstruction: for calibration defect δ and sampled reducing-line defect β, comparator leakage is bounded below by [1−C_S(δ+β)]_+, with C_S given explicitly by finite singular-value margins. A scalar Schur construction proves that every bound of this form must deteriorate at least as 2 exp(9S/20)(1+o(1)); hence uniform robustness is impossible for the chosen clustered calibrations.For uniformly nondegenerate bath spectra, the signal-level separation is squared at the Kossakowski-rate level. A closed Markov pure-dephasing model includes all auxiliary vacuum ports exactly, producing an architecture-independent measurable baseline and an explicit total Ramsey-rate advantage. Finally, we prove that strong passive suppression requires large dwell time: under a peak-delay budget D, the rate-improvement factor is asymptotically at most quadratic in D/S. The construction therefore moves the coherence-maintenance resource into passive memory, vacuum noise and conditioning rather than eliminating it. All certificates, figures and numerical audits are publicly reproducible.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0042", "abstract_url": "https://www.ai.vixra.org/abs/2608.0042", "first_submitted_at": "2026-08-10T08:28:18+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T08:28:18+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0042-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T08:28:18+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0042v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "6d5df4084d80f9d639365e05015cd89ff4a7f85761c5e6d449403882541cd28c", "canonical_bytes": 450629 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:46a61f59-5ab4-40bb-be42-724d5a5e94c2", "version_id": "arr:version:c50cb064-17c1-49d2-8fea-1d43277cf3da", "id": "ARR-2026-26MRFNJPNM82XVWG", "version": "v1", "record_type": "research_paper", "title": "Irreducible Channel Mixing and Exponential Calibration Laws for Matrix-Polynomial and Linear-Phase MIMO FIR Filters", "abstract": "Scalar Chebyshev filtering treats every vector in a block Krylov iterate with the same polynomial, while simultaneously diagonalizable matrix coefficients amount to independent scalar filters after a fixed channel rotation. We study the larger class of Hermitian matrix-polynomial filters under tangential pass constraints. Already at fixed channel dimension d=3, we construct rationally generated signatures with quantitative full-spark margin for which an irreducible symmetric filter has stopband leakage O(exp(-cN)). In contrast, every exactly calibrated symmetric coefficient family with any common nontrivial invariant channel subspace has leakage at least one; this comparator strictly contains the pairwise-commuting class and permits a fully noncommutative 2 by 2 block. A quantitative theorem covers approximately reducible filters by charging their sampled off-block coupling together with calibration error. The signature margin and the admissible combined error are both exp(-O(N)), not exp(-N^3). This exponential scale is unavoidable: for arbitrary pass nodes and signatures in the same separated bands, an explicit scalar binomial-tail polynomial has both pass error and stopband leakage at most exp(-2N/81). Thus constant-error separation is impossible, while the irreducible construction achieves the correct exponential scale class. An affine cosine substitution gives the same robust law for fixed-latency reciprocal linear-phase MIMO FIR filters. We also give an exact rational five-tap certificate with stopband norm at most 25/32 and prove that its advantage survives reducible calibration errors delta < 7/1920. A second exact-arithmetic certificate is calibrated from a public triaxial pump-vibration data set: it gives leakage below 0.96 versus one for every exactly calibrated reducible symmetric class, while its maximum directional error on six held-out records is 0.00385. In a frequency-domain-decomposition test on the frozen held-out cospectra, filtering rotates the leading modal direction by at most 0.222 degrees and changes its leading spectral ordinate by at most 2.4 × 10^-5 relatively. Numerical programs test the mechanism and expose an ordinary graph-denoising setting in which scalar Chebyshev filtering is instead preferable. Tangential matrix interpolation, MIMO filtering, scalar two-band approximation and convex FIR design are not claimed as new; the contribution is the fixed-order reducible/irreducible separation together with its two-sided calibration scale.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0029", "abstract_url": "https://www.ai.vixra.org/abs/2608.0029", "first_submitted_at": "2026-08-10T02:01:56+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-10T02:01:56+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0029-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-10T02:01:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0029v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Digital Signal Processing" ], "subjects": [ "Digital Signal Processing" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "aad5b1f543544dc52954e1d2328e6021bb374550472d083c9a129c8b13f1fef4", "canonical_bytes": 423636 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:3672af73-cb8a-4742-9e10-4bcf07d7c146", "version_id": "arr:version:b0b36996-0a07-4144-9687-1f3dbe217d15", "id": "ARR-2026-1PEAQQ7JWA8X19W4", "version": "v1", "record_type": "research_paper", "title": "The Reconstructed Theory Has One Mass: a Machine-Checked Volume-Uniform Spectral Gap with Exact Identification Against the Gibbs Sums", "abstract": "For the spatial Z_2 (Ising-slice) system inside the Dobrushin window 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1, we machine-check in Lean 4 an end-to-end chain from the Gibbs measure to the spectrum of the reconstructed transfer operator. (i) The Osterwalder-Schrader (site-form) reconstruction of the transfer operator is unitarily conjugate, by the explicit sqrt(w) boundary dressing, to the symmetrised Dobrushin kernel. (ii) The unnormalised Gibbs sums themselves are exact matrix elements of that operator's powers: gibbsPathSum(w,beta,N,A,B) = lambda^N , with the partition function the same shape at the dressed constant. These are identities, not bounds, and they hold at every real beta and every positive weight. (iii) There is one mass m > 0 such that for every spatial extent L the projected operator norm is at most e^{-m} and every mixed connected correlator obeys | - | <= ||u|| ||v|| (e^{-m})^n, the zero-time case included. (iv) The connecte two-point function of the normalised Gibbs measure decays at that same rate with a constant independent of the time depth; dividing by the partition function is licensed by a denominator floor uniform in N, which the positive cone supplies and the spectrum does not, since the spectral route controls only the even powers. (v) The N -> infinity limit state exists, is the vacuum state of the reconstructed operator, and does not depend on the strictly positive observable terminating the chain. (vi) The reconstructed operator is a reversible Markov chain -- stochastic and in detailed balance for pi = Omega^2, both proved -- and in that stationary state the connected correlator of bounded observables obeys |E_pi[f P^N g] - E_pi[f] E_pi[g]| <= K_f K_g (e^{-m})^N, with quantifier order \"there exists m, for all L\": no factor depending on the spatial extent. Summing over time separations gives a susceptibility bound K_f K_g / (1 - e^{-m}), independent of the cut-off and of the extent. The window is non-empty at an interacting point (beta = gamma = 1/10, alpha = 1/2), machine-checked, so none of these conditionals is vacuous. The analytic input is inherited: the mass is the one the Dobrushin corollary already produced, and the window is not widened. What the reconstruction contributes is the identification, the exact identities, and the normalisation in which both the rate and the constant lose their dependence on the volume.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-05", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0018", "abstract_url": "https://www.ai.vixra.org/abs/2608.0018", "first_submitted_at": "2026-08-05T21:39:01+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-05T21:39:01+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0018-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-05T21:39:01+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0018v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e7b1de004e105996fddc4ce98c7b825ff8f3db402e79fa2a392ff9c90bf3b259", "canonical_bytes": 424886 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:cedfc2f1-22d3-479b-8374-3b00d77143b1", "version_id": "arr:version:5e824c9d-4906-470b-b362-e3884005d816", "id": "ARR-2026-6EVZ1F28PK8YDR6X", "version": "v1", "record_type": "research_paper", "title": "Faithfulness, Not Algebra Type, Controls the Rapid-Maintenance Singularity", "abstract": "We determine when rapid exact maintenance of a rank-deficient quantum target produces logarithmically divergent free-energy restoration power in algebraic quantum field theory. On every sigma-finite properly infinite factor we construct a bounded quantum Markov semigroup, a nonfaithful normal target and a faithful invariant reference state for which Araki relative entropy reduces exactly to a binary divergence. We derive the semigroup first from localized thermal fermionic probe collisions and then from one autonomous finite-bandwidth Dirac KMS reservoir with fixed smooth coupling. Exact memory equations yield an explicit finite-coupling Davies bound on finite van Hove windows. For a displayed compactly supported massless Dirac form factor, Araki—Wyss regularity, threshold behaviour and Fermi-golden-rule positivity give a completely bounded Davies approximation uniformly for all times with error of order (O(|lambda|)); the sharper (O(lambda^2)) result is isolated under additional reduced-resonance hypotheses. We construct a background-covariant two-Dirac-field completion using Green operators, Møller maps and relative Cauchy scattering, proving naturality, causal factorization and exact spacelike triviality. A locality obstruction shows why a strictly local multiplier cannot coincide exactly with the solvable rank-one reservoir coupling, while a Feshbach reduction quantifies the correction. Finally, we prove that no fixed faithful vacuum or KMS restriction can exhibit the rank-boundary mechanism, but faithful families with a vanishing spectral floor recover its complete coefficient. The results separate algebra type, target faithfulness, microscopic realizability and regulator uniformity, and provide reproducible numerical audits of the finite-dimensional identities and explicit Dirac form factor.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-05", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0019", "abstract_url": "https://www.ai.vixra.org/abs/2608.0019", "first_submitted_at": "2026-08-05T18:19:22+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-05T18:19:22+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0019-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-05T18:19:22+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0019v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b0370f2ed9e30282f6dcc09f6e4aa32130340c5898f96dca59f84b398eaf34c0", "canonical_bytes": 681842 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:a16642ef-9262-470f-a58f-5fd3413ffcf8", "version_id": "arr:version:c615796b-eda0-4053-a1a1-0564cc133282", "id": "ARR-2026-51CS1EZ4K28W7TB3", "version": "v1", "record_type": "research_paper", "title": "From Dobrushin Comparison to a Quasi-Local C*-State: A Lean-Checked Construction for the Two-Dimensional Ising Model", "abstract": "We present a Lean 4 formalization of a thermodynamic-limit construction for the anisotropic nearest-neighbour Ising model on the two-dimensional integer lattice. A telescoping comparison argument and the classical Dobrushin resolvent produce a volume-uniform expectation bound. Exact restriction and reindexing maps between finite Gibbs measures yield convergence of the complete free-boundary sequence, independence of auxiliary envelopes and cofinal samplings, stability under receding boundary perturbations, and equality of free and periodic limits.Finite-support cylinder presentations are quotiented by equality of their represented functions on the full spin space. The resulting local algebra carries a genuine lattice-translation action, and the limiting functional is positive, normalized, real-linear, and invariant under every integer translation. We equip this algebra with its intrinsic uniform norm, construct its complex star-algebra representation, take the corresponding commutative C*-closure, and extend the limiting functional to a positive complex-linear functional of norm one. We also formalize normalized Gibbs conditional kernels for arbitrary finite conditioning sets and prove positivity, exterior locality, idempotence, and the exact finite-volume Gibbs tower identity.All results remain within the classical anisotropic Dobrushin region. The infinite-volume DLR fixed-point equation for the completed state is not claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-05", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0020", "abstract_url": "https://www.ai.vixra.org/abs/2608.0020", "first_submitted_at": "2026-08-05T18:09:44+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-05T18:09:44+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0020-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-05T18:09:44+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0020v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7faecbb1a2799a00b93da255597030e2561104a98d01abe1c3b455e2661f8993", "canonical_bytes": 377505 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:eeb507b1-b6c7-4996-bc62-a4e7c416be00", "version_id": "arr:version:44c1db02-4eae-4b1c-ba2a-bb5d6b994c97", "id": "ARR-2026-7EPM3V3DP796BBRR", "version": "v1", "record_type": "research_paper", "title": "Exact-Kernel Fourier Families Obstruct Every Penalty Factored Through a Block Map in a Flat Lattice Gauge Form", "abstract": "We study whether a flat lattice-gauge Hodge form supplemented by a penalty depending only on a line-integral block variable can control the full fine one-cochain norm uniformly in the block side. The constant-field sector selects the exponent (d-2)/2 only under exact scale neutrality, but this scaling test does not address the kernel of the block map. We construct transverse, divergence-free, block-periodic Fourier cochains that are annihilated exactly by the block map. Their first-mode Hodge Rayleigh quotient is 4 sin²(pi/L), forcing every admissible full-space Poincaré constant to grow at least quadratically with L. The obstruction applies to every scale-dependent scalar functional factored through the block variable and satisfying only that it vanishes at the coarse zero field; no linearity, continuity, positivity, or growth condition is required. For linear postconditioners, higher Fourier frequencies yield an orthogonal real subspace of dimension 2R and a min—max bound on the 2R-th eigenvalue, establishing a growing low-energy spectral cluster. We also derive an exact repair identity and a necessary witness-channel budget for modified block measurements and additional fine-space terms. The kernel construction, Hodge energy, factorized no-go theorem, repair identity, and necessary repair budget are formalized in Lean 4. The result concerns a finite periodic flat full-domain form and makes no claim about interacting coercivity, gauge quotients, continuum limits, or the Yang—Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-04", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0015", "abstract_url": "https://www.ai.vixra.org/abs/2608.0015", "first_submitted_at": "2026-08-04T19:42:27+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-04T19:42:27+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0015-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-04T19:42:27+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0015v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "48b2b725422263a272d9862621fa723d3d82c9d186dd7151be39c6ff1e3ff2e7", "canonical_bytes": 365036 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6f8e700b-9b84-4f46-879b-065d621ebc12", "version_id": "arr:version:1d851dd3-a508-45f2-9890-89dfa78c346c", "id": "ARR-2026-3FHSR0Q6W49X38F6", "version": "v1", "record_type": "research_paper", "title": "Endpoint Parity Loss in a Bessel Wronskian: an Exact Obstruction to Kernel-and-Anchor Proofs of Global Ratio Monotonicity", "abstract": "For beta > 0 let I_m = I_m(beta) denote the modified Bessel functionof the first kind and define a_m = I_m^2 ((m-1) I_(m-1)^2 + (m+1) I_(m+1)^2), b_m = m I_m^4,with sine series F_A(t) = sum_(m>=1) a_m sin(mt) andF_B(t) = sum_(m>=1) b_m sin(mt). The associated Wronskian is negativeexactly when F_A/F_B is decreasing. We isolate what can and cannot beproved from two natural inputs: the Neumann convolution kernelI_0(2 beta sin(phi/2)) and the small-coupling anchor whose normalizedlimit is 4 sin^3(t).First, the convolution does prove F_B(t) > 0 for 0 < t < pi. Second,the endpoint is governed by two alternating quantities, c_3 and B_pi,through an exact cubic law. We prove B_pi > 0, derive integralrepresentations, and establish that the cancellation lost by replacingthe alternating quantities with positive-term majorants has exponentialrate 8 - 4 sqrt(2). Finally, we prove a smooth one-parameter perturbationtheorem: one may keep F_B and its kernel unchanged, preserve positivityand strict coefficient-ratio ordering, and preserve every jet at beta = 0,while choosing either sign of the endpoint cubic coefficient.Consequently those structural data, even taken together, do not implyglobal Wronskian negativity. This is a no-go theorem for a proofarchitecture, not a counterexample to the original Bessel conjecture.A short high-precision kill-test accompanies the paper; nocomputer-assisted inequality is used in the proofs.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-04", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0016", "abstract_url": "https://www.ai.vixra.org/abs/2608.0016", "first_submitted_at": "2026-08-04T19:14:39+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-04T19:14:39+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0016-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-04T19:14:39+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0016v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c51cd46c1dc577e4d3bb6f2e36df748e715d2e6dc614c7290d8e9837d92986be", "canonical_bytes": 398436 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6bba1d5e-d506-4667-b20d-75ff7733810e", "version_id": "arr:version:69e74c82-501d-4014-ad79-caf93e9ac630", "id": "ARR-2026-3BQ8ENXN868SKV43", "version": "v1", "record_type": "research_paper", "title": "The Row Sums Were the Method, Not the Theorem: a Machine-Checked Chain from a Positive Weight to Exponential Decay of Correlations, and a Misattributed Uniformity Wall", "abstract": "A formal Lean 4 development revisits a two-dimensional spatial transfer kernel whose earlier uniform spectral argument relied on constant row sums. We show that the loss of row-sum constancy obstructs that method, not the conclusion. With no sorry and no project axiom, we prove twelve machine-checked theorems.The chain establishes the sharp field-uniform one-bond influence envelope tanh J; assembles these bounds into a finite-volume Dobrushin matrix; proves a volume-independent resolvent estimate under row-sum bounds alpha < 1 without assuming constant rows; mechanises Dobrushin's comparison inequality with the attained 1/4 covariance constant; constructs Gibbs measures, heat-bath kernels and intrinsic influence matrices from arbitrary strictly positive finite weights; and specialises to anisotropic Ising interactions. For L x T rectangles with free boundary, the condition 2 tanh|beta| + 2 tanh|gamma| <= alpha < 1 yields exponential decay of correlations with beta, gamma, alpha and the prefactor fixed before the volume quantifiers.The transport into the operator formulation is closed: an exact finite band identity relating endpoint covariances to matrix elements; an abstract theorem showing that a common exponential decay rate for band covariances - a hypothesis on finite path measures, carrying no operator, norm or spectrum - implies a uniform positive gap for a family of projected transfer operators; a Perron-boundary tilt identity that preserves the decay rate while absorbing boundary costs into extent-dependent constants; an exact currying identification of the free strip measure with the rectangle Ising measure; and the resulting corollary: inside the window there is one m > 0 bounding the projected transfer operator of the coupled kernel's normalised Perron data by exp(-m) at every extent, with m = -log alpha.Numerical measurements at L <= 12 provide counterevidence to attributing spectral degeneracy solely to nonzero spatial coupling. No infinite-volume state, thermodynamic limit or boundary-condition independence is constructed; the window is sufficient, not sharp. The underlying Dobrushin mathematics is classical; the contribution is a non-vacuous, reproducible mechanisation and composition of the full chain, ending at a volume-uniform operator gap. No consequence for Yang-Mills theory is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-03", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0013", "abstract_url": "https://www.ai.vixra.org/abs/2608.0013", "first_submitted_at": "2026-08-03T20:07:25+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-04T10:13:23+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0013-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-03T20:07:25+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0013v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-04T10:13:23+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0013v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "18a02ac2d5aecc1090396e0eff6ba6207e66a4d10ad501e6f918e44f28f9cc92", "canonical_bytes": 501466 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:c23d9e15-9273-4ef5-8f69-8f60e131388e", "version_id": "arr:version:312aae5b-380c-4ccd-bb0b-df4c76672b74", "id": "ARR-2026-627PF1B4KK9VTRYT", "version": "v1", "record_type": "research_paper", "title": "Fourier Transverse Modes Obstruct Volume-Uniform Critical Coercivity in a Flat Lattice Gauge Block Form", "abstract": "Let a fine periodic lattice have side LN' and let Q_L be the L^{-d}-normalized block average of length-L line integrals. In four dimensions, the rescaling Q_L -> LQ_L repairs the elementary constant-field scaling obstruction to a Poincare estimate. We prove that it cannot yield coercivity on the full one-cochain space with a constant uniform in the block side.For every L >= 2, every fixed N' >= 1, and N_c >= 2, we embed the first within-block Fourier phase zeta_L = exp(2 pi i/L) in a real two-plane of the internal coordinate space and construct a transverse one-cochain A_L. It satisfies Q_L A_L = 0 and div A_L = 0. For every dimension d >= 2,||A_L||^2 = (LN')^d, = (LN')^d lambda_L,where lambda_L = 4 sin^2(pi/L) <= 4 pi^2/L^2.Thus the Rayleigh quotient of K_0 + (s_L Q_L)^*(s_L Q_L) is exactly lambda_L for every scalar rescaling s_L. Every admissible full-space Poincare constant obeys C_P(L) >= 1/lambda_L >= L^2/(4 pi^2), so no constant chosen before L can work. Here \"volume-uniform\" means uniform while the block/fine side L varies at an arbitrary fixed positive coarse side N'; it is not a claim about N' -> infinity at fixed L.The construction, kernel identities, exact Hodge energy, Rayleigh identity, and quantified no-go theorem are formalized in Lean 4. The focused axiom audit reports only propext, Classical.choice, and Quot.sound. The theorem concerns the stated flat full-domain form; it does not contradict gauge-restricted propagator constructions and makes no infinite-volume, continuum, or Yang-Mills mass-gap claim.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0004", "abstract_url": "https://www.ai.vixra.org/abs/2608.0004", "first_submitted_at": "2026-08-02T19:25:02+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T19:25:02+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0004-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T19:25:02+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0004v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b8e655d3f1253d0ea915ba54df00a5c72f4ce5b5d229f74fe82ec152333ea726", "canonical_bytes": 303938 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:bb2ccda3-36fa-4c91-9f18-8c3d59db4b9e", "version_id": "arr:version:a3902a60-4faf-4102-9e02-f695e4c99ecb", "id": "ARR-2026-5V5K6T6DQT9J8SY6", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Haar and Differential Descent at an SU(2) Crossing: A Four-Edge Compensated-Flow Ward Identity", "abstract": "We machine-check the exact measure and differential bridge between thefour-edge SU(2) crossing chart and the two effective group coordinates used bya finite-dimensional Ward identity. The quotientr(a)=(a2 a4^-1,a1 a3^-1) pushes normalized four-fold Haar measure exactly tonormalized two-fold Haar measure. Two gauge-compensated flows on the originalfour edges intertwine with independent right multiplication of the quotientcoordinates, so first and mixed derivatives of the crossing Wilson worddescend without choosing a gauge. The three Pauli directions are verifiedindividually, their mixed generators close into direct and reverseresolutions, and the two-coordinate Ward theorem lifts to a literal four-edgeintegral with coefficients -1/4 and -1/2. This compensated operator is notidentified with the ordinary-edge mixed operator of Driver-Hall-Kemp: thepaper writes both operators and their distinct reverse resolutions and markstheir comparison as open. The Lean producer has 26 public declarations and 16audited theorems. No weak four-face heat-kernel identity, area derivative, orfull Makeenko--Migdal equation is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0005", "abstract_url": "https://www.ai.vixra.org/abs/2608.0005", "first_submitted_at": "2026-08-02T19:16:06+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T19:16:06+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0005-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T19:16:06+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0005v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "2bb66657a544e9af4a30d682dc69f92e18a5d3b1ab8f53c105d0dfde767cc7c1", "canonical_bytes": 413987 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:12d7e30c-6c2c-4412-8d52-a9a6295bdd1f", "version_id": "arr:version:862c484d-62c3-43c4-aeda-0c9d75897dc2", "id": "ARR-2026-0JTZHGRV1C8G98TM", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Extended Gauge Invariance at an SU(2) Crossing: Four-Edge Wilson Holonomy, Haar-Preserving Quotient Coordinates, and Reduction to the Ward Chart", "abstract": "We formalize extended gauge invariance at a simple four-edge SU(2) crossing and connect the geometric edge chart to the two-coordinate chart used by a machine-checked crossing Ward identity. On SU(2)^4 we define the two opposite-edge right actions from the abstract Makeenko--Migdal theorem, prove that they are commuting product-Haar-preserving actions, and show that their common parameter composes to ordinary vertex gauge invariance. The four-edge Wilson word tr2(a3^-1 beta a2 a4^-1 alpha a1) is proved invariant under both half-actions. We construct the explicit quotient r(a)=(a2 a4^-1,a1 a3^-1), a canonical section, and prove existence and uniqueness of the universal factorization for every extended-gauge-invariant complex function. The complete map from the cyclic four-edge chart to physical and gauge coordinates is proved to preserve literal four-fold Haar measure in one public endpoint. Finally, the four-edge Wilson word is identified exactly with the prior two-coordinate crossing word evaluated on r(a). The Lean producer has 56 public declarations in 488 physical lines; all 36 theorems depend only on propext, Classical.choice, and Quot.sound, with no local proof escape. No heat-kernel area derivative or full Makeenko--Migdal equation is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0006", "abstract_url": "https://www.ai.vixra.org/abs/2608.0006", "first_submitted_at": "2026-08-02T16:46:30+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T16:46:30+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0006-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T16:46:30+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0006v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8a9b9356f1cfa3c2d69a9371bb62f01d243e7725d203f2726f31772a8b821d9e", "canonical_bytes": 380462 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6b3d395c-cb21-46bc-a512-d082b39404f5", "version_id": "arr:version:27e9d132-504c-449a-a91b-88d306871522", "id": "ARR-2026-3B7MWNSJS18TYAA4", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Finite-Edge SU(2) Crossing Ward Identity: Pauli Generator Transfer and Single-Trace Closure", "abstract": "We formalize a finite-dimensional crossing Ward identity for fundamental SU(2) Wilson words. On every finite edge space SU(2)^E, two distinct coordinates are inserted into a concrete normalized trace word. Lean proves entrywise that right multiplication by each of three explicit SU(2) curves produces the normalized Pauli generators i sigma_a/2, differentiates the trace word once at each selected coordinate, and identifies the Pauli-summed mixed derivative with the rank-two Fierz contraction. Two applications of Haar integration by parts transfer the corresponding mixed generators from a density to the Wilson word. The resulting integral closes exactly on the direct and reverse single-trace resolutions, with coefficients -1/4 and -1/2 in the chosen normalization. The producer contains 19 public declarations in 487 physical lines; all 13 new theorems depend only on propext, Classical.choice, and Quot.sound, with no local sorry, admit, or axiom. This is not a full Makeenko--Migdal area equation: the remaining physical input is a weak four-face identity against crossing-certified extended-gauge-invariant observables. In the program's heat time, generated by the Pauli Laplacian, its coefficient is kappa = 2.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0007", "abstract_url": "https://www.ai.vixra.org/abs/2608.0007", "first_submitted_at": "2026-08-02T14:02:27+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T14:02:27+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0007-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T14:02:27+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0007v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3a0ac2c21fe44aa524ad26bf29f15ec245d2c74f14108dc29d934d261d30d17d", "canonical_bytes": 421658 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:f90f543b-7dcb-4de8-87dc-152edbb04800", "version_id": "arr:version:ab4edc2b-0c2e-4197-89c2-af0b90c0eb10", "id": "ARR-2026-7S1XA3PZEB9QM8FQ", "version": "v1", "record_type": "research_paper", "title": "Congruence Rigidity and the Fusion Bound: What a Positive Weight Can and Cannot do to the Spectrum of a Transfer Kernel", "abstract": "A positive site weight acts on a transfer kernel by congruence, K -> DKD with Dpositive diagonal, not by similarity. Similarity preserves the entire spectrum;congruence preserves strictly less, and strictly more than nothing. We determineboth halves for the kernel of L decoupled Ising bonds. Rigid half: the sign ofevery quadratic form value survives, so definiteness in either sign is acongruence invariant -- the definite case of Sylvester's law of inertia, in aform a machine can check without diagonalisation. Fragile half: the subdominantratio r (second eigenvalue modulus over the Perron root) does not survive atall, and we locate exactly how far it moves. Restricting the L-site kernel tothe two antipodal configurations leaves one Ising bond of coupling bL, of ratiotanh(bL) for b>0: a weight concentrating there fuses the L sites into a singleeffective site carrying L times the coupling. Since tanh(bL) -> 1, no boundr <= rho < 1 holds simultaneously in L and over the whole positive-diagonalcongruence orbit; the obstruction to volume-uniformity is a property of thecongruence, not of any spectral estimate, so an argument bounding r throughcongruence invariants alone cannot produce an L-uniform bound. For arbitraryweights we prove sup_{D>0} r(DMD) = (1-m)/(1+m), where m is the leastoff-diagonal entry: the least correlated pair determines the supremum. (Weevaluate the supremum; we do not classify its maximisers.) The proof isgeometric rather than spectral -- Hilbert's projective diameter is itself acongruence invariant, and Birkhoff's contraction theorem converts it into thebound -- and uses no definiteness, only positivity of the entries. The lowerbound uses no limiting argument about spectra: a two-supported fluctuationvector gives the estimate at each strictly positive epsilon, so no continuity ofeigenvalues is imported anywhere.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0008", "abstract_url": "https://www.ai.vixra.org/abs/2608.0008", "first_submitted_at": "2026-08-02T11:55:22+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T11:55:22+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0008-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T11:55:22+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0008v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "42d202e0b2998443b8a3d9507afdb86e93094b68b271e70b6ecb0bc39d856aff", "canonical_bytes": 391673 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:4f9da410-79d9-4281-ae3b-a068261c4ce4", "version_id": "arr:version:26e7ca62-d060-437a-b10a-4ffccc52bd2d", "id": "ARR-2026-2FKPJ10YES8A0TWE", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Haar Integration by Parts on Finite SU(2) Edge Spaces: Pauli Flows and Two-Generator Transfer", "abstract": "We formalize the finite-dimensional integration-by-parts mechanism used inlocal proofs of the Makeenko—Migdal equation. For a measure-preserving realflow on a finite measure space, Lean verifies differentiation under theintegral from an explicit locally uniform integrable majorant and proves thatthe integral of the generator vanishes. A bounded dominated product interfacethen yields integration by parts, and two successive applications transfer amixed pair of generators from a density to an observable with positive sign.These results are instantiated on normalized Haar probability measure ofconcrete SU(2) and on every finite product SU(2)^E, for left and rightmultiplication of one selected edge. To fix the representation normalization,we construct three explicit trigonometric curves in SU(2) and prove entrywisethat their tangents at the identity are i sigma_1/2, i sigma_2/2, and isigma_3/2. The producer contains 30 public definitions, structures, andtheorems in 519 physical lines; its audit contains no local sorry, admit, oraxiom, and the headline results depend only on propext, Classical.choice, andQuot.sound. This closes the Haar integration-by-parts layer. It does not claimthe full four-area Makeenko—Migdal identity: the remaining formal inputs arethe heat-density directional identity, extended gauge invariance at acrossing, and their geometric assembly.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0009", "abstract_url": "https://www.ai.vixra.org/abs/2608.0009", "first_submitted_at": "2026-08-02T07:14:51+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T07:14:51+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0009-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T07:14:51+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0009v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "0e54d8958a227518f611c84be7b911c15f744549cd848f26f8999680e97254c7", "canonical_bytes": 537529 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:9144be63-0faa-4f58-ba56-be4bfc1ce3f7", "version_id": "arr:version:be09e317-ffee-49e9-940c-a0e46e531634", "id": "ARR-2026-4H8JZ663XA9XCBMN", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Positive-Area Evolution of the Infinite SU(2) Class Heat Kernel and Migdal Face Amplitudes", "abstract": "We give a kernel-checked positive-area calculus for the concrete SU(2) classheat kernel used in two-dimensional Yang—Mills theory. With irreducible labeln, dimension n+1, and Casimir c_n=n(n+2)/4, Lean verifies at every positivetime and every derivative order that the infinite spectral jet converges anddifferentiates term by term to the next jet. The hierarchy is packaged as aC-infinity map on the positive-time half-line, using explicit uniform summablemajorants on positive-time neighbourhoods. We then differentiate the literalnormalized-Haar two-face Migdal integral, prove that its left and right areaderivatives equal the first spectral jet at the merged area, and showinfinitesimal invariance under (s,t) -> (s+u,t-u). Finally, every normalizedWilson character satisfies its exact Casimir area ODE as an actual Haarintegral against the infinite heat kernel. The artifact contains 25 publicdefinitions and theorems, no local placeholders, and audited dependencies onlyon propext, Classical.choice, and Quot.sound. We do not claim the four-faceMakeenko—Migdal crossing equation; the remaining inputs are local Lie-groupintegration by parts and certified crossing geometry.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0010", "abstract_url": "https://www.ai.vixra.org/abs/2608.0010", "first_submitted_at": "2026-08-02T03:33:12+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-02T03:33:12+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0010-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-02T03:33:12+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0010v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f0add12e208879f02800b44eeae1e50aacd41ec16133c3c8f1dac77e2ab836d7", "canonical_bytes": 522836 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:ec3b8f6c-283e-452a-ae4d-785cfaff8a74", "version_id": "arr:version:4161639c-7ebb-4a3c-bdcb-de7384428c56", "id": "ARR-2026-7C7E7PRA1Y8MNAWK", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Finite-SU(2) Trace-Skein Closure for Makeenko-Migdal Crossing Terms", "abstract": "Finite-rank Makeenko-Migdal equations generate products of Wilson traces at self-intersections. For SU(2), this apparent multitrace obstruction closes exactly on single traces, but the statement is normalization-sensitive: the traceless Lie algebra contributes a finite-rank correction that disappears for U(2) and must not be dropped. We give a Lean 4/Mathlib formalization of the complete group-algebraic closure mechanism on Mathlib's concrete special unitary matrix group. With normalized trace tau(A)=Tr(A)/2 and normalized anti-Hermitian Pauli directions X_j=i sigma_j/2, the kernel checks the Casimir identity, the rank-two Fierz identity, the induced crossing contraction, and the SU(2) trace-skein identity tau(g)tau(h)=(tau(gh)+tau(gh^{-1}))/2. Consequently, the finite-SU(2) crossing term tau(g)tau(h)-tau(gh)/4 equals tau(gh)/4+tau(gh^{-1})/2. We then formalize a universal local interface with four cyclically ordered branch holonomies, an independent orientation on each branch, the two opposite-strand words, and precisely the two direct/reversed reconnections. Its corrected crossing term closes on those reconnections for every branch assignment and orientation choice. A recursive theorem also extends the reduction to products of arbitrarily many fundamental traces. The identities are classical; the contribution is a concrete, kernel-checked normalization bridge from Pauli contraction to the single-trace closure used in finite-rank loop equations. We do not claim a formal derivation of the Yang-Mills area derivative, planar loop geometry, or the full Makeenko-Migdal equation.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-08-01", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2608.0001", "abstract_url": "https://www.ai.vixra.org/abs/2608.0001", "first_submitted_at": "2026-08-01T18:50:53+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-08-01T18:50:53+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2608.0001-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-08-01T18:50:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2608.0001v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a6647d22bfc044acb060d94030e794cf8c2952b2ae373d2063967282da2c3bc8", "canonical_bytes": 508873 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:421f57cb-a2d7-47c5-86e4-eccbcb7171b2", "version_id": "arr:version:32701382-7b4f-4f7c-b201-123fd3442ffd", "id": "ARR-2026-223XBWQ8PQ8Z2RDS", "version": "v1", "record_type": "research_paper", "title": "The Collapse: Machine-Checked Bond Reflection Positivity and a Site Reflection Form for the Coupled Z_2 Slice", "abstract": "BOND REFLECTION, AND THIS ONE IS ABOUT THE MEASURE. A whole path X of 2m+2slices has a past half past(X) and a future half; write rev(X) for the futurehalf READ BACKWARDS FROM THE FAR END, which is the reflected copy. Let F be acomplex observable of an entire half. Then for every L, every m, everystrictly positive source weight w and every beta >= 0, sum over whole paths X of conj(F(past X)) * F(rev X) * W(X) >= 0the sum running over all whole paths and W being the ordinary Gibbs weight.This is the finite-volume Osterwalder-Schrader reflection-positivityinequality for this model at odd separation. The sum is UNNORMALISED, which isthe form the axiom is about; dividing by the partition function is division bya positive number and preserves the sign. The Gram matrix of a finite familyof such observables, with complex coefficients, satisfies it as well. It isobtained by proving that assembling a past half, a crossing bond and areversed future half is a BIJECTION onto paths, and that the weights multiplywith exactly one crossing factor.SITE REFLECTION, AND THIS ONE IS NOT, YET. Through a site the two halves SHAREthe middle slice, so the assembly is not a product of two independent halvesand its bijection is a different statement. What is proved there is thehalf-chain form, its collapse identity and its Gram positivity -- at EVERYbeta, negative coupling included -- but NOT its identification with the pathmeasure. For that geometry the object remains a candidate, and the statustable says so row by row.ON THE BETA HYPOTHESIS. beta >= 0 is proved SUFFICIENT and is not provednecessary here; at L = 0 it could not be, since the bare kernel is then thescalar 1. The witness that would make the boundary exact from one site upwardsis authorised by a gate and is not written.THE MECHANISM, IN ONE SENTENCE. Summing out the interior of a half sends F toa vector indexed by its boundary slice alone, after which the bond casereduces to positive semidefiniteness of the kernel -- machine-checked in thecompanion paper -- and the site case to a weighted squared norm, which uses noproperty of the kernel at all.WHERE THE TWO REFLECTIONS DIFFER, AND IT IS NOT COSMETIC. Through a bond thetwo halves are disjoint and meet through one kernel factor, so positivityneeds the kernel itself positive semidefinite -- which, for L >= 1, holdsexactly when beta >= 0. Through a site the halves SHARE the middle slice; theform is then a sum of squared moduli divided by the weight of that slice, soit is non-negative for EVERY beta, negative coupling included, and no propertyof the kernel is used at all.WHAT THE SOURCE WEIGHT DOES. In the companion paper the weight was handled bycongruence: conjugation by sqrt(w) cannot change the sign of a quadratic form.Here it is not conjugated away, it is SUMMED away -- and what is left overdiffers between the two geometries. In the bond case every source weight isabsorbed into the collapse and the bare kernel remains; in the site case theshared boundary slice survives as a factor 1/w(sigma), because each halfcarries that slice's weight and the product would count it twice. Differentreasons, same conclusion: nothing in the hypotheses depends on w beyondpositivity.WHAT THIS IS NOT. No reconstruction: the physical Hilbert space as thequotient of the past algebra by the null space of this form is not built.Nothing here concerns uniformity in the extent, SU(N), the continuum limit, orthe Yang-Mills mass gap.ON THE PRE-REGISTRATION. Four gates were committed before a line of the modulewas written; the status table reports what happened to each. Two of them reada minimum eigenvalue rather than sampling observables, which is the instrumentthe previous campaign's autopsy said was needed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-31", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0094", "abstract_url": "https://www.ai.vixra.org/abs/2607.0094", "first_submitted_at": "2026-07-31T16:03:53+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-31T16:03:53+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0094-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-31T16:03:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0094v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d50bf2479828bf5abb2570f38680df1d8e13f984a5a11f47ff952940e4a389c7", "canonical_bytes": 307752 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:02f639d2-8db0-4d07-8060-e69764e41416", "version_id": "arr:version:c4a0c5c6-96a8-4c6b-88d8-dcf8cfe8b814", "id": "ARR-2026-02YRWX53DG9M3R0R", "version": "v1", "record_type": "research_paper", "title": "The Weight That Could Not Break It: Machine-Checked Endpoint Reflection Positivity for the Coupled Z_2 Slice", "abstract": "WHAT IS PROVED, STATED BEFORE ANYTHING ELSE. The reflected two-point form ofthe Gibbs measure, at the two ENDS of a path, for REAL observables of a SINGLEslice, is non-negative under the parity and coupling hypotheses stated below-- at even separation for every beta, and at every separation exactly for beta>= 0 -- and the Gram matrix of a finite family of such observables is positivesemidefinite under the same hypotheses. THIS IS NOT YET THEOSTERWALDER-SCHRADER AXIOM, which quantifies over observables of the wholepast half-chain and over complex ones. The half-chain algebra, the reflectionmap and the sesquilinear form are not built here; the scope section says whatis missing and why it is a construction rather than a further inequality.Eleven papers in this lane end with REFLECTION POSITIVITY IS UNTOUCHED. Thistouches the endpoint form of it, and the interesting part is what the spatialsource weight does -- namely nothing. Earlier papers do prove statements aboutthe coupled kernel; specGap < lambda holds there too. What is new is that thisresult is UNCHANGED by the weight: same hypothesis, same conclusion, and noconstant that depends on w. Every earlier coupled-kernel statement contains anumber that moves when w does. Positivity is the SIGN of a quadratic form, andconjugation by sqrt(w) is a congruence, so there is nothing for the weight tomove.TWO REFLECTIONS, TWO HYPOTHESES. The reflected two-point sum is with v the dressed observable, and the two cases have genuinely differentcontent. Through a SITE (N even) the sum is a square, hence non-negative forEVERY beta -- negative coupling included -- with nothing used but symmetry ofthe kernel. Through a BOND (N odd) it is , which needs Kitself positive semidefinite; that holds exactly for beta >= 0, by aninduction on the extent.AND THE SECOND HYPOTHESIS IS ACTIVE. At beta < 0 and odd separation thesingle-site sign observable gives the reflected sum in closed form, 2(e^beta -e^-beta)^N, which is negative. Congruence is invertible, so the same witnessdivided by sqrt(w) shows the COUPLED kernel is indefinite below zero for EVERYstrictly positive weight, at every extent with at least one site. At L = 0there is nothing to witness -- one configuration, and there the decoupledkernel is 1 while the coupled one is the positive scalar w(empty) -- and thatexception is recorded rather than left to be found. The boundary beta = 0 issharp and exhibited, not inferred.WHAT THIS IS NOT. Neither the full axiom (above) nor any reconstruction: thephysical Hilbert space as the quotient of the past algebra by the null spaceof this form is not built. And the degeneration of specRatio(L) under a ringweight is MEASURED, not proved; no theorem here or elsewhere in the lane saysthe weight destroys uniformity, only that no uniform bound is proved for it.Nothing here concerns uniformity in the extent, SU(N), the continuum limit, orthe Yang-Mills mass gap.ON THE PRE-REGISTRATION. Three ACTIVE gates were committed before any Lean waswritten, and the gates section reports what happened to each. A fourth ispreserved there and not counted: the original Gate B, which failed because ofa design error of ours, and which two of the three active gates replaced.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-30", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0090", "abstract_url": "https://www.ai.vixra.org/abs/2607.0090", "first_submitted_at": "2026-07-30T20:31:57+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-30T20:31:57+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0090-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-30T20:31:57+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0090v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "2cf776265eafc5f35eeb234a4d671d574bd889bbccc44995ff5468407a2a6c1a", "canonical_bytes": 299014 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:b9857cd5-670b-4ed3-b7a7-97b174ebe28f", "version_id": "arr:version:adf5c25b-193f-4b5a-b502-c3a9f0f40e82", "id": "ARR-2026-5SGNYDASRB9V9VF9", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Thermodynamic Limit for Local Lattice Gauge Gibbs States", "abstract": "We formalize in Lean 4 the thermodynamic limit of bounded local Gibbs expectations for a periodic lattice gauge model in a uniform Kotecky-Preiss regime. The proof treats the complete finite-volume sequence: an exact one-volume marked expansion cancels the extensive far gas algebraically, common-window terms are transported exactly, and the remaining boundary contribution is bounded by an existing volume-uniform pinned cluster tail. The resulting explicit Cauchy modulus tends to zero, so completeness constructs an infinite-volume positive normalized real local state. On the intrinsic integer-coordinate local-observable algebra, the state carries a genuine additive action of Z^d and is invariant under every integer translation, including inverses. For SU(2), Haar probability measure, and the physical Wilson plaquette energy Re tr(U), the hypotheses are discharged throughout the explicit punctured intervals 0 < |beta| <= 10^-5 in d=2 and 0 < |beta| <= 10^-6 in d=4. We construct a genuine centered free-boundary exhaustion and prove that its complete cofinal sequence converges to the same state as periodic boundary conditions. The normalized finite-volume two-plaquette truncated-correlation bound also passes to the state under explicit eventual realization and separation hypotheses. We do not claim arbitrary boundary conditions, a C*-algebraic state, a continuum limit, Osterwalder-Schrader reconstruction, or progress on the continuum Yang-Mills mass-gap problem.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-30", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0091", "abstract_url": "https://www.ai.vixra.org/abs/2607.0091", "first_submitted_at": "2026-07-30T18:51:18+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-30T18:51:18+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0091-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-30T18:51:18+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0091v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "0a494cd745da4760428ad4e915075469c95eab7e638856b5e49925ec662a0919", "canonical_bytes": 104063 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6eef69d9-3421-4c83-8363-80e3bbaf73ef", "version_id": "arr:version:b2a8d268-57a6-4553-b1f9-c1d006c84dd3", "id": "ARR-2026-3EXXMXJD119J1R6R", "version": "v1", "record_type": "research_paper", "title": "The Rate Without the Extent: a Machine-Checked Uniform Spectral Modulus for the Decoupled Z_2 Slice", "abstract": "Every rate in this lane so far has been a fixed-extent rate. The gap paper provedstrict spectral separation at each extent and said plainly that it was notuniform; the modulus paper gave that separation a number, specRatio(L), andreported measurements saying the number tends to 1 outside the disordered region.A geometric bound whose rate tends to 1 is empty in the volume limit, so nothingin the lane survived L -> infinity, and the word CLUSTERING was never used.PROVED. For the DECOUPLED kernel - the transfer kernel at constant source weight- the modulus is specRatio = tanh(beta) at EVERY extent, with L nowhere in it.Both directions: an operator bound by induction on the extent, and attainment bythe single-site observable the extent paper already built. Composing with themodulus paper's endpoint, the normalised Gibbs two-point function obeys|E[A(X_0)A(X_N)]| <= C_A tanh(beta)^N past one threshold serving everyobservable - a bound whose RATE contains no L, and therefore the first statementin this lane that survives the volume limit.WHY THE PROOF IS NOT THE SPECTRAL DECOMPOSITION. The decoupled kernel is aproduct over sites, so its spectrum is a product; that route needs the spectrumof a Kronecker power, which the library does not carry. It is not needed. Themodulus paper proved that specGap is the GREATEST norm ratio on the fluctuationsector, so bounding it above is an operator inequality and nothing else, and thatfalls to induction: the even part of an observable keeps its mean zero andinherits the rate, the odd part keeps nothing and gets only Schur's test, and thetwo recombine EXACTLY, because tanh(beta) Z = D with Z the row sum and D the oddeigenvalue of a single bond.NOT PROVED, AND A JUDGE THAT FAILED. The COUPLED kernel is untouched. Before anyof this was written we pre-registered two falsifiable predictions. The first -that the decoupled rate is exactly tanh(beta) at every extent - passed to 1e-16,and authorised the work above. The second - that the coupled uniformity boundaryis the Onsager curve - failed on one of eight pre-registered cells, and it staysfailed: that claim is reported as NOT ESTABLISHED, not softened. At constantsource weight the spatial slices are independent, so what is proved here is astatement about a product measure; that is exactly why it is reachable, and it issaid in the paper rather than left to be noticed. Reflection positivity isuntouched, and nothing in this paper is a claim about SU(N), the continuum limit,or the Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-30", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0092", "abstract_url": "https://www.ai.vixra.org/abs/2607.0092", "first_submitted_at": "2026-07-30T14:48:32+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-30T14:48:32+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0092-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-30T14:48:32+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0092v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8c87e83ee84f11aa4688fa6c17c3a6bb02f916968ef7265f02a46f6ef8bfd593", "canonical_bytes": 96375 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2a3f324c-b5e0-4248-bb64-095fbbfbf103", "version_id": "arr:version:4a762b74-ff12-49d7-bd44-67f38c259be3", "id": "ARR-2026-1A7WS4SDF0894BPS", "version": "v1", "record_type": "research_paper", "title": "The Modulus: a Machine-Checked Operator Bound on the Fluctuation Sector of the Coupled Z_2 Slice", "abstract": "Two companion papers were left carrying the same debt from opposite sides. Thegap paper proved that every eigenvalue of the coupled slice other than thePerron eigenvalue is STRICTLY smaller in modulus, and said plainly that thisprovides NO MODULUS of separation. The bridge paper proved that the Gibbscorrelations of the spatial system are matrix elements of a self-adjointtransfer operator, and obtained geometric decay only UNDER A CONTRACTIONHYPOTHESIS IT DID NOT DISCHARGE. The missing step is identical in both: finitelymany strict inequalities are not an operator-norm bound.PROVED. We construct specGap, the largest |mu| over the eigenvalues differentfrom the Perron eigenvalue lambda, and prove specGap < lambda. We then prove theoperator bound: for every observable u orthogonal to the Perron vector,||Ku|| <= specGap*||u||. That is exactly the hypothesis the bridge papercarried, so its bound becomes unconditional. The bound is SHARP: whenever thestate space has at least two points, some nonzero fluctuation observable attainsit. The argument splits at specGap = 0, where the maximising index need notsupply a NON-PERRON eigenvector (it does supply the Perron one), hence none inthe fluctuation sector. Stated about an object too: the set of Rayleighnorm ratios on the fluctuation sector has a greatest element, equal to specGap(same two-point hypothesis: with fewer, that set is empty).A WARNING WE STATE BEFORE ANYONE ELSE HAS TO. specGap < lambda is NOTspecGap < 1: the kernel is unnormalised, so both are typically far above one andspecGap^N GROWS. On its own the unnormalised bound controls growth, it does notexhibit decay. The rate that is below one is the RELATIVE one,specRatio = specGap/lambda < 1, and the decay statement is that the fluctuationcontribution is suppressed by specRatio^N RELATIVE to the Perron scalelambda^N. Both forms are proved; only the second is called decay.The step that does not follow from the inequalities is the one abouteigenvectors AT lambda: geometric simplicity, proved in the Perron paper for anarbitrary eigenvector rather than a positive one, makes them INVISIBLE to afluctuation observable, so the top term of the spectral sum vanishes instead ofmerely being bounded.NOT PROVED. specGap DEPENDS ON THE EXTENT, and nothing here bounds it away fromlambda uniformly. Direct diagonalisation gives specGap/lambda = 0.9205, 0.9829,0.9964, 0.9992 at L = 2,3,4,5 for one parameter pair: a geometric bound whoserate tends to 1 is empty in the limit, and that is reported, not hidden. Thenormalised Gibbs EXPECTATION is now bounded too: splitting the dressed constantobservable along the Perron direction bounds the partition function below withno eigenbasis index identified, so at a fixed extent the two-point function isbounded by C*specRatio^N past an explicit threshold. That rate depends on theextent, so this is not clustering. The bound and its attainmentare both proved, which is what it means for specGap to be the operator norm onthe fluctuation sector; what is NOT done is introducing that norm as a definedobject and proving an equation about it. And the threshold N_0 does not dependon the observable: it is built from the dressed CONSTANT observable, so ONE N_0serves every fluctuation observable at once and only C sees A. Reflectionpositivity is untouched, and nothing in this paper is a claim about SU(N), thecontinuum limit, or the Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-30", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0093", "abstract_url": "https://www.ai.vixra.org/abs/2607.0093", "first_submitted_at": "2026-07-30T06:19:09+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-30T06:19:09+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0093-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-30T06:19:09+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0093v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "200cfe770180f86aa725683d20424772e009ccc980c991faa7f03f99b42287b8", "canonical_bytes": 106838 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5ad281cc-dd7a-427a-9311-5905be9f2a72", "version_id": "arr:version:2a65def0-5480-49c4-a86f-226c90fd1c64", "id": "ARR-2026-2TTA0WSQBT89X964", "version": "v1", "record_type": "research_paper", "title": "The Measure the Spectral Results Were About: a Machine-Checked Transfer Bridge for the Spatial Z_2 Slice", "abstract": "Four companion papers studied an OPERATOR: a strictly positive kernel on thespatial configuration space of a Z_2 slice, its Perron vacuum, and the strictseparation of its spectrum. None of them exhibited a MEASURE. That omission isthe kind this programme is built to notice: a transfer operator is a matrixuntil something says which Boltzmann weights it transfers, and until then avacuum is an eigenvector and a gap is a statement about eigenvalues. Neither isyet a statement about a statistical-mechanical system.PROVED. We define the two-dimensional Gibbs weight of the spatial system fromBoltzmann factors alone - a spatial factor at every time slice, a time-bondfactor between consecutive slices - and prove the DRESSING IDENTITY: that weightequals the path weight of the SYMMETRISED kernel multiplied by a factorsupported entirely on the two boundary slices. Hence every UNNORMALISED Gibbstwo-point sum of the spatial system is a matrix element of an iteratedSELF-ADJOINT transfer operator between boundary-dressed observables, and theNORMALISED expectation is the RATIO of two such matrix elements - the numeratoralone is not the correlation. The generic half holds for an arbitrary symmetrickernel on an arbitrary finite type; no positivity and no structure of theconfiguration space enter it. We further show that the operator the bridge landson is the one the companion papers analysed, that the fluctuation sector isinvariant, and that under an explicit contraction hypothesis the connectedtwo-point function decays geometrically in the time separation.NOT PROVED, AND THIS IS THE POINT OF THE LAST SECTION. The contractionhypothesis is carried as a theorem hypothesis and is NOT discharged. Thecompanion papers prove a STRICT gap with no modulus, and a strict inequalityamong finitely many eigenvalues does not by itself produce the operator-normbound a decay rate requires. Converting one into the other needs the spectralmaximum over the fluctuation sector, which is not constructed here. Inparticular NOTHING UNIFORM IN THE SPATIAL EXTENT is obtained, and none issuggested: with r = r(L) approaching 1, the bound is empty in the limit.Reflection positivity is not addressed. Nothing in this paper is a claim aboutSU(N), the continuum limit, or the Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-29", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0083", "abstract_url": "https://www.ai.vixra.org/abs/2607.0083", "first_submitted_at": "2026-07-29T14:35:16+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-29T14:35:16+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0083-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-29T14:35:16+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0083v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "0a0acc85773ff6557ca65b5a49027c29aeee99cd45e7861c474bd0bbe876ca18", "canonical_bytes": 86757 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2a30116d-434c-4f7a-997c-48ad16211b9d", "version_id": "arr:version:b818e296-b5ce-49d4-9d9b-a11b873bab4f", "id": "ARR-2026-1A608PTGTC9XX9JZ", "version": "v1", "record_type": "research_paper", "title": "Strict but Not Uniform: a Machine-Checked Spectral Gap at Every Finite Extent of the Coupled Slice", "abstract": "A companion paper supplied the vacuum of the coupled Z_2 slice at every spatialextent: a strictly positive eigenvector, unique up to scale, carrying thespectral radius. It listed PERIPHERAL SEPARATION as out of scope, and thatomission is not cosmetic - without it |mu| <= lambda leaves mu = -lambda open,and no gap follows at all.This paper closes it, and then draws the consequence that matters, which isnegative.PROVED. For a strictly positive kernel on a finite nonempty type, -lambda is notan eigenvalue, hence every real eigenvalue other than the Perron eigenvalue isSTRICTLY smaller in absolute value. Specialised to the coupled slice: at everyextent L, every beta, and every strictly positive source weight, the transferoperator has a strict spectral gap. The proof of peripheral separation avoidsthe equality case of the triangle inequality, which is where the classicalargument spends its effort: writing u = |w|, p = u - w and q = u + w, one getsA p = lambda q and A q = lambda p, so a nonzero p would make A p strictlypositive, hence q strictly positive, hence w nonnegative, hence p = 0.The separation is then extended from the real eigenvalues to ALL of them. Thecoupled kernel is conjugate by a positive diagonal to its symmetrised form,which is symmetric; and a real symmetric kernel has real eigenvalues, by acomputation that pairs the eigenvector against its image twice and is tworearrangements of a double sum. So there are no complex peripheral eigenvaluesleft to exclude, and the strict gap is a statement about the whole spectrum.That composition is itself a single machine-checked theorem(coupled_gap_all_eigenvalues), not a step left to the reader. We also deliverthe vacuum in Euclidean normalisation, norm(Omega) = 1 with T Omega = Omega.NOT PROVED, AND THIS IS THE TITLE. The gap is STRICT, not QUANTITATIVE: thetheorem provides no modulus of separation, and in particular nothing uniform inL. Direct numerical diagonalisation shows the subdominant ratio running0.9205, 0.9829, 0.9964, 0.9992 at L = 2,3,4,5 for beta = 0.8, gamma = 1.2 -collapsing towards 1. That computation is reported as measured and unproved, andno theorem here depends on it; its role is to say that a paper reporting onlythe positive half would be reporting the half that does not matter.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-29", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0084", "abstract_url": "https://www.ai.vixra.org/abs/2607.0084", "first_submitted_at": "2026-07-29T10:08:56+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-29T10:08:56+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0084-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-29T10:08:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0084v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e8063013965ea1699718d08f2bce1646e73f0dd2b970a518bb9e6339c68d78a0", "canonical_bytes": 83708 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5e6b8829-bdbe-4786-a500-bf0e3c82ccf9", "version_id": "arr:version:fed2d79c-93bc-44a4-845f-3f143ef6fc49", "id": "ARR-2026-2YDE42KFDY8Y3AA0", "version": "v1", "record_type": "research_paper", "title": "The Vacuum Was Never Absent: A Machine-Checked Perron Theorem for Strictly Positive Kernels, and the Coupled-Slice Vacuum at Every Spatial Extent", "abstract": "Two companion papers established, for a Z_2 lattice gauge slice with a spatialcoupling, that the elementary route to the vacuum stops, and that the naturalreplacement - the Hilbert projective metric - is blind to the coupling anddegenerates in the volume. Both had to work around the same absence: the pinnedmathlib carries no Perron-Frobenius theorem. The first paper could therefore onlysay the vacuum had become unavailable; the second had to build its dominationbound from scratch, and could exhibit the vacuum in closed form only at two sites.This paper discharges that dependency. For a strictly positive kernel on a finitenonempty type we prove, in Lean 4 with mathlib: a strictly positive eigenvectorEXISTS; its eigenvalue is strictly positive; any two strictly positiveeigenvectors are proportional and share their eigenvalue; and every realeigenvector for that eigenvalue is a scalar multiple of it. Together with thedomination theorem of the companion paper this gives the Perron statement thelane needs: the eigenvalue is the spectral radius.The existence proof does not use a fixed-point theorem, because the pinnedmathlib revision contains none. It maximises r over the compact set of pairs(r,x) with x in the simplex and r x <= A x; maximality forces equality, since astrict inequality anywhere would let one further application of A produce anadmissible pair with a larger r. The bound that keeps the set compact is obtainedby summing the constraint: r = r * sum x <= sum (A x).The application is the point. At EVERY spatial extent, and for EVERY strictlypositive weight on the source configuration - the class that contains the coupledkernel of the first paper - the vacuum exists, is unique up to scale, and carriesthe spectral radius. The obstruction of that paper was never an absence; it wasan unavailability, and it was an unavailability of one route rather than of theobject.NO SPECTRAL GAP IS PROVED HERE, uniform in the volume or otherwise, and none isclaimed. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-29", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0085", "abstract_url": "https://www.ai.vixra.org/abs/2607.0085", "first_submitted_at": "2026-07-29T06:36:35+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-29T06:36:35+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0085-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-29T06:36:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0085v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "6349c8e555f10fde30e0457f54c841da9d05e252cf34e65f6a8064d463318e74", "canonical_bytes": 88762 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:d445a9b8-ea91-47be-9ab7-eee4e87befae", "version_id": "arr:version:c5dacf30-0cc3-4432-86aa-98de5b5813d6", "id": "ARR-2026-6M8PMVHTMH8YZ9ND", "version": "v1", "record_type": "research_paper", "title": "Blind to the Coupling: a Second Machine-Checked Obstruction at Spatial Extent", "abstract": "A companion paper proved that when a spatial coupling is switched on in a Z_2lattice gauge slice, the transfer kernel loses constant row sums, so the uniformvector is no longer fixed and the elementary route to the vacuum stops. Thestandard replacement, when row sums fail, is the Hilbert projective metric: astrictly positive kernel contracts it, and the contraction factor bounds thesubdominant spectral ratio. This paper asks what that replacement gives here, andanswers in Lean 4 with mathlib.It gives no coupling-sensitive and no volume-uniform information, for twoindependent reasons, and both are proved. First, BLINDNESS: the projectivecross-ratio is invariant under multiplication by any nowhere-zero function of thesource configuration alone. The coupled kernel is exactly such a product, so themetric assigns the interacting and the non-interacting kernels the same diameterat every spatial extent - the route cannot see the coupling at all. Second,VOLUME DEGENERATION: two constant configurations realise the cross-ratioe^(4 beta L), so every admissible projective diameter is at least 4 beta L andevery contraction factor obtainable this way is at least tanh(beta L), which lieswithin 2 e^(-2 beta L) of the trivial bound 1. At the one place where the truthis known - the decoupled kernel, whose subdominant ratio the companion papercomputes to be exactly tanh beta at every L - this route already returnstanh(beta L) instead. The degeneration is the method's, not the model's.We then hand over the object the elementary route stopped producing, at thesmallest interacting size. In the character basis the coupled two-site kernelsplits into two 2x2 blocks, and we exhibit a strictly positive eigenvector inclosed form, together with a second exact eigenpair. The identity A - B = 4between the two decoupled even-sector eigenvalues drives every estimate. Theblindness is proved two-sided, so it covers the symmetrised conventionw^(1/2) K w^(1/2) as well, and the positive eigenvector is proved to dominateevery eigenvalue, real or complex - so its eigenvalue is the spectral radius,which is the Perron statement this development needs and proves without aPerron-Frobenius theorem in the library.NO VOLUME-UNIFORM STATEMENT ABOUT AN INTERACTING SYSTEM IS PROVED HERE, AND NONEIS CLAIMED; the general-L behaviour is recorded separately as measured andunproved. Nothing in this paper is a claim about SU(N), the continuum limit, orthe Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0088", "abstract_url": "https://www.ai.vixra.org/abs/2607.0088", "first_submitted_at": "2026-07-28T23:30:40+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-28T23:30:40+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0088-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-28T23:30:40+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0088v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "42617528c0df0ad3e813ee77c11722c53e5ea1b4b97dc93f22d9ece45d29e4cb", "canonical_bytes": 118268 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6c772273-0e70-4116-8d52-3e12f5843c8d", "version_id": "arr:version:2b5fae60-df49-4f05-9dcf-533b299dd72b", "id": "ARR-2026-3CEWH763KG84B8TM", "version": "v1", "record_type": "research_paper", "title": "Global Ratio Monotonicity for a Killed von Mises Bridge", "abstract": "For beta > 0 let I_m = I_m(beta) denote modified Bessel functions ofthe first kind, and set a_m = I_m^2 [(m-1) I_(m-1)^2 + (m+1) I_(m+1)^2], b_m = m I_m^4, F_A(t) = sum_(m>=1) a_m sin(mt), F_B(t) = sum_(m>=1) b_m sin(mt), E(t) = F_A(t)/(2 F_B(t)).The global ratio-monotonicity problem for the surface expansion of atwo-dimensional SU(2) lattice gauge observable is: (i) F_B > 0 on(0,pi), and (ii) E' < 0 on (0,pi), for every beta > 0. Bothstatements are proved. Positivity of F_B has two exact proofs. Ratiomonotonicity is reduced to exact algebraic identities andoutward-rounded interval certificates: small and compact beta arehandled by pair identities and interval Taylor models;20 <= beta <= 1000/9 by a direct Wronskian cover; andbeta >= 1000/9 has three certified moving-edge lambda lanes. Theremaining lambda >= 3 lane is closed by the exact identityE'/(-sin(t/2)/2) = Q + X_full, where Q > 19/20, an exactmain--mirror--rest decomposition, and a division-free covariancecertificate proving X_main > -1/20 on two adjacent rectangles thatcover the full angular interval. The exact near and far relay marginsare positive. All load-bearing production and independent replaytranscripts are checked for exact rational coverage, dependencyhashes, strict outward-rounded decision endpoints, and byte equality.The structural core is exact: E is, as an algebraic identity, the meanof cos(psi) under the midpoint law of a four-step killed von Misesbridge; the generating kernels reduce, via the Neumann additiontheorem, to two-dimensional integrals of a single Bessel functionwhose saddle deficit is an exact sum of two squares; and exact saddlecancellations yield the coefficients of the verified closedsecond-order law E = cos(t/2)(1 - c(t)/beta) + O(beta^-2), c(t) = (4 cos^2(t/4) - 1)/(2 cos(t/4) cos(t/2)).Three certified negative results (interval arithmetic, twoimplementations, nested enclosures) kill every monotone full-pathcoupling, with an exact mechanism at threshold beta |cos t| = 3/2. Atthe pi endpoint we also give exact identities for the cubiccoefficient c_3 (telescoped alternating form, integral form, parity)together with its verified prefactor law. Every claim is labelledexact / certified / verified; the machine-checked lemmas are Lean4/Mathlib, machine-checked modulo classical Bessel inputs carried asnamed hypotheses.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0089", "abstract_url": "https://www.ai.vixra.org/abs/2607.0089", "first_submitted_at": "2026-07-28T22:32:03+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-28T22:32:03+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0089-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-28T22:32:03+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0089v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e8cc61a1c370d941baff0ae9019dde4c0d528dbeb42f7c81b221667c1e67333e", "canonical_bytes": 668250 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:9d02090d-abcf-41ec-b1bd-695d50fc994f", "version_id": "arr:version:37e86e12-47c7-43f7-a023-73f008fcaeca", "id": "ARR-2026-4X084GVAYF87PB3F", "version": "v1", "record_type": "research_paper", "title": "Where the Elementary Reconstruction Stops: Spatial Coupling Breaks the Uniform Vacuum, Machine-Checked", "abstract": "Two companion developments verified an Osterwalder-Seiler reconstruction end toend for a lattice gauge chain whose spatial slice is a single point. Every stepof that chain begins by knowing the vacuum, and in the one-dimensional case thevacuum is free: the normalised transfer kernel has constant row sums, so theuniform vector is fixed, and T*Omega = Omega follows from normalisation alone.This paper asks what survives when the slice acquires spatial extent, andanswers in Lean 4 with mathlib.The algebraic half survives untouched. With time bonds only, the row sums of thetransfer kernel are constant for every spatial extent L, so the uniform vacuumpersists on a space of dimension 2^L; and the single-site sign observable is aneigenvector whose normalised eigenvalue is exactly tanh beta, with L free in thestatement.The uniform vacuum does not survive. Switching on a coupling between sites inside aslice makes the spatial weight depend only on the source configuration, so itfactors out of the sum over the target and the row sums becomeconfiguration-dependent. We exhibit two explicit configurations of a two-siteslice with different row sums, and conclude that no constant row sum exists: theuniform vector is not fixed, so T*Omega = Omega is FALSE for it. The vacuumbecomes a Perron vector that row-sum normalisation no longer supplies in closedform, and every later step of the reconstruction loses its starting point.We state plainly what the positive half is and is not. The decoupled system is Lnon-interacting copies of a two-state system, and the rate it yields - theeigenvalue tanh beta of the single-site sign mode - is independent of L fortrivial reasons, so it is physically empty and is recorded only because itisolates which half of the construction survives. NO GAP FOR THE COUPLED SYSTEM IS PROVED HERE, AND NONE IS CLAIMED.Nothing in this paper is a claim about SU(N), the continuum limit, or theYang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0075", "abstract_url": "https://www.ai.vixra.org/abs/2607.0075", "first_submitted_at": "2026-07-28T19:17:42+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-28T19:17:42+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0075-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-28T19:17:42+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0075v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c519a6a1592ee25b36df6e1710c7d629d2305ee3885f0c7993b60a2b6639bef4", "canonical_bytes": 86493 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5a5e1b51-35c5-4a27-9eb4-9f660a89dfbd", "version_id": "arr:version:10ee9dc2-8abd-4b8b-8afe-d4257394b81a", "id": "ARR-2026-2TBRDN2DE598KSXD", "version": "v1", "record_type": "research_paper", "title": "The Quotient That Is Not the Identity: A Machine-Checked Degenerate Reflection Pairing and Its Gelfand-Naimark-Segal Quotient", "abstract": "The Osterwalder-Seiler reconstruction passes from a reflection-positive measureto a Hilbert space by quotienting out the null space of the reflected pairing.In a companion development that step was present but did nothing: the pairingthere was definite, so the quotient was the identity, and that paper says so inits own abstract. This paper supplies the missing case, in Lean 4 with mathlib.For the Z_2 lattice gauge chain we take half-space observables of two timeslices - a four-dimensional space - and form the reflected pairing directly fromthe Boltzmann weights. For beta > 0 the reconstructed physical space istwo-dimensional. Integrating out the future collapses four observables onto twostates, and that collapse is the null space. We prove: the pairing factors through anindependently defined reconstruction map Phi; its self-pairing rearranges into amanifest sum of two non-negative terms, from which positivity and the null spacefollow together; the null space is EXACTLY ker Phi, not merely non-empty; anexplicit non-zero observable lies in it; and the quotient is isomorphic to thephysical space BY THE MAP Phi ITSELF, not by a dimension count.The degeneracy is the mechanism the reconstruction exists to handle, and the oneexpected to reappear in systems with larger half-space algebras. What is notclaimed: this is twotime slices and not m; still Z_2, one variable per slice, fixed finite size, andnot volume-uniform; Z_N for N > 2 is untouched; and the completion step of thereconstruction is trivial here because every space in sight isfinite-dimensional, which we state rather than present as work done. Nothing inthis paper is a claim about SU(N), the continuum limit, or the Yang-Mills massgap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0076", "abstract_url": "https://www.ai.vixra.org/abs/2607.0076", "first_submitted_at": "2026-07-28T17:10:48+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-28T17:10:48+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0076-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-28T17:10:48+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0076v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "ee99c158af94fced1eecfc0aa0a26121aadea576e7dd0ba33d7e2538c309dd1f", "canonical_bytes": 92307 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:75723207-9c00-426c-8b3e-ae21a5b75b40", "version_id": "arr:version:1e12d166-bd59-4477-b34f-f1dede2f42d5", "id": "ARR-2026-3NE8S0F70089P8PF", "version": "v1", "record_type": "research_paper", "title": "The Reconstructed Theory Has One Mass: A Machine-Checked Volume-Uniform Transfer Gap for a Finite Ising Strip", "abstract": "We give a finite-dimensional Osterwalder-Schrader reconstruction for an anisotropic Ising model on open rectangular strips and prove a spectral gap whose rate is uniform in the finite spatial extent. For temporal coupling beta, spatial coupling gamma, and parameters satisfying 0 < alpha < 1 and 2 tanh|beta| + 2 tanh|gamma| <= alpha, one number m > 0 works for every spatial length. Reflection positivity is proved directly for the Gibbs measure; the null space of the reflected form is identified with the kernel of an explicit boundary-collapse map; the OS quotient is linearly equivalent to the finite boundary-vector space; and the transfer operator forced by the site and bond forms is intertwined with a symmetrised transfer matrix.Dobrushin comparison supplies positive Perron data and a projected operator norm bounded by exp(-m) for every spatial length. Consequently, connected reconstructed correlations decay at the same common rate. Lean 4 checks thecomposition without assuming reflection positivity, Perron data, a vacuum, a gap, or clustering at the public endpoint. This replacement extends the point-slice, fixed-size v1 to finite strips with one rate uniform in spatial size. It does not construct an infinite-volume operator or Hamiltonian, provea unique particle excitation or relativistic mass shell, or claim a Yang-Mills mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0078", "abstract_url": "https://www.ai.vixra.org/abs/2607.0078", "first_submitted_at": "2026-07-28T13:19:32+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-05T21:41:37+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0078-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-28T13:19:32+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0078v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-05T21:41:37+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0078v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7fdc9d22f8fca69a174efad3e9384b5756775af44d2ac202a8dd8daa86bfa377", "canonical_bytes": 304834 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2094a60d-b199-41f7-abc7-94a131ce0b68", "version_id": "arr:version:a2998826-7b2c-4597-a54a-92dc570f4d50", "id": "ARR-2026-10JJK0VCCS87VTQH", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Reflection-Positivity Framework for Z_N Lattice Gauge Theory, with the Z_2 Wilson Instance", "abstract": "We machine-check, in Lean 4 with no sorry and no project axioms, theOsterwalder-Seiler reflection positivity of a lattice gauge theory with finiteabelian gauge group. The development is organised so that the three ingredientsare separated and each is proved on its own: an analytic step, a geometric step,and the single place where a property of the Boltzmann factor is actually used.The analytic step is that a crossing kernel of the formK(x,y) = sum_i c_i phi_i(x) conj(phi_i(y)) with c_i >= 0 is positivesemidefinite, that this class is closed under products, and that it is closedunder conjugation by a positive diagonal. Formulating the hypothesis as anon-negative combination of characters rather than as non-negativity of Fouriercoefficients removes any need for Bochner's theorem on a finite abelian groupand for the Schur product theorem: the development uses no spectral and nomatrix-positivity API.The geometric step is a splitting of the configuration space across thereflection plane under which the reflection is the swap and the Gibbs weightfactors as w(x) w(y) K(x,y). We prove that the Osterwalder-Seiler pairing of anobservable of one half against its reflection is then exactly the quadratic formof w(x) K(x,y) w(y), so that reflection positivity follows from the analyticstep.The physical step is the instance. For Z_2 the Wilson factor exp(beta s),s = +-1, expands in the two characters with coefficients(exp(beta) +- exp(-beta))/2, both non-negative exactly when beta >= 0; so theZ_2 Wilson crossing kernel is positive semidefinite at non-negative coupling. Asingle endpoint combines a gauge system with a nontrivial time reflection, aconcrete splitting, that weight at positive coupling, and the conclusion; itsplaquette straddles the reflection plane, so the entire Gibbs weight is thecrossing kernel. It is a two-edge system, and a full temporal box is nottreated. For Z_N with N > 2 the coefficients are discrete Bessel-type sums andtheir non-negativity is not established here.We are explicit about what is absent: no Gelfand-Naimark-Segal quotient, notransfer operator, no identification of a Euclidean correlator with a matrixelement, and therefore no mass gap. Nothing here is a claim about SU(N), thecontinuum limit, or the Clay problem.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-27", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0073", "abstract_url": "https://www.ai.vixra.org/abs/2607.0073", "first_submitted_at": "2026-07-27T21:33:38+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-27T21:33:38+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0073-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-27T21:33:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0073v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "95c85d5b89f10b07e83fc699af0e03d45b35aec75851dda0d263b3c788e8f47c", "canonical_bytes": 91268 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6173494d-4d81-44ad-96ba-9cd440b02c86", "version_id": "arr:version:e09b870e-524e-4920-a3e0-0b9efab1dc8c", "id": "ARR-2026-31ED4MTKC18JPSDE", "version": "v1", "record_type": "research_paper", "title": "Clustering and the Transfer-Operator Gap: A Machine-Checked Dense-Family Criterion", "abstract": "Inside a Lean 4 formalization programme for four-dimensional SU(N_c) latticeYang-Mills, we machine-check the operator-theoretic criterion that standsbetween exponential decay of a Euclidean correlator and a spectral gap of atransfer operator. Let T be a bounded self-adjoint operator on a Hilbert spaceand W a unit vector fixed by T, so that TW = W, and put S = T - |W> - ||^2 at every v is equivalent to the operator-norm bound||S|| <= r.The substantive part is the dense-family criterion. WritingD_r = {v : there is C with ||S^n v|| <= C r^n for all n}, we prove that D_r isa linear subspace and that its density alone forces ||S|| <= r, the constantsbeing entirely unconstrained: a family of observables whose span is dense, eachcarrying its own finite constant, suffices. Consequently prefactors that growwith the support of the observable - the shape cluster expansions produce - donot obstruct the gap, provided the exponential rate is common to the family andthe family spans densely. Those two provisos are essential; without them thestatement is false.No mathematical novelty is claimed for the criterion itself, which we expect tobe known in the language of local spectral theory; what is offered is itsmechanization, its packaging for families of observables, and the consequencefor prefactors. We also record what the formalization does not contain: noOsterwalder-Seiler Hilbert space for any gauge theory, no reflection positivityof the Wilson measure, no identification of a Euclidean correlator with a matrixelement. Nothing here is a claim about the continuum limit or about the Clayproblem. All results are machine-checked with no sorry and no project axioms. (W stands for the vacuum vector Omega. If the form's preview renders Unicode cleanly you may substitute the real symbols; the ASCII form above is the safe default and matches the PDF's content either way.)", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-27", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0070", "abstract_url": "https://www.ai.vixra.org/abs/2607.0070", "first_submitted_at": "2026-07-27T16:38:14+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-27T16:38:14+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0070-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-27T16:38:14+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0070v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "56dcba9f6c88452570c427d337fa4e00a0ff9bfeb9087faa28826094d1f72ad5", "canonical_bytes": 112653 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:250ca2ec-6948-4672-be4b-7f3e3ab56390", "version_id": "arr:version:664255fc-49e0-4bf8-94ce-90b9f027fa58", "id": "ARR-2026-151JHERTA88SSBWJ", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked CMP116 Fluctuation Reduction: Physical Constraint Coordinates and the Interacting-Hessian Frontier", "abstract": "We give a machine-checked reduction of the finite-dimensional fluctuation integral in Balaban's CMP116 large-field analysis. Starting from the physical block constraint Q, the formal development constructs a sparse right inverse E and the constraint-elimination operator C = I - EQ. It proves QE = I, QC = 0, C² = C, the exact sparse norm ||EB|| = M^(d-1)||B||, and the volume-independent bound ||C|| ≤ 1 + M^(d-1) for d ≥ 3. An exact physical/CMP116 isometry transports C to finite Gaussian coordinates without norm loss. The same development constructs the physical localization projector P_Z0, evaluates the complex quadratic Gaussian, localizes its determinant to rank |I(Z0)|, performs the outer Gaussian integration, and absorbs both costs into an explicit exp(c|Z0|) factor.Two corrections exposed by formalization are central. First, the useful domination occurs after Gaussian integration rather than through an unavailable pointwise supremum in the fluctuation field. Second, the localized quadratic matrix is A = -alpha_5 P_Z0. In the exactly identified trivial-background sector, the terminal Lean theorem inserts the concrete C, the flat Hessian, complement localization, and covariance root directly into the printed source Gamma_k = C^T Delta_k (C P_Z0^c)(C^(k))^(1/2), returning an explicit Cauchy bound without an ambient-volume factor. CMP116, however, requires the base Hessian at a generally nontrivial small background Ubar. We do not construct D²S_Wilson(Ubar) or the random-walk estimate (2.16), and therefore do not prove the physical domination, (2.26), hraw, hRpoly, a continuum limit, or a mass gap. The contribution is an auditable reduction that closes the constraint and Gaussian layers and identifies the first genuinely missing interacting construction.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-15", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0044", "abstract_url": "https://www.ai.vixra.org/abs/2607.0044", "first_submitted_at": "2026-07-15T20:22:56+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-16T04:47:03+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0044-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-15T20:22:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0044v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-16T04:47:03+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0044v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "90de465e44a0b3a03130023bef1eedef08cbb1c5049afac08ace11b74dfeba58", "canonical_bytes": 362509 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5658cdec-0168-4f32-b384-c10acb6b58d5", "version_id": "arr:version:87a1d45c-8b68-452e-9a03-cd13fb4e2a94", "id": "ARR-2026-2PB36YR0B89WSB71", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Exact Evaluation of the Two-Dimensional SU(2) Heat-Kernel Lattice Model on Certified Finite Combinatorial Disk Cellulations: From Haar Measure to Conditioned Original-Edge Amplitudes", "abstract": "We present an end-to-end Lean 4/Mathlib formalization of the exact evaluation of the two-dimensional SU(2) heat-kernel lattice model on certified finite combinatorial disk cellulations. The development starts from normalized Haar probability on the concrete matrix group SU(2). It identifies its transport to S^3 with the canonical spherical measure, proves an all-order orbital integration formula, derives translated character convolution, and passes from finite character sums to the infinite heat-kernel semigroup by dominated convergence. A genuine shared-edge integral then yields the two-face Migdal move.The geometric layer is independent of any reduction tree. A cellulation stores vertices, paired half-edges, cyclic face words, incidence, Euler characteristic, and positive face areas. Connected dual graphs admit certified elimination schedules, every valid schedule reduces to the heat kernel at total area, and all schedules give the same amplitude. For the original edge model, a rooted spanning tree produces a measurable, product-Haar-preserving gauge equivalence SU(2)^E ≃ SU(2)^(V{r}) × SU(2)^(ET). A compatible tree-cotree construction then retains the exterior holonomy rather than integrating it out. For every certified physical disk cellulation, the boundary-conditioned original-edge amplitude is exactly the SU(2) heat kernel at the total face area. Coefficient extraction gives, for every irreducible label n, the normalized exterior-boundary identity E_P[W_n(H_boundary)] = exp[-n(n+2)(sum_f t_f)/4], where H_boundary is the retained holonomy of the complete exterior boundary word. The universal record is demonstrably inhabited: a concrete three-spoke disk has (V,E,F)=(4,6,3) and derived dual graph K_3. A reproduced audit covers 177 audited declarations, explicitly including both headline theorems, and finds only propext, Classical.choice, and Quot.sound in their dependency cones. The analytic solution is classical. The contribution is a concrete kernel-checked composition from Haar measure and characters to physical edge variables, gauge fixing, tree-cotree elimination, and the exact boundary-observable endpoint.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0039", "abstract_url": "https://www.ai.vixra.org/abs/2607.0039", "first_submitted_at": "2026-07-14T18:49:45+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-01T15:44:49+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0039-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-14T18:49:45+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0039v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-01T15:44:49+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0039v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "453b066c26d2d1ca9d724022eb3992d8988fe5786cc9938a9e731cdc84e22a77", "canonical_bytes": 611982 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:7706e27b-52bb-4313-bbb9-13cd45a33de6", "version_id": "arr:version:4f550b85-7b67-4b71-acd5-20a214b27e2f", "id": "ARR-2026-3Q0VH7PMNV8C9VQE", "version": "v1", "record_type": "research_paper", "title": "The Volume-Uniform Poincaré Walls: Machine-Checked Obstructions for Flat and Fluctuation-Sector Block-Poincaré Routes to Combes—Thomas Coercivity in Lattice Yang—Mills", "abstract": "Inside a Lean 4 formalization programme for four-dimensional SU(Nc) lattice Yang—Mills, we report two machine-checked negative results and the machine-checked infrastructure that makes them meaningful. The positive substrate is: (i) a fixed-volume Combes—Thomas chain for self-adjoint coercive finite-range lattice operators, instantiated on the flat gauge-fixed covariance of the physical shell, with coercivity constant c = min(1,a)/C_P fed by a proved fixed-volume flat Hodge/block-Poincaré inequality; and (ii) the concrete adjoint model of SU(n) — su(n) with the trace inner product, dim_R su(n) = n² − 1, and the isometric transport to Euclidean coordinates — so that the abstract adjoint-model interface has a concrete nontrivial inhabitant and the flat-lane results can be instantiated with the genuine matricial adjoint model. The first wall states that, under the block normalization actually used by the formalized chain, every flat Hodge/block-Poincaré constant obeys L^d/L² ≤ C_P on the fine torus of side LNu2032, hence the volume-uniform Poincaré gate is provably false for d ≥ 3 and Nc ≥ 2, and no positive coercivity constant survives all volumes through this route. The route consumed by the fixed-volume endpoint is therefore closed by theorem. A second wall stands in the fluctuation sector. For d ≥ 3 and a transported half-period square-wave mode on the exact fine side (2M)Nu2032, the formalization proves ||QA||² ≤ (2M)u207b¹||A||², the exact identity = 8((2M)Nu2032)u207b¹||A||², and therefore a Rayleigh numerator at most 9(2M)u207b¹||A||². Every quotient Poincaré constant is thus at least 2M/9, so the volume-uniform fluctuation-sector gate is also provably false for every positive Nu2032, d ≥ 3, Nc ≥ 2, and every adjoint model. Everything stated here is checked by Lean 4 against a pinned Mathlib, with zero sorry, zero project axioms, and a committed axiom-oracle transcript. A dependency record, theorem-artifact map, and reproduction instructions expose the complete proof chain. Both walls concern the current unscaled line-integral block map with the current unweighted coarse norm; neither gate is claimed to be necessary, equivalent, or exhaustive for Yang—Mills theory. No claim toward a continuum construction or a mass-gap theorem is made.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0042", "abstract_url": "https://www.ai.vixra.org/abs/2607.0042", "first_submitted_at": "2026-07-14T13:24:23+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-14T13:24:23+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0042-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-14T13:24:23+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0042v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "1f5334e93e8c7a72207c47c237537f4e6bd4c108f3f631b5d9df7c65b06fa1c0", "canonical_bytes": 156889 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:1c827cdf-156a-4e47-8793-7cd0374cd07e", "version_id": "arr:version:7b704785-95c0-4bfd-81ba-2d96926a80a5", "id": "ARR-2026-0WG9YDY5BA9S3RF4", "version": "v1", "record_type": "research_paper", "title": "A Mechanized, Non-Circular Renormalization-Group Interface for Wilson Lattice Gauge Correlators", "abstract": "For SU(N_c) Wilson lattice gauge theory on d-dimensional periodic tori (d >= 2), we present a machine-checked (Lean 4, pinned Mathlib) renormalization-group interface for two-plaquette truncated correlators, in which every structural ingredient is a theorem rather than a postulate: the scale transformation is a concrete decimation map, defined once -- measurable, local, and gauge-covariant -- and its induced pushforward preserves probability; the effective measures are its literal iterated pushforwards of the Wilson Gibbs measure; the multiscale decomposition of the correlator is proved by telescoping, never carried as data; the terminal scale of the decomposition is a fixed index kTerm(n) = n with typed range 1 <= kTerm(n) <= n, which excludes, in the type, the circular depth-zero layer in which an infrared clause would hypothesize the bound being sought; the conditional decay conclusion is stated in the physical distance 2^n u with a single constant pair (C, m) quantified before every torus base and depth; and the terminal observable is operationally support-certified: the infrared object consumed by the interface equals a base-measure integral of an explicitly composed pullback observable whose dependence is contained in a transported support set, for which the separation lower bound 2^n(2u) - (2^n + 1), strictly positive on the whole interface window, is proved. The design is deliberately adversarial: four natural naive formulations are presented together with the explicit countermodels that defeat them -- scalar relabeling of known decay, sink flows on measures, clamped scales and per-volume constants, and depth-zero circularity -- and with the typed repairs that exclude each. The central hypothesis, PhysicalTerminalScaleWilsonGate, is an open proposition: no witness is provided, and the infrared/ultraviolet bounds it demands of the actual Wilson measure are exactly the open analytic mathematics (Balaban-type single-scale estimates). The final theorem is conditional: a witness of the gate yields |Cov(2^n u)| <= C e^{-m 2^n u} with one pair (C, m), m > 0, for every base M_0 >= 4 and every depth n >= 1. No mass-gap claim, no claim of gate satisfiability, and no thermodynamic or continuum limit is made or implied.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0043", "abstract_url": "https://www.ai.vixra.org/abs/2607.0043", "first_submitted_at": "2026-07-14T05:39:24+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-14T05:39:24+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0043-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-14T05:39:24+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0043v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "2878f2ab6e10693e189e14c71dec3826a4ccc23fead6cc1d40cb3ef4e28621a3", "canonical_bytes": 201072 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2dabcff4-bca7-4f51-9baa-ab864c8daa9c", "version_id": "arr:version:c89510eb-018e-46e7-be76-193cd1bdec4c", "id": "ARR-2026-1DNF7Z9F579X8SQA", "version": "v1", "record_type": "research_paper", "title": "Exact Two-Dimensional SU(2) Yang-Mills in Lean: Weyl Integration, Heat-Kernel Convolution, Migdal Invariance, and the Exact Simple-Loop Area Law", "abstract": "SUPERSEDED BY AI.VIXRA:2607.0039V1 FOR THE ORIGINAL-EDGE AND TREE-COTREE CLOSURE. This replacement preserves public version 1 and corrects its publication-level scope. Version 1 establishes the compact-group analytic chain, heat-kernel reductions, schedule independence and reduced-model results, but pages 7 and 9 leave open the bridge from the post-gauge-fixed evaluator to the original-edge physical integral for arbitrary cellulations. ai.viXra:2607.0039v1 supplies the missing original-edge gauge fixing, simultaneous face-holonomy transport and compatible tree-cotree closure and is therefore the authoritative source for the full exact simple-loop area-law theorem at the stated finite two-dimensional SU(2) heat-kernel scope. Neither paper constructs four-dimensional continuum Yang-Mills theory or proves a four-dimensional mass gap. The preserved version 1 follows the two-page notice unchanged.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0035", "abstract_url": "https://www.ai.vixra.org/abs/2607.0035", "first_submitted_at": "2026-07-13T20:23:27+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-01T08:42:41+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0035-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-13T20:23:27+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0035v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-01T08:42:41+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0035v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "86a3891fcc5b0dae0e000501909e5926ab225bb60b2881809432eb701a9f0727", "canonical_bytes": 207545 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:69f01e81-bc9f-4ca6-9041-63f82f9bc5c6", "version_id": "arr:version:b1abea5a-ea5c-41fa-9d3e-65cfeda1e4a4", "id": "ARR-2026-39Y0F83F4Z9JK90G", "version": "v1", "record_type": "research_paper", "title": "The Diagonal Amos-Type Family at Real Order: a Machine-Checked Quantitative Crossing Classification", "abstract": "For the one-parameter family B(x) = x/(nu+c+sqrt((nu+c)^2+x^2)) of Amos-type expressions, whose member c = 1/2 is the classical Amos-type upper bound for the modified Bessel ratio I_{nu+1}/I_nu, we formalize in Lean 4, at every real order nu >= 0 over the Gamma-power series, the classification of the parameter: B is a uniform upper bound for the ratio exactly when c <= 1/2, and a uniform lower bound for every c >= 1, with explicit rational counterexample witnesses (the classification itself is known mathematics, due to Ruiz-Antolin and Segura; we claim only the machine-checking). The contribution is the regime between the ends: for every nu >= 0 and c strictly between 1/2 and 1 we prove that the fixed family member crosses the ratio exactly once on (0, infinity) -- a transversal crossing in an explicit finite window, strictly above an explicit threshold, with globally determined sign on both sides and a two-sided scale law; degenerate contact is excluded by an exact second-derivative identity. The chain carries the axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis beyond nu >= 0, x > 0; a pre-registered certified interval-arithmetic companion verifies the crossing phenomenon independently of the crossing theorems at 30 parameter pairs spanning the hard regimes, all passing at 128 bits.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0037", "abstract_url": "https://www.ai.vixra.org/abs/2607.0037", "first_submitted_at": "2026-07-13T05:29:47+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-13T05:29:47+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0037-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-13T05:29:47+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0037v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "95eed84d8c6f85b03bb92ba8f3fe29e3e7664aafb06c4d0c9998e7f5840ec2f0", "canonical_bytes": 144103 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:de7bab48-417e-4dac-b784-b2aac6c17083", "version_id": "arr:version:e019845f-b062-4e9f-99a2-cb5fe76145f1", "id": "ARR-2026-6YFENMGGBY9PPBF1", "version": "v1", "record_type": "research_paper", "title": "Many-Body Filling Turns Soft Spectral Leakage into a Maintenance Floor: Exact Filled-SSH Sum Rules and an Interaction-Stable Obstruction", "abstract": "Soft spectral filtering has a more severe effect at finite filling than in a dilute edge-mode code. We consider two odd Su-Schrieffer-Heeger (SSH) rails, fill every negative-energy orbital, and encode one additional fermion in the zero mode of either rail. The code has fixed total number and supports physical coherence. For a boundary transfer at a site with zero-mode weight w_x, the desired logical Davies line has squared matrix element w_x^2. We prove the exact many-body leakage identity W_leak^filled(x) = (1 + 2w_x - 3w_x^2)/4. At the remote boundary, w_x = Theta(zeta^(2 ell)), so the logical line is Theta(zeta^(4 ell)) while the summed particle-hole leakage tends to 1/4. This differs qualitatively from the dilute identity w_x(1 - w_x) = Theta(zeta^(2 ell)).For a Davies filter whose off-target tail is epsilon_ell = exp[-q ell + o(ell)], the bounded-latency exact-refresh power obeys the exponent law lim_(ell to infinity) -(1/ell) log P_(ell,tau) = min{4m,q}, where m = -log zeta, under explicit uniform-envelope and resource-ledger assumptions. A width-independent tail, a special case with q = 0, produces a nonzero maintenance floor rather than merely halving the membrane exponent. More generally, q = 0 means only that the decay is subexponential. Every nonzero tail also makes the exact rapid-refresh limit logarithmically singular at each fixed width.The floor is not a free-fermion accident. For arbitrary interacting number-conserving rails, we prove an exact static identity expressing leakage as a local occupation product minus the logical matrix element. Uniform finite filling and remote-edge indistinguishability force a positive leakage floor. A new local spectral-window lemma places a fixed fraction of that weight in a width-independent Bohr-frequency window using only a commutator norm. Consequently, any bath tail bounded below on that window yields an interaction-stable Davies leakage floor. Quasi-local spectral flow shows persistence in a neighborhood of a symmetry-preserving gapped SSH phase. Exact diagonalization of the interacting spinless SSH chain shows that repulsive and attractive interactions change the observed edge-localization exponent while the leakage is already driven close to 1/4 at accessible widths.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0038", "abstract_url": "https://www.ai.vixra.org/abs/2607.0038", "first_submitted_at": "2026-07-12T23:40:59+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T23:40:59+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0038-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T23:40:59+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0038v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e7cd053ae4bdaa129d62e4acd6102c487507d587234bf2f1c11c610abf084140", "canonical_bytes": 324005 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:56f67088-f68a-461a-8c6c-fca4c6c69fb4", "version_id": "arr:version:f29ef703-7cdd-4407-9310-f02f8c813186", "id": "ARR-2026-2PYSR8HXMA8RD8RV", "version": "v1", "record_type": "research_paper", "title": "Support Leakage Makes Rapid Quantum Maintenance Singular: Soft Spectral Filters and Exponent Transmutation in Dual-Rail SSH Codes", "abstract": "Exact rapid maintenance behaves singularly at the boundary of quantum state space. Let a finite-dimensional target rho have support projector P, and let an uncontrolled quantum Markov semigroup have outward support-leakage rate a = Tr[(1-P)L(rho)]. We prove that, whenever a > 0, the nonequilibrium free-energy loss has the universal short-time form F(rho) - F(exp(tL)rho) = k_B T a t log(1/t) + O(t). Under an explicit fresh-resource-cell ledger, the optimal period-t exact-refresh power therefore diverges as k_B T a log(1/t). For GKLS generators, a is a positive sum of squared support-crossing jump amplitudes. We prove the complete dichotomy: a > 0 gives logarithmically infinite rapid power, while a = 0 gives finite rapid power even when Hamiltonian rotation produces population outside the fixed initial support at second order. We also define a periodic threshold-reset corridor and prove its sharp k_B T a log(1/r) + O(1) small-corridor law.The general singularity has an unexpected geometric consequence. In a fixed-parity dual-rail SSH code, a boundary transfer has desired logical weight w_x^2, but its exact summed zero-mode-to-bulk weight is w_x(1-w_x). At the remote boundary, these scale respectively as Theta(zeta^(4 ell)) and Theta(zeta^(2 ell)). Thus a soft spectral tail changes the exponential rate of bounded-latency refresh from 4|log zeta| to 2|log zeta| unless the tail itself is suppressed at least as zeta^(2 ell). We prove the general rate formula min{4m, 2m+q}, where m = -log zeta and q is the exponential suppression rate of the spectral tail. Exact rapid maintenance and the wide-membrane limit do not commute: every nonzero tail gives infinite rapid power at fixed width, while fixed-period power still vanishes exponentially with width. The result turns perfect filtering from a technical convenience into the sharp boundary between finite and singular exact maintenance.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0028", "abstract_url": "https://www.ai.vixra.org/abs/2607.0028", "first_submitted_at": "2026-07-12T23:01:56+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T23:01:56+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0028-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T23:01:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0028v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "48f762cecad5655f63c76e9db00c17001a1d2077d7a9b261c0061d3603e167d2", "canonical_bytes": 294393 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:909583dc-9d0a-497b-9344-6407031db95d", "version_id": "arr:version:0b053b9f-fcec-473d-a93f-0b8b92b609bd", "id": "ARR-2026-4GJP1XS78A95XS6H", "version": "v1", "record_type": "research_paper", "title": "Exact Stabilization by Additive GKLS Control Is Impossible at a Leaky Boundary", "abstract": "The tangent cone of quantum state space at a rank-deficient density matrix is known to have a positive exterior block, and recent work identifies all of its directions with Lindbladian velocities. We derive a quantitative stabilization consequence of this geometry. Let rho be a finite-dimensional target with support projector P, set Q = 1 - P, and let an uncontrolled GKLS generator L have outward support-leakage rate a = Tr[Q L(rho)] > 0. Every additive GKLS controller, including a bounded time-dependent controller, has its own nonnegative outward rate at rho and therefore cannot cancel a. Consequently, no finite-rate additive Markovian controller can keep the system exactly at the target. The conclusion persists for arbitrary finite-dimensional autonomous ancillas, provided the adverse system generator remains additive and local to the system.Under induced trace-norm bounds ||L|| <= M and ||K_t|| <= Gamma, we prove the dynamic corridor inequality limsup ||rho_t - rho||_1 >= 2a/(M + Gamma), without assuming convergence to a stationary state. An autonomous Poisson-reset generator supplies a matching inverse-rate upper bound, establishing the order-optimal minimax law Theta(Gamma^{-1}).For a soft-filter dual-rail SSH family, the microscopic leakage coefficient scales as exp[-(2m + q)ell + o(ell)], whereas the ideal logical disturbance scales as exp[-4m ell + O(1)]. We derive the exact controller-growth threshold g_min = max{0, 2m - q}. Thus, below the filter threshold q = 2m, retaining ideal logical accuracy requires an exponentially growing autonomous correction intensity.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0029", "abstract_url": "https://www.ai.vixra.org/abs/2607.0029", "first_submitted_at": "2026-07-12T23:00:29+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T23:00:29+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0029-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T23:00:29+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0029v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4ba6c31bf1af2998962b552bec28adbdade0ba36a9fd3856413e3286bcc2a206", "canonical_bytes": 326702 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e7a600b5-85c4-41d8-af61-943e295fe1bc", "version_id": "arr:version:1cbf15ae-1471-4e89-9921-fd97329fcd11", "id": "ARR-2026-77MR0BB1E487CAYR", "version": "v1", "record_type": "research_paper", "title": "Maintenance Is Not Restoration: Endpoint No-Go Theorems, Exact SSH Resource Horizons, and Quantum Rapid-Replacement Equality", "abstract": "Lower bounds based on the instantaneous free-energy loss of a target state are often interpreted as lower bounds on the power required to maintain that state. We show that this interpretation depends decisively on the control task. If maintenance only requires exact restoration at periodically sampled endpoints and the intervention period is unrestricted, the infimal average power can vanish even when the target has strictly positive instantaneous entropy production. A full-rank dephasing qubit gives an exact energy-conserving SWAP counterexample. We repair the formulation by separating endpoint restoration, bounded-latency maintenance, and continuous holding.For continuous-time finite Markov chains we adopt the established trajectory-relative-entropy holding cost and review the known reversible optimizer and Dirichlet-form representation. Our first composition result is then an exact geometric additivity theorem for suppressible and persistent generators sharing a detailed-balance reference. A two-state counterexample shows that this hypothesis is essential: channels with incompatible equilibria can cancel at a finite membrane width. A dual-rail pair of odd fermionic SSH chains supplies the microscopic layer: exact edge modes, a uniform bulk gap, and an explicitly filtered number-conserving Davies coupling produce two-sided holding-cost bounds without an assumed rate-inheritance bridge. The logical basis has fixed particle number and parity, so arbitrary logical coherence is physical under fermionic superselection. Finally, under a fully axiomatized resource-cell ledger, fresh target-state cells and energy-conserving SWAPs saturate the fixed-period free-energy bound; the correctly ordered rapid-control limit closes the SSH theorem for coherent logical targets. The fresh-copy construction is related to earlier collision-model stabilization work and is not claimed as a work-only controller. The remaining frontier is autonomous work-only control without preloaded target copies.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0031", "abstract_url": "https://www.ai.vixra.org/abs/2607.0031", "first_submitted_at": "2026-07-12T22:58:40+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T22:58:40+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0031-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T22:58:40+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0031v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a3eb2f8fcea49b5c6de4312aead239ccb60bba17e93ec314a44658fb77a456aa", "canonical_bytes": 228675 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:6a91f855-e475-4ef0-89d1-1bd050e956a5", "version_id": "arr:version:604967e7-8f02-4635-b56a-26109f629d4e", "id": "ARR-2026-3AJ7W5BS3N9VR8KM", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Proof of an Amos-Type Bound for Modified Bessel Ratios at Real Order", "abstract": "The Amos-type upper bound for the modified Bessel function ratio, rho_nu(x) = I_{nu+1}(x)/I_nu(x) < x/(nu + 1/2 + sqrt((nu+1/2)^2 + x^2)), is classical, and its derivation through the qualitative theory of the associated Riccati equation is an established technique. A companion paper formalized the bound at integer order over a factorial power series. This paper extends the formalization to every real order nu >= 0: the function I_nu is defined by its Gamma-power series (real exponents via rpow), and the complete chain — convergence, positivity, the three-term recurrence, termwise differentiation with a dominated-derivative argument that must treat the leading term separately (its exponent nu-1 is negative for nu < 1), the Riccati equation, a small-argument zone bound uniform in nu, and a first-crossing barrier — is machine-checked in Lean 4 with axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis beyond nu >= 0, x > 0. Two structural locks tie the result to the integer development: an identification theorem proves that at nu = n the Gamma-series object coincides with the factorial-series object, so the integer-order theorem of the companion development is recovered as a corollary in three rewrites; and a genuinely non-integer instance at nu = 1/2 witnesses that the endpoint lives outside the natural-number embedding. The theorem is proved for the in-core Gamma-series definition; no identification with an external special-functions library object is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0030", "abstract_url": "https://www.ai.vixra.org/abs/2607.0030", "first_submitted_at": "2026-07-12T20:21:46+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T20:21:46+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0030-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T20:21:46+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0030v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "fdd3c8e52d46dba22d9eebab7295059c8930cd1f9ffc903234faa2cd526753f9", "canonical_bytes": 122265 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2799e78c-1ab1-4ff6-a74a-83a7bc30c2d2", "version_id": "arr:version:d8778fcd-fabe-4fca-92d1-126286529603", "id": "ARR-2026-17K7KRR6NH9ZVAEJ", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Proof of the Amos Bound for Modified Bessel Function Ratios", "abstract": "Amos's upper bound for the modified Bessel function ratio, rho_n(x) = I_{n+1}(x)/I_n(x) < x/(n + 1/2 + sqrt((n+1/2)^2 + x^2)) = B_n(x), is a classical theorem, and its derivation through the qualitative theory of the associated Riccati equation is an established technique. This paper contributes, to our knowledge, the first formalization: a complete, machine-checked Lean 4 proof of the bound for every integer order n >= 0 and every x > 0, over the power-series definition of I_n carried in the same pinned development, with axiom oracle [propext, Classical.choice, Quot.sound] and no analytic hypothesis of any kind. The formalized route runs through the Riccati equation rho_n' = 1 - ((2n+1)/x) rho_n - rho_n^2 (itself derived from the formalized series calculus), the observation that B_n is exactly the positive root of the Riccati quadratic, a small-argument zone bound uniform in n obtained from pure geometric tail estimates, and a first-crossing barrier argument in a transformed variable psi_n = x(1/rho_n - rho_n) whose structural feature — every touch of the critical level forces rho_n' = 0, so the barrier never needs to be differentiated — is the simplification this formalization contributes. As corollaries, the unit-step inequality, the strict monotonicity of the logarithmic derivative across orders (in deriv form), and a phi-monotonicity step used by a lattice-gauge surface expansion all become unconditional theorems. The theorem is proved for the in-core power-series definition of the integer-order modified Bessel function; no formal identification with an external special-functions library object, and no extension to noninteger order, is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0032", "abstract_url": "https://www.ai.vixra.org/abs/2607.0032", "first_submitted_at": "2026-07-12T13:23:29+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T13:23:29+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0032-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T13:23:29+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0032v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "6337febe84ee7c6154c0d0801863241effbe84f7bec6c2b3e569f9d27382cb16", "canonical_bytes": 115661 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:cdb232dc-7cc7-4452-af26-e5f962b97bfe", "version_id": "arr:version:9dc7d047-f3d5-4784-ba5d-9f3b58137267", "id": "ARR-2026-6DP8SDRZ678H9AY9", "version": "v1", "record_type": "research_paper", "title": "One Amos Bound, Three Consumer Sites: Machine-Checked Bessel-Ratio Calculus for Lattice Gauge Expansions", "abstract": "The Amos-type upper bound on the modified-Bessel ratio, I{nu+1}(x)/I_nu(x) < x/(nu + 1/2 + sqrt((nu+1/2)^2 + x^2)), has a distinguished algebraic property: its right-hand side U satisfies the exact calibration identity 1/U - U = (2nu+1)/x. From that identity alone — by ordered-field algebra, with no further analytic input — follow a unit-step inequality rho_nu - rho{nu+1} < 1/x for consecutive ratios, the strict increase of the log-derivative (log I_nu)' = rho_nu + nu/x across orders, and the strict monotonicity of a phi-sequence arising in a two-dimensional lattice-gauge surface expansion. We formalize this calculus in Lean 4: a single module defines the bound once (AmosBound) and proves the calibration engine and four consequence theorems through that one definition, together with two rational satisfiability witnesses whose Amos hypothesis holds by exact Pythagorean arithmetic; all eighteen Lean statements of the development pass the axiom oracle with exactly [propext, Classical.choice, Quot.sound] against a pinned Mathlib. A certified companion (256-bit interval arithmetic, self-contained series-plus-tail enclosures, committed transcript) certifies the bound provably strictly at all 1206 points of a pre-registered grid covering the arguments the applications consume. A Bessel interface completes the closure: integer-order I_n is defined by its power series in the same pinned development, with positivity, the three-term recurrence, the termwise-differentiated derivative identity I_n' = I_{n+1} + (n/x) I_n, and the logarithmic-derivative identity (log I_n)' = rho_n + n/x all proved as theorems, so the consequence theorems — including the unit step read as strict log-derivative monotonicity, in deriv form — hold for genuine Bessel ratios with the Amos bound as the single remaining hypothesis. The scope is stated exactly: the Amos bound itself remains a classical cited theorem taken as hypothesis — this paper unifies its three previously scattered uses in our formal development into one named proposition with one oracle and one certified numerical witness, and no downstream result changes its verification class.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0033", "abstract_url": "https://www.ai.vixra.org/abs/2607.0033", "first_submitted_at": "2026-07-12T13:19:13+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-12T13:19:13+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0033-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-12T13:19:13+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0033v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d13ccb296b9d4f9fc9fca1624487328eab40d5d32bdb213a220eb0cfc2adc972", "canonical_bytes": 138893 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:a02d6ff8-e0f6-4eae-8ca8-f314520f9f3a", "version_id": "arr:version:173a18fe-dea1-4eae-b7ca-8e9db8461921", "id": "ARR-2026-505NQZHR7P9TQ8SA", "version": "v1", "record_type": "research_paper", "title": "Machine-Checked Rooted-Tree Majorants for Polymer Expansions with Holes", "abstract": "We present a machine-checked quantitative toolkit for cluster expansions of polymer systems with excluded regions (holes), in the discrete cube geometry of Balaban-Dimock renormalization-group analyses. Five Lean 4 theorems, checked against a pinned Mathlib revision, provide: (i) the identity sum_T prod_v c_T(v)! = n! C_n for child factorials over spanning trees of the complete graph K_(n+1), with the rooted-tree majorant 4^n as corollary; (ii) a marked-root leaf summation for the tree-graph majorant of an Ursell-type expansion with holes, with the moment constant M paid once at the root and closed leaf ratio 4M^2 per additional vertex, together with its Catalan-sharpened form M^(2n+1) C_n (a gain of order n^(3/2) in the n-th coefficient); and (iii) a target-preserving orderwise bound in which the target union itself survives until the modified-metric exponential is extracted. A certified companion (interval arithmetic, 120-bit precision, committed transcript with a committed reproduction witness) tabulates the smallness gate and encloses every derived constant. Non-vacuity is machine-checked: a concrete hole family satisfying every hypothesis is exhibited in Lean, and the two distinct hypothesis sets among the polymer-facing theorems are both instantiated at it with a strictly positive weight. Each claim is labelled with its verification layer: exact (Lean theorem), certified (interval transcript), or paper-level.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0025", "abstract_url": "https://www.ai.vixra.org/abs/2607.0025", "first_submitted_at": "2026-07-11T21:28:54+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-11T21:28:54+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0025-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-11T21:28:54+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0025v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c4d403868cbecb70309d714c005f20d441208287e80c3833fb1dd11294cc94ba", "canonical_bytes": 155324 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2fb3d41d-669e-4d07-a4e7-dfc16b44f73a", "version_id": "arr:version:2f8d60f8-26eb-40b1-80a4-3f2aeddc7a49", "id": "ARR-2026-1FPFA1TSMY9M3T9S", "version": "v1", "record_type": "research_paper", "title": "Ratio Monotonicity for a Killed von Mises Bridge: Exact Bridge Structure, Certified Negative Results, a Single-Bessel Reduction, and a Two-Scale Closure Map for a Surface Expansion in Two-Dimensional Lattice Gauge Theory", "abstract": "SUPERSEDED BY AI.VIXRA:2607.0089V1 FOR THE TERMINAL GLOBAL-SIGN CLAIM; INDEPENDENT REPLAY PENDING. This replacement preserves public version 1 and records the later terminal-claim paper without overstating its audit status. Version 1 proves positivity of F_B, the ratio sign for 0 < beta <= 3, exact bridge and single-Bessel reductions, certified negative results, asymptotic structure and a two-scale closure map; pages 11-13 leave the global sign as a quantified conjecture. ai.viXra:2607.0089v1 claims the global ratio-monotonicity theorem through exact identities and outward-rounded interval certificates. It supersedes this record for that terminal claim, but independent replay of every exact-to-Arb handoff and interval regime remains pending in this audit. No PASS is inferred from a printed or green transcript alone. The preserved version 1 follows the two-page notice unchanged.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-09", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0023", "abstract_url": "https://www.ai.vixra.org/abs/2607.0023", "first_submitted_at": "2026-07-09T23:37:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-01T08:44:13+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0023-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-09T23:37:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0023v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-01T08:44:13+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0023v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7aa4ba1e0304105992b1e3cc4b5dd778ed946dba5e4809bcb9a69725951923c5", "canonical_bytes": 534914 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e2807396-56b0-479b-b60b-3229e1a6e6c8", "version_id": "arr:version:85887c0e-1e00-489b-97f0-8b6e6a721191", "id": "ARR-2026-72G1SSCNNG8YDVC2", "version": "v1", "record_type": "research_paper", "title": "A Weighted Turan-Type Monotonicity Lemma for Modified Bessel Functions via the Calibrated Amos Bound, with an Application to the Ordering of a Surface Expansion in Two-Dimensional Lattice Gauge Theory", "abstract": "For x>0 and real m>=1 define phi_m(x) = [(m-1) I_{m-1}(x)^2 + (m+1) I_{m+1}(x)^2] / (m I_m(x)^2), with I_mu the modified Bessel function of the first kind. We prove phi_m(x) < phi_{m+1}(x) for every x>0 and everyreal m>=1 - a weighted Turan-type monotonicity statement we have not found in the literature, although every ingredient of the proof is classical. The proof is fully elementary: eliminating the neighbouring ratios by thethree-term recurrence, the difference factorizes exactly as (S-3c)(P-(2m+1)c) + (2m+1)c^2, with u = I_{m+1}/I_m, c = 1/x, S = u+1/u, P = 1/u-u; the second factor is positive by the calibrated Amos bound (it is precisely the unit-step inequality of the companion note), the first because the same bound forces u < x/(2m+1) <= x/3. As an application we obtain thestrict determinant ordering c_mn < 0 (m", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-09", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0017", "abstract_url": "https://www.ai.vixra.org/abs/2607.0017", "first_submitted_at": "2026-07-09T19:34:39+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-09T19:34:39+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0017-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-09T19:34:39+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0017v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b6307a215b321c380f1f76b117e6cb6c660239c176b0b25c45fe2fe5a3c59d50", "canonical_bytes": 305866 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:b1c3076c-a63f-4f1a-a517-f539fae928fb", "version_id": "arr:version:913ff5f2-f32f-416e-8aeb-33fe7ab2c8d9", "id": "ARR-2026-5HRC3PS9HZ9WDAA5", "version": "v1", "record_type": "research_paper", "title": "Parity Barriers for Decoupling Inequalities: Why No Comparison Functional of Bounded Marginal Order Can Certify Uniform Decoupling", "abstract": "For every r>=1, the uniform measure on the even-parity subset of {+-1}^{r+1}is r-wise independent, yet the last coordinate has unit variance while beingan a.s. function of the others. This example is classical - parity-checkcodes are the standard construction of k-wise independent distributions inthe pseudorandomness literature (Joffe; Alon-Babai-Itai; Alon-Goldreich-Mansour) - and no novelty is claimed for it. What is recorded here is aconsequence we have not seen isolated as a statement: any \"comparisonfunctional\" whose value depends only on marginal data of order <= r, withconstants uniform over finite measures, takes identical values on the paritymeasure and on the uniform product measure, and is therefore consistent withperfect decoupling on a measure where decoupling fails maximally. Hence noinequality built from bounded-order functionals can imply uniform decouplingprinciples - Dobrushin-type mixing, approximate tensorisation withmeasure-free constants, covariance decay - on any class of measurescontaining the parity family. The case r=1 recovers, and explainsstructurally, the failure of raw-oscillation/Doob and Efron-Stein-type stepsfound repeatedly in an adversarial audit of a constructive Yang-Millsprogramme; no repair within bounded-order data can succeed, because thebarrier recurs at every order. Statements (a) and (b) are machine-checkedin Lean 4/Mathlib parametrically in r (all n; no sorry; standard axiomsonly), the abstract certifying-barrier schema is formalized as well, andfinite decide instances (r<=4) plus exact rational arithmetic (r<=6) serveas independent audits.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-09", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0018", "abstract_url": "https://www.ai.vixra.org/abs/2607.0018", "first_submitted_at": "2026-07-09T14:57:20+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-09T14:57:20+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0018-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-09T14:57:20+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0018v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "dc3b243efcb6f161516b48a7f17bd0e79092b59d17476f3cf8f3f40a7bd9ba4b", "canonical_bytes": 284127 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:b6eb7d5c-09d8-4263-abc1-7fb433545f45", "version_id": "arr:version:7940f817-5aa1-48bf-854d-632efe51b7cf", "id": "ARR-2026-5PXDYNR2ER89HTQG", "version": "v1", "record_type": "research_paper", "title": "Recurrence-Amos Proof of the Unit-Step Order-Monotonicity of (log I_nu)', with a Feynman-Hellmann Application to Two-Dimensional Lattice Gauge Theory", "abstract": "Let I_nu denote the modified Bessel function of the first kind and, forx>0, let rho_nu(x) = I_{nu+1}(x)/I_nu(x). We give a four-step, fullyelementary proof of the sharp difference inequality0 < rho_nu(x) - rho_{nu+1}(x) < 1/x (x>0, nu>=0), whose right-handinequality is exactly the strict increase of the logarithmic derivative(log I_nu)'(x) under the unit shift nu -> nu+1; consequentlynu -> (log I_nu)'(x) is strictly increasing along every unit-spaced gridnu_0 + N, in particular on the integer and half-integer orders arising inthe application. The stronger continuous-order statement is known(Freitas-Laugesen, arXiv:1810.07461, Lemma 10, via Bessel zeros); we makeno elementary claim about fractional steps. The proof given here uses noinformation about Bessel zeros: it combines the three-term recurrence withthe classical Amos-type upper bound rho_nu < x/(a+sqrt(a^2+x^2)),a = nu+1/2, and rests on the observation that this bound is exactlycalibrated for the problem: 1/U - U = 2a/x is an algebraic identity, and(2nu+1)/x is precisely the threshold the unit step requires; in fact theunit-step monotonicity and the Amos bound are equivalent. As anapplication we record the following consequence in two-dimensional latticegauge theory: for the Wilson action, every mass gap between charactersectors of the 2D transfer operator - for U(1) and SU(2) alike - is astrictly decreasing function of the bare coupling beta, by theFeynman-Hellmann identity. The algebraic core of the proof ismachine-checked in Lean 4/Mathlib (no sorry; axiom oracle: Lean's threestandard axioms), and an independent high-precision numerical audit ofevery inequality used is reported.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-09", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0020", "abstract_url": "https://www.ai.vixra.org/abs/2607.0020", "first_submitted_at": "2026-07-09T13:40:14+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-09T13:40:14+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0020-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-09T13:40:14+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0020v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "98a312e39cb60ad102f19da4b831a0c0c09ad6e6a7febcc6ec2600580c09ebd3", "canonical_bytes": 338164 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5fb99e53-d451-4520-90ee-c47f11270175", "version_id": "arr:version:c30837b8-aafd-4dd0-9b7e-a09fbc0ed8a7", "id": "ARR-2026-2ZQ6F57N2H8MG91V", "version": "v1", "record_type": "research_paper", "title": "A Machine-Checked Volume-Uniform Wilson-Loop Area Law via a Formalized Cluster Expansion", "abstract": "We report a complete formalization, in Lean 4 over Mathlib, of volume-uniform Wilson-loop area laws for SU(N c ) lattice gauge theory in an explicit strong-coupling window - including the case of the exact Wilson Boltzmann factor, not a linearized surrogate. The headline theorem bounds the normalized Wilson-loop expectation by N c e P·4dK σ Area(C) e P·4dS(σ) , where Area(C) is an intrinsic combinatorial filling area of the loop, P is its edge-support size, and every constant is volume-free: the bound holds uniformly over all finite lattice sizes. The partition function is cancelled through a fully formalized volume-restricted cluster expansion (loop-tagged factorization, restricted Mayer inversion, Z-ratio bounds, and a pinned-gas resummation built on a Kotecky-Preiss layer with Penrose-style spanning-tree counting). A reusable repackaging converts the bound into manifest exponential area decay with a strictly positive string tension, and the non-vacuity of every hypothesis window is itself machine-checked - both the cluster smallness window and the decay-repackaging window, the latter with an explicit witness of tension log 2 - 1/2. For every exported theorem in this chain the Lean kernel's axiom oracle reports exactly [propext, Classical.choice, Quot.sound]; there is no sorry and no project axiom in the dependency cone. To our knowledge this is the first machine-checked cluster-expansion proof in lattice quantum field theory. All artifacts are public, with per-theorem oracle records in a verification ledger and continuous-integration builds.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0005", "abstract_url": "https://www.ai.vixra.org/abs/2607.0005", "first_submitted_at": "2026-07-02T21:47:02+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-02T21:47:02+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0005-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-02T21:47:02+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0005v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b1001b2f446e84e9d4c46975406aaca5f4befa0ab863850c6a00f494af44816e", "canonical_bytes": 286065 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e0f3bf90-6388-4099-bad0-8ebde065c7ca", "version_id": "arr:version:ebaf0a10-af62-44f2-a576-de99e1a6548a", "id": "ARR-2026-70YEZS0RW882CVNM", "version": "v1", "record_type": "research_paper", "title": "A Machine-Verified Bijective Proof of the Rooted Child-Factorial Catalan Identity over Spanning Trees of the Complete Graph", "abstract": "Let K n+1 be the complete graph on the vertex set {0, 1, ..., n}, and for a spanning tree T of K n+1 , rooted at 0, let c T (v) denote the number of children of the vertex v. We prove the exact identity: the sum, over all spanning trees T of K n+1 , of the product over vertices v of c T (v)! equals n! C n , where C n is the n-th Catalan number. Equivalently, the normalized sum (n+1)((n+1)!) -1 times the weighted tree sum equals C n exactly. The proof is bijective: pairs consisting of a spanning tree together with a linear ordering of every child set are placed in explicit bijection with vertex-labeled plane trees on n+1 nodes whose root carries the label 0. The identity arises as the exact \"second-Ursell\" normalization constant in the author's audit-first programme on four-dimensional SU(N) Yang-Mills existence and mass gap, where it had been isolated as a named open proposition in a public challenge repository; the present paper is self-contained combinatorics and makes no claim about that programme. The entire proof has been formalized in Lean 4 against a pinned Mathlib snapshot: the headline declarations compile with no sorry, and the kernel's axiom oracle reports exactly [propext, Classical.choice, Quot.sound]. All artifacts, including a pinned continuous-integration replay of the full verification, are public.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-07-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2607.0001", "abstract_url": "https://www.ai.vixra.org/abs/2607.0001", "first_submitted_at": "2026-07-02T19:14:41+00:00", "latest_declared_version": "v1", "latest_submitted_at": "2026-07-02T19:14:41+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2607.0001-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-07-02T19:14:41+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2607.0001v1.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4fa970934eea954103fafd9f02250c9f04c79e487efaf8bd704aeff9efbdb99c", "canonical_bytes": 282891 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:07e4c827-03f8-4c50-aeb8-3d503a6681e3", "version_id": "arr:version:06d30ccc-2fe7-4b45-aeda-b646bef4e02e", "id": "ARR-2026-07WK42E0ZR9H8AXE", "version": "v1", "record_type": "research_paper", "title": "THE MASTER MAP - Audit Experiments Report: Mechanical Audit Experiments and Reproducibility Appendix for the 2602-Series Programme on 4D SU(N) Yang-Mills", "abstract": "This is the experiment-first audit report for the 2602-series programme: a runnable mechanical suite (repository ym-audit) with declared pass/fail criteria, a 2D Yang-Mills benchmark, gauge/infrastructure/UV-flow proxy layers, and a reproducibility manifest. Version 3 aligns the report with the fully audited programme and corrects three defects in the harness itself. Scope statement (sharpened): the 29 tests adjudicate exact identities, toy models, and group-theoretic facts; they cross-validate the per-paper suites of THE-ERIKSSON-PROGRAMME (verification/2602-*, 15 papers, independent implementations agreeing where they overlap, e.g. the triangular-lock dimension counts); they do NOT discharge any entry of the programme ledger - a 29/29 run leaves the hypothesis set {(H1), (H2)+beta_LF, (H3), (H2'), (H-LOC), L6.2-import, (H-Rbeta), (H-P0'), structural+window, lambda != 0 traceable, ...} exactly as it was. Corrections: the d=4 harmonic coefficient is 1/2 (harness had 3/2, a dropped-term bug; the paper chain had 3/5, the d=3 value - three-way inconsistency now settled and machine-adjudicated); the non-triviality test is rescoped (Haar kurtosis != 3 is a single-link fact - exactly 2 for SU(2) - present even at strong coupling; what it verifies is C4(N) > 0); the super-polynomial large-field test is restated under the audited log-power profile. The 2D YM benchmark (transfer-matrix gap Delta = g^2 N/2 to 1e-14) and the dependency DAG survive; \"Papers 86-90\" are pinned to 2602.0088 v3 / 0087 v3 / 0092 v2 / 0091 v2 / 0096 v2.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-26", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0117", "abstract_url": "https://www.ai.vixra.org/abs/2602.0117", "first_submitted_at": "2026-02-26T19:59:49+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-07T04:01:30+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0117-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-26T19:59:49+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0117v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-27T02:16:52+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0117v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-07T04:01:30+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0117v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8c9dc4bc5bb8670a3414772b01608a5d9c62fb50d81e99da5f7e1d0dfe3008f6", "canonical_bytes": 315523 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:ddc2464e-fab2-4ec2-b059-c48e7ca4974a", "version_id": "arr:version:f2f735f3-0722-4567-914e-1e43e41d7c42", "id": "ARR-2026-6XR934XYNJ9V1B0P", "version": "v1", "record_type": "research_paper", "title": "THE MASTER MAP: An Audit-First Navigation Guide to the Conditional Construction of 4D SU(N) Yang-Mills with Mass Gap - the Audited-Ledger", "abstract": "This is the navigation guide and audit manifesto for the 2602-series programme on 4D SU(N) Yang-Mills. Version 2 is the audited-ledger edition: the dependency graph, Clay/Jaffe-Witten checklist and threat model of v1 are retained, but every node is now pinned to its audited version and carries its named hypothesis loads; the claim is stated as what it is - a conditional assembly: relative to the declared external mathematics (abstract KP, OS reconstruction, lattice reflection positivity) AND to the internal ledger {(H1), (H2)+beta_LF, (H3), (H2'), (H-LOC), per-scale decoupling, (H-Rbeta), (H-P0'), structural+window loads, lambda != 0 traceable}, the chain assembles OS0-OS4 and OS1 and reconstructs a Wightman QFT with mass gap. v1's \"unconditional\" (in any sense) is withdrawn. Version 2 also corrects two mathematical defects in v1's new material: the hypercubic harmonic's coefficient (3/5, the d=3 value) is corrected to 1/2 in d=4; and the Large-Field Annihilation Lemma's hypothesis p0(g) >= c/g^2 - attributed to a source whose actual profile is (A0 log g^{-2})^{p*} - is replaced by the honest (H2') trichotomy. The genuinely structural new content survives and is machine-verified: the marginal anisotropic sink at d=4 is empty (exact group averaging over W4 on Sym^2(Lambda^2 R^4): quotient dimension 0, versus 1 at d=6), hence renormalization mixing is triangular in the anisotropic channel and the a^2 x a^{-2} -> O(1) objection has no landing site.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-20", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0096", "abstract_url": "https://www.ai.vixra.org/abs/2602.0096", "first_submitted_at": "2026-02-20T06:04:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-07T03:45:06+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0096-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-20T06:04:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0096v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-07T03:45:06+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0096v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8b9fc960236d9bdba9929e8cba82846d8670dd63fb4643506a2fb2b647087733", "canonical_bytes": 351643 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:21a64859-f917-47b5-9a98-def6581a3cc1", "version_id": "arr:version:ba1da87a-e292-4b87-ae92-7660b85671fd", "id": "ARR-2026-11MS45KY8Q8YTSN6", "version": "v1", "record_type": "research_paper", "title": "A Source-Mapped Terminal KP Bound and a Conditional Clay Checklist for the 4D SU(N) Yang-Mills Programme", "abstract": "Part I (terminal KP bound). We isolate explicit hypotheses (H1)-(H3) on the terminal polymer activities of the 4D SU(N) lattice Yang-Mills programme and prove that, together with a profile condition (H2') made explicit in this version, they imply the Kotecky-Preiss convergence criterion used as Hypothesis (H-KP) in 2602.0088 v3. The implication is elementary and fully machine-verified (exponential inequality, weighted lattice-animal bound with d(X) >= |X|-1, explicit smallness threshold in g). This refines the ledger: (H-KP) <= (H1)+(H2)+(H3)+(H2'). Status of the hypotheses: v1 declared them \"verified from primary sources\"; per the audited bridge (2602.0069 v2) the correct statement is: (H1) and (H3) are traceable to Balaban's CMP papers; (H2) is traceable with loads (the beta_LF dichotomy, and the unpinned profile (A0,p*) - the recurring (H-P0) datum of the audited series). Part II (assembly map + Clay checklist). We give the dependency graph assembling 2602.0088 v3, 2602.0087 v3 and the (unaudited) rotational Ward companion, and a Clay/Jaffe-Witten checklist with statuses: activating KP does not activate the mass gap of 2602.0088 v3 by itself - that theorem additionally carries (H-LOC), a per-scale decoupling import, and coupling-control loads; OS1 remains open pending the Ward companion's audit. No unconditional Clay claim is made. All adjudicable content is verified in a deterministic companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0091", "abstract_url": "https://www.ai.vixra.org/abs/2602.0091", "first_submitted_at": "2026-02-19T12:16:47+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-07T03:16:58+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0091-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-19T12:16:47+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0091v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-07T03:16:58+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0091v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "ac6833cff2d630d4e9769c610532edef26df6270f956621d5ea743570a946fa5", "canonical_bytes": 345614 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:4a13315c-59ac-4f19-86df-31601e511cfa", "version_id": "arr:version:dc76a706-f0c7-4481-b127-d5bc0ea9a550", "id": "ARR-2026-2A2CRNRPDC9WCRDQ", "version": "v1", "record_type": "research_paper", "title": "Rotational Symmetry Restoration and the Wightman Axioms for Four-Dimensional SU(N) Yang-Mills Theory", "abstract": "Info de reemplazo — ai.viXra:2602.0092 (v1 → v2)Paper a reemplazar: 2602.0092Method: replacement of existing paperPDF: ward_v2.pdf — sha256 9564aec01a4836c9 — 4 páginasCategory: Mathematical Physics (como v1)Title: Rotational Symmetry Restoration and the Wightman Axioms for Four-Dimensional SU(N) Yang-Mills TheoryAuthor: Lluis ErikssonAbstract (texto plano):We derive a lattice Ward identity for infinitesimal Euclidean rotations of the Wilson theory, identify the breaking term as a dimension-6 anisotropic operator insertion (in the classification of 2602.0087 v3), and show that the breaking distribution is O(eta^2 |log((Lambda_YM eta)^{-1})|) -> 0, establishing axiom OS1 (full O(4) covariance) for subsequential continuum limits - conditionally on the audited companion inputs. Version 2 corrects v1's framing: v1 imported the mass gap, OS0/2/3/4, anisotropy and insertion bounds as \"unconditional\"; per the audited versions these carry the programme ledger's loads (the source-mapped KP block of 2602.0091 v2, (H-LOC), per-scale decoupling and coupling control for 2602.0088 v3; window and structural loads for 2602.0087 v3). The assembled result - a non-trivial Poincare-covariant Wightman theory with mass gap Delta_phys >= c_N Lambda_YM > 0 - therefore holds under the explicit composed hypothesis set, stated in Section 5; v1's \"no unproved hypotheses remain\" is withdrawn. The native content survives audit and is machine-verified: the Ward mechanism on an exactly solvable lattice Gaussian model (breaking = O(eta^2) measured), the lambda_{mu nu} != 0 mechanism in the exact quartic model (rotations annihilate O(4) invariants, not the hypercubic harmonic), the Lie-algebra-to-group invariance lemma, the symmetric-difference eta^2/6 error constant, and the eta^2 log vanishing arithmetic.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0092", "abstract_url": "https://www.ai.vixra.org/abs/2602.0092", "first_submitted_at": "2026-02-19T12:13:41+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-07T03:30:44+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0092-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-19T12:13:41+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0092v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-07T03:30:44+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0092v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "9564aec01a4836c98cac7c3779c801dc9dc654e52cb467b1f07d8469f64d4131", "canonical_bytes": 314961 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:4baefc34-8577-4a8b-ba1a-171d4167f416", "version_id": "arr:version:750c651f-3897-431a-b473-20e82c488ce0", "id": "ARR-2026-2BNVY391BQ9A5VM6", "version": "v1", "record_type": "research_paper", "title": "Irrelevant Operators, Anisotropy Bounds, and Operator Insertions in Balaban's RG for 4d SU(N) Lattice Yang-Mills: Symanzik Classification and Quantitative Irrelevance of O(4)-Breaking Operators", "abstract": "We classify gauge-invariant local lattice operators of classical dimension 6 on the four-dimensional hypercubic lattice into O(4)-invariant, hypercubic-invariant but O(4)-breaking (anisotropic), and on-shell-redundant components, following the Symanzik improvement programme and the on-shell technique of Luscher-Weisz. The anisotropic sector is one-dimensional (Theorem 3.6, Proposition 3.7: uniqueness of the hypercubic harmonic) - a purely representation-theoretic fact, machine-verified in the companion suite together with the classical Symanzik a^2/12 anisotropic term of the Wilson plaquette itself. Inside Balaban's renormalization group framework (small-field regime, g_k <= gamma_0, k <= k* - the window bookkeeping of the audited chain), we extract the anisotropic projection of the effective action via local Taylor (jet) expansion of polymer activities and prove the quadratic bound |c^(k)_{6,aniso}| <= C a_k^2, uniformly in lattice spacing eta, physical volume, and RG step k within the window - conditionally on the structural package, whose audited status is now attached (traceable per 2602.0069 v2; beta_LF dichotomy for the large-field remainder). We further prove an insertion integrability estimate for connected correlators with one anisotropic insertion; Version 3 corrects its status: v1-v2 called it unconditional, resting on an imported clustering/mass-gap bound (Theorem 4.5, from the unaudited companion [1]) claimed uniform in eta and L_phys - per the audited program (2602.0053/0054 v2) such a gap is conditional on (H-DOB-blk)+(H-P0) and windowed, so Theorem 6.6 is conditional on that input. Combined with the rotational Ward identity of the companion [2] (unaudited, identifier pending), the O(4)-breaking distribution tested against Schwartz functions is O(eta^2 |log((Lambda_YM eta)^{-1})|) and vanishes as eta -> 0 - under the same conditional load. This paper thereby supplies, conditionally, the operator-classification input required by 2602.0063 v3 (Proposition 5.3/Remark 5.4) for continuum SO(4) restoration. All verifiable content (representation counts, the unique hypercubic harmonic, the plaquette's own a^2/12 anisotropy, Cauchy-jet mechanics, the a_k^2/log bookkeeping, and the clustering-to-integrability conversion) is adjudicated in a companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-18", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0087", "abstract_url": "https://www.ai.vixra.org/abs/2602.0087", "first_submitted_at": "2026-02-18T18:58:54+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-07T01:19:53+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0087-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-18T18:58:54+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0087v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-19T12:12:41+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0087v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-07T01:19:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0087v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "bb04b5dd196464ae1d67e75697ab7b41b58afe4dcd19a16d9b7257c73e9624f6", "canonical_bytes": 343285 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:9608fde4-626a-411f-85de-83d1dd12a2d9", "version_id": "arr:version:dca3e148-7bc1-4f2e-8edf-e24087b9bf46", "id": "ARR-2026-4P13YY8RKA84FRBQ", "version": "v1", "record_type": "research_paper", "title": "Exponential Clustering and Mass Gap for Four-Dimensional SU(N) Lattice Yang-Mills Theory via Balaban's Renormalization Group and Multiscale Correlator Decoupling", "abstract": "We assemble a proof architecture for exponential clustering with a strictly positive mass gap for four-dimensional pure SU(N) lattice Yang-Mills theory with Wilson's action, Cov(O(0),O(x)) <= C exp(-m|x|/a*), m > 0, a* ~ 1/Lambda_YM, with constants uniform in lattice spacing eta and physical volume L_phys - conditionally on three identified inputs. (1) Balaban's structural package (polymer decompositions, exponentially decaying activities), traceable per 2602.0069 v2 with the beta_LF dichotomy attached. (2) A terminal-scale Kotecky-Preiss smallness bound, Hypothesis (H-KP): v1-v2 cited it as proved in an unpublished companion with no identifier; Version 3 retags it as a hypothesis until that companion exists and survives audit. (3) A localization hypothesis (H-LOC) for conditioned observables, made explicit for the first time in v3: the telescoping step compares the terminal clustering bound against O~ = E[O | sigma_a*], whose support is not local. The coupling control (Proposition 4.1) is proved by Cauchy bounds conditionally on the uniform-in-k analyticity radius of Balaban's discrete beta-function and on the large-field penalty profile satisfying the (A0,p*) trichotomy of the audited ledger. What is unconditional and machine-verified: the multiscale telescoping identity (exact for any measure and any nested sigma-algebra chain), the summation-over-scales arithmetic, the lattice-animal bounds, the implications KP => exponential clustering and clustering => spectral gap in exactly solvable settings, and the coupling-control recursion. We verify OS0, OS2, OS3 unconditionally at the lattice level and OS4 conditionally; OS1 (full O(4) covariance) is not established here - its natural conditional supplier is 2602.0087 v3 via 2602.0063 v3. All adjudicable content is verified in a deterministic companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-18", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0088", "abstract_url": "https://www.ai.vixra.org/abs/2602.0088", "first_submitted_at": "2026-02-18T17:31:06+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-07T02:13:55+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0088-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-18T17:31:06+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0088v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-19T12:11:33+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0088v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-07T02:13:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0088v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "e4f976817401b36e4ebffb80d0a13c6534cf425fcd723fd6da184ac1411f8914", "canonical_bytes": 385625 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:eab599a4-4281-4a1d-8adb-0fae157a944d", "version_id": "arr:version:87421777-240b-4ef2-9405-641cf68b7381", "id": "ARR-2026-7APPCT8GM198ERNP", "version": "v1", "record_type": "research_paper", "title": "Spectral Gap and Thermodynamic Limit for SU(N) Lattice Yang-Mills Theory via Log-Sobolev Inequalities and Complete Analyticity", "abstract": "We present two parallel results for SU(N) pure gauge lattice Yang-Mills in four Euclidean dimensions, at fixed lattice spacing eta > 0 and weak coupling g0 <= g*, both conditional on a single shared input, the Dobrushin-Shlosman complete analyticity condition (H-CA): (A) a log-Sobolev inequality Ent(f^2) <= (2/rho) E(f,f) with rho > 0 independent of L, via Cesi's quasi-factorisation seeded by a Bakry-Emery/Holley-Stroock local LSI; and (B) a spectral gap m_gap >= m0 > 0 for the Osterwalder-Seiler Hamiltonian, via Dobrushin clustering and reflection positivity. The two outputs are logically parallel; neither implies the other here (the bridge lemma remains open, Remark 6.3). Version 2 corrects the status of the shared input: v1 declared (H-CA) verified from Balaban's infrastructure; per the audited chain (2602.0053/0054 v2) that route is conditional on (H-DOB-blk)+(H-P0) and valid only in the volume window L <= exp(C/g0^2). Accordingly all results are stated in two regimes: windowed (audit-backed conditional) and all-volume (under the strictly stronger bare hypothesis (H-CA)_infty, required for the thermodynamic limit, Theorem C). What is unconditional and machine-verified: the curvature computation Ric_SU(N) = N/4, the Holley-Stroock block-seed arithmetic, the variance/entropy decompositions and the failure of pointwise inheritance, the Dobrushin contraction machinery and its window arithmetic, the clustering => transfer-gap lemma on explicit operators, and the convergence of Cesi's geometric factor. All bounds remain explicit in N, g0, eta.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-18", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0089", "abstract_url": "https://www.ai.vixra.org/abs/2602.0089", "first_submitted_at": "2026-02-18T09:21:04+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-07T02:48:05+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0089-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-18T09:21:04+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0089v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-07T02:48:05+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0089v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "643a510a9377907bce72f7bf29cc4ea765ec1ef3d2b68596d1c9be87833759e7", "canonical_bytes": 361983 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:d0dd7c9f-373e-46d2-b418-65dec30a7890", "version_id": "arr:version:379062b3-5847-48c7-b59d-82cce33f7d6d", "id": "ARR-2026-6GVNY9YDSY8V9B86", "version": "v1", "record_type": "research_paper", "title": "Almost Reflection Positivity for Gradient-Flow Observables via Gaussian Localization in Lattice Yang-Mills Theory", "abstract": "VERSION 2 RETRACTION AND STATUS NOTE. The principal results of version 1 are withdrawn. Theorem 4.4 and Proposition 3.8 depend on the false Wilson-flow linearisation retracted in ai.viXra:2602.0085 and on further false statements. Lemma 3.1 omits the stationary heat-kernel term; Lemma A.1 gives a variance-oscillation bound that fails for correlated non-product measures; Theorem 5.1 does not obtain a positive self-adjoint generator from its stated hypotheses; Lemma 3.3 uses a non-periodic separation across the torus boundary; and Lemma 3.5 bounds a nonlinear map by a differential at one endpoint rather than an integrated or uniform Jacobian. Definitions 2.2, 2.5 and 2.6 remain definitions, and the cited lattice reflection-positivity Theorem 4.1 is not retracted here. Nothing in this note proves the intended almost-reflection-positivity conclusion false; the printed proof and several printed statements fail. The six-page erratum is followed by the preserved 15-page version 1.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0084", "abstract_url": "https://www.ai.vixra.org/abs/2602.0084", "first_submitted_at": "2026-02-17T19:43:23+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-31T23:12:15+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0084-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-17T19:43:23+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0084v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-31T23:12:15+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0084v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4099349dc23496d5938e5dee8092de991083c92dea15481a3a69d2c1ba008bc9", "canonical_bytes": 667188 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:ae465b93-3688-408c-a5bb-2f83a4404ce6", "version_id": "arr:version:67319398-af36-4211-ae82-e41a0b00c508", "id": "ARR-2026-5E8SDS6DM8826ABE", "version": "v1", "record_type": "research_paper", "title": "Ultraviolet Stability of Wilson-Loop Expectations in 4D Lattice Yang-Mills Theory Via Multiscale Gradient-Flow Smoothing", "abstract": "VERSION 2 RETRACTION AND ERRATUM. The principal results of version 1 are withdrawn. Lemma 3.6, Eq. (16), falsely identifies the Wilson-flow linearisation with a connected weighted scalar Laplacian plus a pointwise adjoint term. At the trivial configuration, gauge invariance forces the true Hessian to annihilate a pure-gauge subspace of dimension at least (|V|-1)(N^2-1), incompatible with the printed connected-Laplacian kernel; if the positive-weight graph is disconnected, the single stationary heat-kernel term used downstream is itself false. Consequently Lemma 3.8, Proposition 3.9, Theorem 3.11 and Theorem 1.1 are withdrawn. Lemma 2.2 and Proposition 1.3 remain intact. Lemma 3.2 is only recoverable as a separately specified scalar heat-kernel theorem; its original instantiation is withdrawn. Reflection positivity, Osterwalder-Schrader reconstruction, thermodynamic limit and mass gap remain open. The five-page erratum is followed by the preserved 21-page version 1.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0085", "abstract_url": "https://www.ai.vixra.org/abs/2602.0085", "first_submitted_at": "2026-02-17T16:18:50+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-31T23:11:08+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0085-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-17T16:18:50+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0085v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-31T23:11:08+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0085v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "deff7be46aa56ddfbcac63addce730a4bc4449768e5920951d1a304912525518", "canonical_bytes": 816370 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:d8603f02-d780-42be-9e35-871caa428fc0", "version_id": "arr:version:57090ab3-ad3a-4e6f-afeb-aa8441bf553e", "id": "ARR-2026-6RC0ZG5NW08AZ9WD", "version": "v1", "record_type": "research_paper", "title": "Ultraviolet Stability for Four-Dimensional Lattice Yang-Mills Theory: Closing the Bałaban-Doob Circuit under Quantitative Blocking and Decoupling Hypotheses", "abstract": "We prove that the continuum limit of pure SU(N) lattice Yang-Mills theory in four Euclidean dimensions exists on the algebra of blocked observables at fixed finite volume, CONDITIONALLY on an explicit hypothesis ledger: a quantitative regularity hypothesis for the blocking map (squared-oscillation summability, Assumption A — equivalently (H-LIP^2), a strengthened form of the (H-LIP) contraction of 2602.0073 v2), the Dobrushin-type decoupling hypothesis (H-DEC/AT) of the sibling audits, and the audited statuses of the Balaban structural package. The argument assembles: (i) Balaban's renormalization group program (polymer representation, irrelevance bounds after beta-function extraction, UV stability of effective densities) — traceable per 2602.0069 v2, with the beta_LF dichotomy for the large-field part; (ii) a Doob-martingale covariance IDENTITY (exact for every measure) together with a conditional-oscillation influence bound — v1's claim that the oscillation control holds \"without product-measure hypotheses\" is withdrawn: v1's Remark 2.3 correctly rejected Efron-Stein for the non-product interpolating measures, but the Doob-oscillation Lemma 1.5 of v1 fails for the same reason (two-spin counterexample, 2602.0070 v2); the repair is (H-DEC); (iii) the RG-Cauchy summability framework of 2602.0073 v2, consumed with its full ledger (including (H-theta)/F-SQRT for the truncation errors). Under the ledger, the telescopic state sequence converges and the resulting state omega_L is gauge-invariant, Euclidean-covariant (hypercubic), and positive. Osterwalder-Schrader reconstruction, the thermodynamic limit, and the mass gap remain open, as in v1. All mechanical steps — the exact covariance identity, both counterexample adjudications, the Assumption A mechanics on explicit blocking maps (including a non-local sharpness example showing locality plus contraction are genuinely needed), and the corrected Proposition 6.1 arithmetic with its exact M 2^(-4k) scale cancellation — are machine-verified in a companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-15", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0077", "abstract_url": "https://www.ai.vixra.org/abs/2602.0077", "first_submitted_at": "2026-02-15T05:11:13+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T22:57:16+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0077-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-15T05:11:13+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0077v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T22:57:16+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0077v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c307815051a40602c81ff252c57b33201176aa271dcc47100df6306f939afece", "canonical_bytes": 300988 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:af65f9f6-2714-4e9e-96ed-dcc473831283", "version_id": "arr:version:cb8d348d-094d-4ec2-b8f3-a80f2264de58", "id": "ARR-2026-5FCQWZC9RM9TF9DV", "version": "v1", "record_type": "research_paper", "title": "The Balaban—Dimock Structural Package: Derivation of Polymer Representation, Oscillation Bounds, and Large-Field Suppression for Lattice Yang—Mills Theory from Primary Sources", "abstract": "We provide a self-contained, equation-level traceability derivation of the three structural hypotheses — polymer representation (A1), per-link oscillation bounds with irrelevance factor (A2), and large-field suppression (B5) — that were assumed in the companions \"Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang-Mills Renormalization\" and \"RG-Cauchy Master Framework\". All results are traced to precise equations in the primary sources: T. Balaban (Commun. Math. Phys., 1984-1989) and the expository trilogy of J. Dimock (2011-2014). The translation from Balaban's analytic norms on gauge-covariant function spaces to the per-link oscillation language of the probabilistic framework is made explicit. Version 2 corrects the status of the discharge: it is TRACEABLE AND CONDITIONAL, not unconditional. (i) The small factor of Theorem 8.4 (= Eq. (1.89) of Balaban, Large field renormalization II) carries the constant 2/(1+beta_LF); whether beta_LF is O(1) or a large reference coupling is precisely the dichotomy adjudicated against the audited series (2602.0052/0056/0057 v2), where the large reading trivializes the factor (e^(-c p0) ~ 0.95) and forces hypothesis (H-P0); the dichotomy is now stated as an explicit open interface question (Remark 8.7). (ii) The summability claim (M3) of the RG-Cauchy interface was justified in v1 by \"super-polynomial decay from asymptotic freedom\"; with the profile p0(g) = A0 (log g^-2)^theta0 the decay in the scale index j (distance to the infrared end) is e^(-A0 (ln j)^theta0): sub-polynomial for theta0 < 1 (sum diverges), j^(-A0) at theta0 = 1 (converges iff A0 > 1), and super-polynomial only for theta0 > 1. (M3) is therefore conditional on the explicit profile condition theta0 > 1 (Remark 12.1; hypothesis (H-theta)). (iii) The irrelevance factor (L^k eta)^(4+alpha) is geometric in the distance to the ultraviolet cutoff, not in the infrared direction; the direction-of-limit bookkeeping for (M1) is made explicit (Remark 10.4) and remains hypothesis-level until the Doob companion is audited. What is machine-verified in the companion suite: the abelian RG operator algebra (Lemma 2.2 mechanics), propagator decay and the random-walk expansion, exponential sum control, lattice-animal counting (Lemma C.1; the illustrative d=4, n=3 count of v1 is corrected from 86 to 84), and the oscillation-analyticity bridge with its Cauchy constants and exact factor-2 saturation. Together with the (unaudited) Doob companion, this package provides a CONDITIONAL discharge of the UV structural inputs at finite volume; the finite-volume, ultraviolet character of the package is what shields it from the infrared volume window of the audited chain (2602.0041 v3, 2602.0051-0057 v2, 2602.0063 v3, now cited).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0069", "abstract_url": "https://www.ai.vixra.org/abs/2602.0069", "first_submitted_at": "2026-02-14T20:48:17+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T21:58:43+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0069-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-14T20:48:17+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0069v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T21:58:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0069v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "9bcb3d30ed9179af32ca72e9fc75201a17342d1724e64392191d40fce99bda4c", "canonical_bytes": 389252 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:25edbec7-ac9a-410e-8381-b8eb83ce8944", "version_id": "arr:version:8e0ba9a1-29f4-40ae-9c99-d97c5bab65bc", "id": "ARR-2026-15XPZCFB4T847870", "version": "v1", "record_type": "research_paper", "title": "Doob Influence Bounds for Polymer Remainders in 4D Lattice Yang-Mills Renormalization — a Corrected and Conditional Influence Bound", "abstract": "We study a uniform Doob martingale influence bound for the irrelevant polymer remainder arising in multiscale renormalization group analyses of four-dimensional SU(N_c) lattice Yang-Mills theory at fixed physical volume, via the Doob influence seminorm sigma_nu(f)^2 = sum_i E_nu[(Delta_i f)^2] and its exact covariance identity. Version 2 corrects a genuine error of v1: the increment-oscillation inequality E[(Delta_i f)^2 | F_{i-1}] <= (1/4) osc_{e_i}(f)^2 was asserted for ARBITRARY probability measures; it is false in general (Example 3.4: two perfectly correlated spins, f = X_2, give E[(Delta_1 f)^2] = 1 while osc_{e_1}(f) = 0), because the Doob increment collects influence transmitted through correlations. The correct, measure-independent statement uses the CONDITIONAL oscillation (Lemma 3.5); passing back to the raw single-link oscillation requires a decoupling hypothesis (H-DEC) bounding the influence-leakage matrix, of Dobrushin type — plausible for the interpolating Gibbs measures nu_{k,t} in the small-field weak-coupling regime, but unproven, and structurally akin to the (H-DOB-blk) family of the audited chain. On exact Gibbs chains the v1 bound is violated already at weak coupling for delocalized observables, while the (H-DEC)-corrected bound holds with the Dobrushin coefficient. Under (H-DEC), the imported oscillation input (A2) (now cited from 2602.0069 v2: traceable, conditional — beta_LF dichotomy included), and the lattice-animal lemma (proved here, verified exactly), the main theorem holds: sup_t sigma_{nu_{k,t}}(V_k^irr) <= C uniformly in the RG scale k, by the exact scale cancellation M 2^{-4k} = 4(L/a_0)^4. The Duhamel interface then delivers a one-step rate delta_k = O(4^{-k}) — precisely the geometrically summable rate that Assumption 3.5 of 2602.0063 v3 requires (its Remark 3.7 with eta = 2) — CONDITIONALLY on (H-DEC) + (A2) + the assumed blocking contraction (H-LIP). v1's closing claim \"this establishes the RG-Cauchy property\" is softened accordingly: this paper supplies the leading candidate for closing (H-CAUCHY), not its proof. All quantitative claims, including the counterexample and the Dobrushin-corrected bound on exact Gibbs chains, are adjudicated in a companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0070", "abstract_url": "https://www.ai.vixra.org/abs/2602.0070", "first_submitted_at": "2026-02-14T18:53:53+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T22:13:35+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0070-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-14T18:53:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0070v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T22:13:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0070v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "b40539a6faa1f229debea10e73ee729a6fdc98de8cd9e8b47339f465528132f4", "canonical_bytes": 364424 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:daaf24aa-b5f9-4840-93b8-49874887d2e7", "version_id": "arr:version:3ac6c0e3-ad5f-4ed3-90f6-5fd12d304619", "id": "ARR-2026-6TNWJANDFS91097E", "version": "v1", "record_type": "research_paper", "title": "Influence Bounds for Polymer Remainders in Balaban's Renormalization Group: an Unconditional Efron-Stein Bound and a Conditional (B6) Closure for the RG-Cauchy Programme in 4D Lattice Yang-Mills", "abstract": "We study the influence estimate — Assumption (B6) — required by the RG-Cauchy summability framework for blocked observables in four-dimensional SU(N_c) lattice Yang-Mills theory, measured by the Efron-Stein seminorm sigma_nu(f)^2 = sum_e E_nu[Var_{nu_e}(f)]. In the small-field regime of Balaban's multiscale effective action, under (A1) a polymer representation, (A2) a per-link oscillation bound with irrelevance factor 2^(-2k), and (A3) lattice-animal counting — all imported from the traceability companion 2602.0069 v2 (conditional) — we prove the UNCONDITIONAL seminorm bound sup_t sigma_{nu_{k,t}}(V_k^irr) <= C independent of the RG scale k: the single-link conditional variance obeys Var_{nu_e}(f) <= (1/4) osc_e(f)^2 for EVERY measure (Lemma 3.2 — conditioning on all other links freezes them, so no influence leaks; this is the sound half, in exact duality with the sibling paper 2602.0070, whose per-link lemma failed but whose covariance identity was exact). Version 2 corrects the unsound half: v1's covariance bound |Cov_nu(f,h)| <= sigma_nu(f) sigma_nu(h) (its Eq. (18)) is FALSE for non-product nu — Example 3.5: perfectly correlated spins give sigma_nu(X_2) = 0 < 1 = Var_nu(X_2) — because Efron-Stein tensorisation is an independence theorem, and the interpolating Gibbs measures nu_{k,t} couple links. On exact Ising chains the tensorisation ratio Var/sum E[Var_e] equals 1.00/1.35/3.40/52.4 at J = 0/0.15/0.5/1.5. Restoring the Duhamel application requires APPROXIMATE TENSORISATION of variance (H-AT): Var_nu(f) <= C_AT sum_e E_nu[Var_{nu_e}(f)] uniformly along the interpolation — a Dobrushin-uniqueness-type condition, the same family as the sibling's (H-DEC) and the chain's (H-DOB-blk), verified here on exact Gibbs chains at weak coupling (C_AT ~ 1.35) and violated without it. There is also a seminorm-interface gap: the companion Duhamel lemma is proved for the Doob seminorm, and sigma_Doob is NOT dominated by the Efron-Stein seminorm for non-product nu (same counterexample; the two seminorms are incomparable in general). Conclusion: (B6) AS CONSUMED by the RG-Cauchy argument is closed conditionally on (H-AT) (or (H-DEC)); the unconditional content of this paper is the Efron-Stein seminorm bound and its scale-uniform M 2^(-4k) = 4(L/a_0)^4 cancellation (with the convergence threshold kappa > log C_anim of v1's Remark B.1 confirmed). Joint statement with 2602.0070 v2: the UV block's only open probabilistic input is Dobrushin-type decoupling of the interpolating measures. All claims, including both counterexample adjudications and the weak-coupling validation of (H-AT), are machine-verified in a companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0072", "abstract_url": "https://www.ai.vixra.org/abs/2602.0072", "first_submitted_at": "2026-02-14T11:43:03+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T22:27:51+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0072-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-14T11:43:03+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0072v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T22:27:51+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0072v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8f817fb47566489fd07ffde0d86ae6a0a647eb80db008c6bd636b4f69a3a79f8", "canonical_bytes": 355928 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e0d24429-dcc2-4929-a113-1f1c49e633be", "version_id": "arr:version:62617124-7b23-43fe-bdfb-bf911e785324", "id": "ARR-2026-70T922KQ6294MT24", "version": "v1", "record_type": "research_paper", "title": "RG-Cauchy Summability for Blocked Observables in 4d Lattice Yang-Mills Theory via Balaban's Renormalization Group — a Conditional Summability Theorem", "abstract": "We prove, conditionally on an explicit hypothesis ledger, that expectations of blocked, bounded Lipschitz observables at a fixed physical scale l > 0 form an absolutely summable telescoping sequence along a Balaban-matched renormalization trajectory in 4d SU(N_c) lattice Yang-Mills theory with a_k = a_0 2^(-k); in particular the continuum-limit state omega(O) = lim_k exists on the blocked class A^block_l. The architecture is unchanged from v1: (i) an exact RG identity (law of iterated expectations — which resolves at the structural level the \"on/off-vs-k->k+1\" gap flagged in the sibling audits: the one-step comparison here genuinely is a scale comparison); (ii) pushforward stability for blocked observables from approximate centering and Gaussian control of fast modes; (iii) measure comparison by Duhamel interpolation with influence control. Version 2 repairs the single broken brick: v1's Lemma 7.1 asserted the covariance bound for the Efron-Stein seminorm for arbitrary measures while proving the Doob martingale identity; per the sibling audits (2602.0070/0072 v2, same two-spin counterexample) the ES bound is false for non-product nu and the two seminorms are incomparable, so converting the ES-form input (B6) into the Doob-form covariance control requires the decoupling hypothesis (H-DEC/AT) (Dobrushin-type, verified on exact Gibbs chains at weak coupling). The main theorem is restated with the full ledger: Assumption 3.6 (blocking contraction, (H-LIP)), Assumption 5.1 with (B6) as the CONDITIONAL Efron-Stein closure of 2602.0072 v2 and with sum_k sqrt(tau_k) < infinity in (B3) tied to the profile condition (H-theta) of 2602.0069 v2 — sharpened here by a new finding (F-SQRT): the square root halves the effective amplitude, so at the representative polylog floor (theta_0 = 1.1, A_0 = 1) the sum is formally convergent but its crossover lies beyond j ~ e^1668, i.e. practically divergent; (B3) realistically requires power-law-strength p_0, and (H-P0) rejoins the ledger unless the amplitude is large — plus (H-DEC/AT) and trajectory matching. Under this ledger, the one-step error is O(4^(-k)) + O(sqrt(tau_k)), absolutely summable, and Assumption 3.5 of 2602.0063 v3 — the RG-Cauchy hypothesis (H-CAUCHY), whose naive bridge is not summable (F-SUM) — HOLDS FOR THE BLOCKED CLASS: the cleanest conditional delivery of (H-CAUCHY) in the series. v1's cross-reference \"Assumption 4.1 of [18]\" is corrected to Assumption 3.5, and the companion references are updated from their withdrawn \"unconditional\" titles to the audited versions. All mechanical steps (exact RG identity, Lipschitz iteration, pushforward stability in a Gaussian toy, telescoping arithmetic, and both counterexample adjudications at the Lemma 7.1 junction) are machine-verified in a companion suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0073", "abstract_url": "https://www.ai.vixra.org/abs/2602.0073", "first_submitted_at": "2026-02-14T09:06:13+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T22:43:46+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0073-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-14T09:06:13+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0073v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T22:43:46+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0073v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d4cca98f18616da4a035528ef54e3e00413620b7537eeca3afd717885ce836d6", "canonical_bytes": 374978 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:364232b1-922c-46c8-9148-aa67d1e106b6", "version_id": "arr:version:8157e024-808a-46ac-94b8-16590985ec57", "id": "ARR-2026-1P88SB34HC8V492J", "version": "v1", "record_type": "research_paper", "title": "Conditional Continuum Limit of 4d SU(Nc) Yang-Mills Theory via Two-Layer Architecture, RG-Cauchy Uniqueness, and Step-Scaling Confinement", "abstract": "Building on the lattice results of Papers [E26I]-[E26IX] — which, per the series audit (all companions now at v2/v3), are WINDOWED and CONDITIONAL rather than unconditional — we give a conditional construction of a scaling-limit state for pure SU(N_c) lattice Yang-Mills theory in four Euclidean dimensions, along dyadic lattice spacings a_k = a_0 2^(-k). The construction proceeds via a two-layer architecture. Layer 1 (Local fields): for bounded gauge-invariant local observables, expectations converge — without extracting subsequences — to a unique limit; precompactness is trivial (| _{a,L}| <= 1), and uniqueness follows from a multiscale RG-Cauchy estimate (Assumption 3.5), the single hard analytic input of this layer: as already recorded in v2 (Remark 3.6, Appendix B), the naive asymptotic-freedom rate g_k^2 ~ c/k is NOT summable, so summability is a genuine hypothesis, not a consequence of the chain. Layer 2 (Confinement): the physical string tension sigma_phys > 0 is established through step-scaling of Creutz ratios at fixed physical loop size, conditionally on Assumptions 4.4, 4.7 and 4.9. The limiting state inherits Osterwalder-Schrader positivity and admits Hilbert-space reconstruction; the mass gap is conditional on a uniform physical transfer-matrix gap (Assumption A.2) and strong continuity (Assumption 5.5). Version 3 retags the input layer to the audited chain: the uniform-LSI inputs are conditional on (H-P0)+(H-YGZ)+(H-SFI)+(H-ABS), the DLR-LSI/mass-gap route on (H-DOB-blk), and all lattice statements hold in the volume window L_vol <= e^(C/g^2+O(1)). A new window-compatibility lemma (Lemma 1.4) shows this window is NOT an obstruction to the continuum limit: along the 2-loop trajectory the required lattice size L/a_k = 2^k L/a_0 satisfies ln(L/a_k) ~ 0.69 k while the audited window allows ln L_lat <= 32.3/g_k^2 ~ 3.12 k — a margin factor ~4.5 at the series' representative arithmetic. Assumption A.2 is now cross-referenced to its conditional lattice supplier (2602.0054 v2: transfer-matrix gap under (H-DOB-blk)+(H-P0), in kernel form). All quantitative claims, and exact validations of both layers in a solvable d = 2 toy, are adjudicated in a companion numerical suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0063", "abstract_url": "https://www.ai.vixra.org/abs/2602.0063", "first_submitted_at": "2026-02-13T16:30:51+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-06T21:28:43+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0063-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-13T16:30:51+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0063v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-14T08:18:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0063v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-06T21:28:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0063v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c8dacbd5e47dcc10bbb4f80ece4c3a516b137288b0c4cd3a806523a6286f716f", "canonical_bytes": 409334 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:0941931e-f907-430f-b2ca-1a709414b23e", "version_id": "arr:version:1603fc06-e5af-4a6d-adcf-d8e54411386d", "id": "ARR-2026-09869HXY878C7V5J", "version": "v1", "record_type": "research_paper", "title": "Uniform Coercivity, Pointwise Large-Field Suppression, and Conditional Closure of the Lattice Yang-Mills Mass Gap at Weak Coupling in d = 4", "abstract": "We address the remaining interface gaps in the programme [E26I]-[E26VIII] toward a uniform log-Sobolev inequality (LSI) and transfer-matrix spectral gap for lattice SU(N_c) Yang-Mills in d = 4 at weak coupling. Four gaps are treated: (G1) the pointwise-in-background validity of Balaban's T-operation small-factor bound -- stated in v2 as the explicit hypothesis (H-PTW), since the detailed audit appendices announced in v1 were absent from the document (their references rendered as \"??\"); (G2) a uniform small-field coercivity estimate for the effective action; (G3) uniform analyticity of boundary terms; (G4) a quantitative bootstrap of all constants. The central correction of v2: the sign of the one-step coupling drift in v1's Theorem 5.2 (g_{k+1}^{-2} = g_k^{-2} + 2 b_0 ln L_RG, coupling weakening toward the infrared) is inverted relative to asymptotic freedom, and contradicts the companions' own use of n_max ~ 1/(2 b_0 g^2 ln 2) (ai.viXra:2602.0032 Sec. 8, 2602.0033, 2602.0041 Sec. 7.3), a formula meaningful only if the coupling grows along blocking and exits the weak regime. With the corrected sign the monotone bootstrap of v1's Theorem 5.3 reverses: the inductive conditions are guaranteed only up to the finite horizon k*(beta) = (g_0^{-2} - gamma_0^{-2})/(2 b_0 ln L_RG) + O(1), and since the multiscale construction uses log_2 L scales, the conclusion holds on the volume window log_2 L <= k*(beta), i.e. L <= e^{C/g^2 + O(1)} with C = 1/(2 b_0) = 24 pi^2/(11 N_c) -- exactly the window of the companion papers ai.viXra:2602.0032/0033 (v2). Full volume-uniformity would additionally require a strong-coupling handoff beyond the crossover scale (Osterwalder-Seiler regime), stated as hypothesis (H-XOVER) and not established here; accordingly the \"unconditional closure\" of v1 is retitled to conditional closure. Version 2 also repairs the dangling \"??\" references, supplies the missing proof of Lemma 3.1, rewrites the proof of Lemma 7.4 in the series' fundamental-trace convention (its statement W''(0) = 1/(2N_c) is correct; the v1 proof mixed normalized and fundamental traces), corrects sum_{k>=0} (k+1) 2^{-3k} = 64/49 (v1: 8/49), and fills in the companion identifiers. All corrections are verified in a companion numerical suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0051", "abstract_url": "https://www.ai.vixra.org/abs/2602.0051", "first_submitted_at": "2026-02-12T19:22:19+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T09:42:09+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0051-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:22:19+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0051v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T09:42:09+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0051v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "110d7c672a9da19afcc562d47caedd589bd8f1ad89a4f1fbe440963dbda7a04d", "canonical_bytes": 333317 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:46495b48-f9d3-4d5c-beb6-57d9b3ec43ce", "version_id": "arr:version:279f2375-867e-4fcd-867d-021377b00360", "id": "ARR-2026-2695DMHYEK9NEBXD", "version": "v1", "record_type": "research_paper", "title": "Interface Lemmas for the Multiscale Proof of the Lattice Yang-Mills Mass Gap", "abstract": "This replacement restores the paper originally submitted as version 1 and retracts its claimed unconditional closure of the weak-coupling lattice Yang-Mills mass-gap chain. The principal-logarithm construction in Lemma A.1 fails at central elements such as -I in SU(2), and the printed argument does not establish the required measurable conditional kernel. The proof of Lemma 6.2 applies the Holley-Stroock comparison in the wrong direction: it does not give a coupling-uniform per-block log-Sobolev bound on the unbounded range beta >= beta_0. A bounded beta window can control that per-block estimate, but it does not prove Lemma 6.3, which separately requires an inter-block contraction hypothesis. Three numerical samples and an upper bound on the oscillation are recorded only as numerical evidence; they do not prove linear growth of the optimum or a vanishing infimum. The remaining horizon-transfer, analyticity, and boundary-uniform interfaces are classified as conditional or not established. Corollary 7.3 and the abstract's unconditional mass-gap conclusion are withdrawn. No numbered lemma is declared false unless the corrective note supplies the stated counterargument; otherwise the status is expressly \"not established.\"", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0052", "abstract_url": "https://www.ai.vixra.org/abs/2602.0052", "first_submitted_at": "2026-02-12T19:21:09+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-31T23:07:04+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0052-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:21:09+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0052v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T10:23:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0052v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-31T23:07:04+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0052v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4ce8cb39d5e47b59c27c88a3398660ca61985dff1f7589cf04c8ea472e09733b", "canonical_bytes": 815103 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:190e13a7-5425-4037-a40a-f565d429c9b2", "version_id": "arr:version:9419ab59-4ce4-47bb-a1bd-92cc73e22eb3", "id": "ARR-2026-0S1R9TEN1580VT82", "version": "v1", "record_type": "research_paper", "title": "DLR-Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang—Mills at Weak Coupling: a Conditional and Windowed Reduction", "abstract": "We study the passage from the uniform log-Sobolev inequality (LSI) on periodic tori, developed in the companion series, to a DLR-uniform LSI for the conditional Gibbs specification of SU(N_c) lattice Yang-Mills in d >= 3 at weak coupling (beta >= beta_0), and from there to a mass gap via Stroock-Zegarlinski and Osterwalder-Seiler reflection positivity. Version 2 corrects the logical status of the main results after a quantitative audit (companion numerical suite included; Appendix A). (i) The fiber assembly (Lemma 3.5) assumes the block Dobrushin condition delta < 1, which v1's own Remark 3.6 left unverified; the printed influence bound c_ij <= tanh(beta n_bd/2) tends to 1 as beta -> infinity and yields delta < 1 only for beta <~ 10^(-2) (d=3) or beta <~ 10^(-3) (d=4) — the opposite of the weak-coupling regime. A rotor exhibit shows the genuine worst-case block influence also tends to 1, so no worst-case criterion can close the gap: the condition is now the explicit hypothesis (H-DOB-blk), and v1's claim of removing the Dobrushin-type Assumption 6.3 of [14] is withdrawn — the present paper reduces that assumption to (H-DOB-blk). (ii) The quantitative absorption in Proposition 4.3 inherits hypothesis (H-P0) of ai.viXra:2602.0052(v2): under the polylog penalty floor p0(g) >= c_0 |log g|^(1+epsilon_0) the required inequality e^(-c p0(g_k)) <= C L_RG^(-(d-1)k) fails already at k = O(1). (iii) The proof assumes g_k <= gamma_0 for all k <= n_max ~ log_LRG diam(Lambda'); with the corrected asymptotic-freedom flow of the series erratum this holds only on the volume window log_LRG diam(Lambda') <= k*(beta), i.e. diam(Lambda') <= e^(C/g^2+O(1)). Theorems 1.1-1.2 are therefore restated as windowed and conditional on (H-DOB-blk) and (H-P0). What survives unconditionally — and is validated numerically — is the boundary-uniformity mechanism itself: the per-plaquette oscillation and gradient bounds (Lemma 3.1; sharp for N_c=2), the \"frozen = slow\" reduction (Lemma 3.2), the refined dynamical large-field event, the energy-penalty identity ||U-1||_HS^2 = 2N_c(1 - Re tr U / N_c), the TV <= tanh(osc/4) lemma with its two-point equality case, and the Bakry-Emery constant N_c/4 in the = -2 tr(XY) convention. The contribution of the paper is thus retagged: a boundary-uniform reduction of the DLR-LSI and the mass gap to (H-DOB-blk)+(H-P0) within the volume window — not an unconditional mass gap.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0053", "abstract_url": "https://www.ai.vixra.org/abs/2602.0053", "first_submitted_at": "2026-02-12T19:11:43+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T10:47:13+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0053-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:11:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0053v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T10:47:13+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0053v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "948096d3c38dba660a5bfc5335257dede9eafd1a46f78100a8d35cf9faffdfdc", "canonical_bytes": 434962 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:547895eb-6d7d-4ecb-a3fa-6778862597b3", "version_id": "arr:version:f906c221-ef59-4abf-a9fc-0c8dbeb9040c", "id": "ARR-2026-2MF2AYPVBX9V5T7Y", "version": "v1", "record_type": "research_paper", "title": "From Uniform Log-Sobolev Inequality to Mass Gap for Lattice Yang—Mills at Weak Coupling: a Conditional and Windowed Assembly", "abstract": "This paper assembles the route from the uniform log-Sobolev inequality (LSI) on periodic tori to a transfer-matrix spectral gap for SU(N_c) lattice Yang-Mills in d >= 3 at weak coupling: periodic LSI + boundary-uniform RG outputs => DLR-LSI => Stroock-Zegarlinski mixing => exponential clustering => (reflection positivity) => Delta_phys > 0. Version 2 corrects the logical status of this assembly after a quantitative audit (companion numerical suite; Appendix A). (i) v1 claimed the route \"bypasses any explicit Dobrushin contraction estimate\". This is withdrawn: the DLR-LSI input (Theorem 5.1) invokes the multiscale fiber assembly of [2], whose inter-block step IS a Dobrushin-type condition — made explicit as (H-DOB-blk) in ai.viXra:2602.0053(v2), the detailed companion treatment which v1 did not cite. v1's supporting claim in the proof of Theorem 5.1, that the fiber oscillation is \"O(1) regardless of beta\", is also withdrawn: the conditional fast potential obeys osc = 2 beta n_plaq + C_poly, LINEAR in beta (2602.0053(v2), Lemma 3.2; reproduced numerically here). (ii) The quantitative absorption in Proposition 4.7 inherits hypothesis (H-P0) of ai.viXra:2602.0052(v2), and the corrected asymptotic-freedom flow restricts all statements to the volume window L <= e^(C/g^2+O(1)): Theorem 1.1 is restated as windowed and conditional on (H-DOB-blk)+(H-P0). (iii) The erratum for [2] in Sec. 10 is corrected: v1's items (a) and (c) (\"Assumption 6.3 is removed\", \"Theorem 1.1(ii) of [2] is now unconditional\") are withdrawn — the assumption is REDUCED, not removed; item (b) (withdrawal of Lemma 6.4 of [2] due to the volume factor (MR^n_max)^d) was correct and stands. (iv) A new technical finding (Remark 2.8): the row-normalized transfer operator T-hat of Definition 2.2 satisfies the correlation identities (12)/(29) exactly only when its normalizer D(sigma) = int K(sigma,sigma') d sigma' is constant (true in the d=2 toy, false for d >= 3 where the spatial factor e^((beta/2)S(sigma)) survives); the correct identities hold in kernel form (with K, or the symmetrized D^(-1/2) K D^(-1/2)). Since D^(-1)K and D^(-1/2)KD^(-1/2) are similar, the spectrum — hence Delta_phys — is unaffected; adjudicated numerically (spectra equal to 10^(-16); the T-hat-form of (29) deviates from the exact path integral by 0.30 in a d=3 toy). What survives and is validated end-to-end in exact toys: the slab splitting (Definition 2.1), self-adjointness and detailed balance (Lemma 2.3), the spectral clustering-to-gap step (Proposition 2.4), Osterwalder-Seiler reflection positivity including the Peter-Weyl positive-definiteness of Re tr(UV^(-1)) (Theorem 2.6), and the gauge-invariance lemmas of Sec. 8. The contribution is retagged: a correct and verifiable transfer-matrix back end for the program, whose front end (DLR-LSI) is conditional and windowed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0054", "abstract_url": "https://www.ai.vixra.org/abs/2602.0054", "first_submitted_at": "2026-02-12T19:10:34+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T11:08:38+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0054-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:10:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0054v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T11:08:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0054v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "359cb2d1bd2a934e305d205ab7a86bc7a48b270f70e8593bbbd3892e97afb7e1", "canonical_bytes": 429551 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:3438b6b8-79cf-4eba-89f2-4abcc295955e", "version_id": "arr:version:f75bf16b-ad24-4b23-982b-72f0b3ff3897", "id": "ARR-2026-1M72VBGYEF9TX8KW", "version": "v1", "record_type": "research_paper", "title": "Residual Derivative Bounds and Windowed Uniform Log-Sobolev Inequality for SU(Nc) Lattice Yang-Mills at Weak Coupling", "abstract": "We prove residual derivative bounds for the polymer expansion of Balaban's multiscale decomposition of the Wilson lattice gauge measure for SU(N_c) in dimension d >= 3, and we assemble them, together with the companion series, into a uniform log-Sobolev inequality. Version 2 corrects the status of this assembly after a quantitative audit. (i) The core mechanism of the paper — locality of polymer functionals, Cauchy estimates on Balaban's analytic domains, and a volume-independent counting bound for connected polymers containing a fixed link — survives intact and is validated numerically; it yields a pointwise derivative bound on the polymer residual with constants independent of the lattice volume, CONDITIONALLY on Balaban's small-field inputs (B1)-(B4). (ii) However, the final step of v1's Theorem 3.5, the inequality k <= C_RG(1+beta_k), relied on the inverted-sign running-coupling flow of the series erratum; with the correct asymptotic-freedom flow the reduced coupling beta_k DECREASES along the cascade, the small-field condition g_k <= gamma_0 is available only for k <= k*(beta), and the derivative bound holds in the windowed form C_res(1+beta) for L_vol <= e^(C/g^2+O(1)). (iii) The assembly of the main theorem inherits two hypotheses identified in the audits of 2602.0052 v2 and 2602.0053 v2: the large-field absorption step requires a power-law penalty exponent — hypothesis (H-P0) — since with the stated polylog floor the suppression factor trivializes (e^(-c_sf p0(gamma_0)) ~ 0.95 at gamma_0 = 0.1) and the absorption inequality fails at every scale (excess >= 10^4.6); and any quantitative use of the conditional fiber LSI via Holley-Stroock carries the penalty e^(-2 beta n_plaq) — hypothesis (H-YGZ) (log10 alpha_blk ~ -5559 at gamma_0 = 0.1, n_plaq = 64). (iv) Version 1's Corollary 1.2 and Remark 5.1 claimed that the Dobrushin-type Assumption 6.3 of Paper I is \"no longer needed\" via the DLR route of the companion 2602.0053; the v2 audit of that companion shows the route REDUCES Assumption 6.3 to an unverified block condition (H-DOB-blk) whose printed bound c_ij <= tanh(beta n_bd/2) trivializes at weak coupling. Accordingly, v1's closing claim is replaced: the uniform LSI of Theorem 1.1 is WINDOWED and CONDITIONAL on (H-P0) and (H-YGZ), and the mass gap of Corollary 1.2 is additionally conditional on (H-DOB-blk). This replacement also records the completed retagging of the chain: the companion 2602.0054 has been audited and replaced (v2, conditional/windowed assembly), so 2602.0051-0055 now all carry their v2 statuses; reference [6] is corrected (v1 listed 2602.0053 under the title of 2602.0054). All quantitative claims are adjudicated in a companion numerical suite (9 deterministic checks).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0055", "abstract_url": "https://www.ai.vixra.org/abs/2602.0055", "first_submitted_at": "2026-02-12T19:09:28+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T20:00:57+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0055-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:09:28+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0055v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T20:00:57+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0055v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "44f350a4c9a0f4c247e4a47cd03583a1640524f20e925a5a5929c500b86311e1", "canonical_bytes": 396324 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:336a3dc6-9a6e-4667-a8de-71036edc5bfd", "version_id": "arr:version:79283467-fa48-438c-aec0-a394e57d9d74", "id": "ARR-2026-1KD8YWD6KE8SKTHQ", "version": "v1", "record_type": "research_paper", "title": "Large-Field Suppression for Lattice Gauge Theories: From Balaban's Renormalization Group to Conditional Concentration — a Conditional and Windowed Verification", "abstract": "We verify, at the level of form, the large-field hypothesis (Hypothesis 4.2) of the companion paper on integrated cross-scale derivative bounds for Wilson lattice gauge theory (Paper III). The proof rests on three ingredients: (i) a dictionary lemma translating the Hilbert-Schmidt large-field condition on plaquette holonomies into Balaban's Lie-algebra formulation; (ii) an interface lemma connecting conditional measures with Balaban's T-operation and its uniform small-factor bound on admissible background fields (Eq. (1.89) of Balaban, Large field renormalization II); (iii) the uniformity estimate (Eq. (1.75) ibid.) ensuring that slow-field dependence contributes only an O(1) multiplicative constant. For d = 2, we give an independent proof via character-positive convolutions that avoids the Balaban machinery entirely. Version 2 corrects the status of these results after the quantitative audit of the series (ai.viXra:2602.0051-0055, all v2). (a) v1's claim that the bound is \"more than sufficient\" for the absorption condition of Paper III is withdrawn: the printed small factor is exp(-c p0(g_k)) with c = 2/(1+beta_0), and with the polylog floor on p0 the suppression trivializes (e^(-c p0(gamma_0)) ~ 0.95) and the absorption inequality fails at every scale (excess >= 10^4.6); effectiveness requires the power-law hypothesis (H-P0) of 2602.0052 v2. (b) v1's premise \"p0(g_k) -> infinity as g_k -> 0 along the flow\" and Sec. 7's appeal to a stability theorem rely on the inverted-sign running-coupling flow of the series erratum; with the correct asymptotic-freedom flow the small-field condition g_k <= gamma_0 holds only for k <= k*(beta), and all statements are windowed: L_vol <= e^(C/g^2+O(1)). (c) v1's Remarks 4.1-4.2 (slow-field identification and Balaban conditional representation) are unproved interface statements; they are made explicit here as hypothesis (H-SFI), cf. the interface lemmas of 2602.0052 v2. (d) In d = 2 the prefactor K_beta(1)/Z(U_B) of Proposition 6.4 is not uniform in beta, so the d = 2 route verifies a fixed-beta variant only; this is now stated in the theorem. What survives unconditionally and is validated in the companion numerical suite: the HS/Lie-algebra dictionary (Lemma 2.1), the gauge-invariance identity (Remark 2.2), the block event inclusion (Lemma 3.2), and the character-positivity mechanism of Section 6 (Peter-Weyl positivity of the Wilson weight, convolution stability, maximum at the identity, and conditional tail domination in an exact d = 2 toy).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0056", "abstract_url": "https://www.ai.vixra.org/abs/2602.0056", "first_submitted_at": "2026-02-12T19:07:45+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T21:03:37+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0056-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:07:45+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0056v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T21:03:37+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0056v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "17aa1773c27cd0be4c452b43e2de7d91050e63842af5fec7cfd01ae74d359207", "canonical_bytes": 328405 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:c2a3b5ac-622f-4dc0-80af-6e431d9dd491", "version_id": "arr:version:a482390b-6e06-49ae-8642-d4f09b166964", "id": "ARR-2026-62METTRRHF9Q081B", "version": "v1", "record_type": "research_paper", "title": "Integrated Cross-Scale Derivative Bounds for Wilson Lattice Gauge Theory: Closing the Log-Sobolev Gap — a Conditional and Windowed Closure", "abstract": "We prove integrated cross-scale derivative bounds that replace the unverified Assumption 5.4 of the companion 2602.0041. Combined with two explicit large-field inputs (Hypotheses 3.2 and 4.2) and the conditional inequalities of 2602.0046, this yields — under the audited hypotheses listed below and within the stated volume window — the corresponding log-Sobolev assembly for the Wilson lattice gauge measure at sufficiently weak coupling, with constant independent of L_vol inside the window. The key decomposition into small-field and large-field contributions survives verbatim from v1, as do the sweeping-out modification (an L^1 bound in place of an essential supremum, and a shifted essential supremum over G_{k+1}), the Rothaus closure, the SU(2), d=2 toy-model analysis, and the correction lambda_1 >= alpha_* to Proposition 6.1(2) of 2602.0041. Version 2 corrects the logical status of the assembly after the quantitative audit of the series (ai.viXra:2602.0051-0056, all v2). (a) The Absorption step in the proof of Theorem 1.1 relied on the premises \"p0(g) -> infinity as g -> 0 along the flow\" and \"if beta_k grows sufficiently with k\": both use the inverted-sign flow of the series erratum and are withdrawn; with the correct asymptotic-freedom flow all statements hold in the window k <= k*(beta), i.e. L_vol <= e^(C/g^2+O(1)). (b) A new finding (F-ABS): the absorption condition (16) consumes Hypothesis 4.2 in the strong exponent form e^(-c beta_k eps_k^2), but the companion verification (2602.0056 v2) delivers only e^(-c_sf p0(g_k)) with c_sf = 2/(1+beta_0) — bounded along the window — so (16) fails at every scale k >= 2 with the Balaban-compatible thresholds (9), even under (H-P0). The strong form is therefore an additional explicit hypothesis (H-ABS), and its saturated variant eps_k = eps_* opens a second window k <= k_abs proportional to beta eps_^2. (c) The inputs are retagged per their v2 verifications: Hypothesis 3.2 is windowed and conditional on Balaban's small-field inputs (2602.0055 v2); Hypothesis 4.2 is form-level and conditional on (H-SFI)+(H-P0) (2602.0056 v2); the fiber LSI consumed by Corollary 1.2 inherits (H-YGZ) (2602.0053 v2). (d) Reference hygiene: v1's reference [8] was a self-citation of the present paper and is removed; the Wilson duplicate is removed; the audited chain 2602.0051-0056 (v2) is cited. What survives and is validated in the companion suite: the per-direction Wilson bound (Lemma 3.1), the energy-distance identity (13), the single-plaquette tail (Proposition 7.1, Table 1 reproduced digit-by-digit, with its caption/values normalization mismatch fixed), the impossibility Remark 7.2, the factorization step (21), the Rothaus closure, and Appendix A's lambda_1 >= alpha_.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0057", "abstract_url": "https://www.ai.vixra.org/abs/2602.0057", "first_submitted_at": "2026-02-12T19:06:11+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T21:06:18+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0057-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-12T19:06:11+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0057v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T21:06:18+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0057v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f7dbac96b0c03e59bd883aa664c9bbf0b48100f29560a2acbf504a067d084bb5", "canonical_bytes": 382115 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e702542c-4156-413c-9f7e-99a1c1df3d66", "version_id": "arr:version:3dc4b4cb-0847-4735-938f-848de523d2f6", "id": "ARR-2026-7709A2RGAP84Y9YZ", "version": "v1", "record_type": "research_paper", "title": "Ricci Curvature of the Orbit Space of Lattice Gauge Theory and Single-Scale Log-Sobolev Inequalities", "abstract": "We establish that the orbit space B = A/G of SU(N_c) lattice gauge theory satisfies the Riemannian curvature-dimension condition RCD*(N_c/4, dim A); in particular, it satisfies CD(N_c/4, infinity) in the sense of Lott-Villani-Sturm. The proof shows that the configuration space A = SU(N_c)^{|B_1(Lambda)|}, with the bi-invariant product metric = -2 tr(XY), is an Einstein manifold with Ric_A = (N_c/4) g_A (Proposition 2.2), and applies the stability of the RCD* condition under quotients by compact groups of measure-preserving isometries (Galaz-Garcia-Kell-Mondino-Sosa). This bypasses O'Neill computations and handles the singular stratum (reducible connections) automatically. As a consequence we derive a conditional log-Sobolev inequality for measures d mu = e^{-Phi} d nu / Z with constant alpha = (N_c/4) e^{-osc(Phi)}. All constants are computed explicitly for SU(2) and SU(3). This provides the geometric input in a program aiming at a volume-uniform log-Sobolev inequality for SU(N_c) lattice Yang-Mills theory at weak coupling; the complementary analytic input is developed in the companion papers cited in Section 6.1. Note added (v3). Version 3 accompanies the paper with a numerical verification suite (full Einstein tensor for SU(2/3/4); the convention triangle N_c/4 <-> N_c/2 <-> 1/2 closing the series' Ricci bookkeeping; the horizontal characterization at machine precision; the Bakry-Emery convention on the Gaussian via the exact Gross optimizers; Holley-Stroock in LSI form; and the exact energy/entropy correspondence for a Z_2 quotient toy). It corrects a sign in Section 5.1 ([T^a,T^b] = +eps^{abc} T^c requires T^a = -(i/2) sigma^a), repairs the attributions in Section 1.4 (the O'Neill-sketch Ricci statement lives in ai.viXra:2602.0036, whose v2 sharpened the -tr-convention value to N_c/2, consistent with N_c/4 here), adds the measured sectional-curvature range of SU(3) to Section 5.2, and fills in the companion identifiers in Section 6.1 with their honest status. No statement of v2 is refuted.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0046", "abstract_url": "https://www.ai.vixra.org/abs/2602.0046", "first_submitted_at": "2026-02-10T18:37:34+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-06T09:13:33+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0046-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-10T18:37:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0046v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-12T19:04:00+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0046v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-06T09:13:33+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0046v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3d98e09edc4ef54efb92a89100e3a3fb2ad0f306021ac84d70de8b55bed9315f", "canonical_bytes": 301920 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:7a822774-734f-4d09-9b1c-29eca0c7bb1f", "version_id": "arr:version:a58f774c-df36-495c-98cf-57888bc13617", "id": "ARR-2026-3TG8KQ8WTF9M4SP7", "version": "v1", "record_type": "research_paper", "title": "Uniform Log-Sobolev Inequality and Mass Gap for Lattice Yang-Mills Theory: A Conditional Reduction", "abstract": "This replacement corrects the title and foregrounds the logical status already partly recorded in public version 3. The uniform log-Sobolev conclusion requires the cross-scale derivative hypothesis (H-XSD), whose purported companion-paper discharge is not re-verified here. The mass-gap conclusion additionally requires the Dobrushin-type hypothesis (H-DOB), or an independently valid alternative DLR-LSI/mixing route. Neither input is proved by this manuscript alone. No unconditional weak-coupling lattice mass gap, continuum construction, Osterwalder-Schrader reconstruction, or Clay-problem result is claimed. The preserved version 3 follows the correction page for provenance.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-09", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0041", "abstract_url": "https://www.ai.vixra.org/abs/2602.0041", "first_submitted_at": "2026-02-09T20:45:44+00:00", "latest_declared_version": "v4", "latest_submitted_at": "2026-07-31T23:15:37+00:00", "mirrored_version": "v4", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0041-v4.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-09T20:45:44+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0041v1.pdf" }, { "version": "v2", "submitted_at": "2026-02-12T19:02:28+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0041v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-06T08:50:32+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0041v3.pdf" }, { "version": "v4", "submitted_at": "2026-07-31T23:15:37+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0041v4.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d268921dd8fd3a1ee4b1440118692ffc53472e1c3ef84f84736b95016b1ba93d", "canonical_bytes": 547537 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:d89ef3e4-cca2-4e35-bc6c-ce4d893b4155", "version_id": "arr:version:0291b9f9-ffea-4e83-984d-e6275b9c4570", "id": "ARR-2026-6RKVSY9K529RTVRV", "version": "v1", "record_type": "research_paper", "title": "Uniform Poincare Inequality for Lattice Yang-Mills Theory Via Multiscale Martingale Decomposition", "abstract": "We prove that the lattice Yang-Mills measure with gauge group SU(N_c) in d = 4 dimensions at sufficiently large beta = 2N_c/g^2 satisfies a Poincare inequality with constant alpha* > 0 uniform in the lattice size L, conditionally on Balaban's constructive RG and an RG-normalized disintegration hypothesis. The proof uses: (i) the Ricci curvature bound of the gauge orbit space -- sharpened in v2 to Ric_B >= N_c/2, following the correction at its source in ai.viXra:2602.0036 (v2) -- giving a uniform spectral gap for conditional fast modes at each RG scale; (ii) Balaban's polymer derivative bounds, controlling residual cross-scale coupling; and (iii) a multiscale martingale variance decomposition avoiding recursive composition losses, with commutator coefficients D_k <= C e^{-2 kappa} 2^{-3k} made summable by the geometric scaling of transversal block averaging. Version 2 corrects the coupling-flow direction in the statement of Balaban's theorem (which improves the fallback bound of Remark 2.7: beta_k <= beta is bounded, rather than O(k)), records that the summability is robust to the block-averaging convention (new Remark 2.8: the Balaban-style convention gives 2^{-(d-2)k}, still summable), clarifies that the commutator coefficient involves the centered gradient of the conditional potential (which is the mechanism by which G_k-measurable parts drop out, as Assumption 2.6 asserts), and updates the companion references. Unlike other v2's of this series, no statement of v1 is refuted: the entire martingale machinery (commutator identity, telescoping, absorption, the assembled constant alpha*) is validated end-to-end in a companion numerical suite, exactly in a two-scale Gaussian model and against the true spectral gap in a compact four-rotor model, where the recipe's alpha* is confirmed as a valid lower bound.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0040", "abstract_url": "https://www.ai.vixra.org/abs/2602.0040", "first_submitted_at": "2026-02-08T19:36:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T08:25:35+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0040-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T19:36:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0040v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T08:25:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0040v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "6ddc16224826633cdbd0930be85d6ab1c3731d902aa214245172ab229ec545e9", "canonical_bytes": 333955 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:8660df8e-4db5-487c-bae0-c92f0994894e", "version_id": "arr:version:3311c2eb-39c8-40b5-aab6-de8f73151bfa", "id": "ARR-2026-46C3FRWKDN91YBNR", "version": "v1", "record_type": "research_paper", "title": "The Yang-Mills Mass Gap on the Lattice: A Conditional Reduction via Witten Laplacian and Constructive Renormalization", "abstract": "We reduce the weak-coupling lattice Yang-Mills mass gap to four explicitly stated hypotheses: assuming them, SU(N_c) lattice Yang-Mills theory in d=4 dimensions with Wilson action at sufficiently weak coupling has a positive mass gap m_gap >= c(N_c) e^{-C(N_c)/g^2} > 0 in lattice units, uniformly in lattice sizes L <= C_0 e^{C/g^2}. The argument combines Balaban's constructive renormalization group, a Morse-Bott/Witten-Laplacian semiclassical spectral gap estimate at the terminal scale, and a transfer-matrix trace identity. Version 1 of this paper presented the result as self-contained modulo Balaban's RG. Version 2 corrects this assessment: the proof is conditional on four explicitly stated hypotheses (Section 1.3). In particular: (i) the Morse-Bott non-degeneracy required by the Helffer-Sjostrand theory fails on the orbifold locus of the flat-connection moduli space -- including the minimum theta=0 of the Born-Oppenheimer potential -- where (d-1)(N_c^2-1-r) quartic \"toron\" zero modes appear, as we exhibit numerically on a real lattice (Proposition 5.3); and (ii) the constants of Balaban's construction must satisfy a quantitative compatibility window kappa > C' N_c^{3/2}/gamma^2 together with gamma^2 <= 2 N_c h_0, which is empty for typical O(1) decay constants and is not known to follow from Balaban's papers. Version 2 also corrects the sign of the coupling flow in the statement of Balaban's theorem, an inverted extraction regime in the transfer-matrix doubling argument (replaced by a finite-window extraction with explicit error), the definition and Hessian normalization of the Born-Oppenheimer potential (whose v1 form is numerically non-positive), and the Ricci constant of the orbit space (N_c/2, not N_c/4; direction favorable). All corrections and the surviving ingredients are verified in a companion numerical suite. None of this yields an unconditional result, and the continuum, infinite-volume problem remains expressly out of scope.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0032", "abstract_url": "https://www.ai.vixra.org/abs/2602.0032", "first_submitted_at": "2026-02-08T19:11:44+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-06T05:54:46+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0032-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T19:11:44+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0032v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T05:54:46+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0032v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "81e84ea27474bfa519ebde9af24ed40419b6a6ec57673256ab9ab20f4c5209a4", "canonical_bytes": 435318 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:101cc526-e4cf-48d9-afca-15f6b34d85f5", "version_id": "arr:version:a9ebbb3f-c4e9-4fa6-9824-fa3ee34d022a", "id": "ARR-2026-0G3K2JDS6F93CTZJ", "version": "v1", "record_type": "research_paper", "title": "The Yang-Mills Mass Gap on the Lattice: A Conditional Synthesis", "abstract": "This replacement preserves the published version 2 and appends a page-fixed erratumand an object-provenance sheet. The erratum withdraws the printed derivations ofTheorems 1.1, 3.1, and 4.1 without claiming that their conclusions for the intendedYang-Mills operators are false. It separates defects in the Euclidean-measure toground-state-measure identification, the use of a four-dimensional effective actionon a three-dimensional spatial orbit space, the volume-dependent transfer-operatortrace extraction, the finite-error resolution window, the factorisation-erroraccumulation, and the admissible-volume quantifiers. Three explicit positivetrace-class counterexamples show why ordinary spectral convergence, positivityimproving, first-excited multiplicity control, and total-tail control do not bythemselves imply gap doubling. A sufficient exact-trace repair is stated at thefinite-volume scale: the leading-eigenvalue normalisation error must be little-o ofthe sum of the two actual first-excited contributions, together with subexponentialfirst-excited multiplicities and vanishing relative excited tails. The previous v2text remains included solely for provenance; no unconditional four-dimensional orcontinuum mass-gap result is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0033", "abstract_url": "https://www.ai.vixra.org/abs/2602.0033", "first_submitted_at": "2026-02-08T15:01:30+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-31T23:09:54+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0033-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T15:01:30+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0033v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T06:19:19+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0033v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-31T23:09:54+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0033v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "878dba7cc659477ea9172a24f9dba88498d41ba49af44cfdcb1a73baa13f6285", "canonical_bytes": 1187585 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:00f66ed2-bdf7-4792-9ffd-83873a454097", "version_id": "arr:version:1ebec1ac-1150-46e7-a875-f22f30b92090", "id": "ARR-2026-00YSQD5FFQ8Y99ZZ", "version": "v1", "record_type": "research_paper", "title": "Morse-Bott Spectral Reduction and the Yang-Mills Mass Gap on the Lattice", "abstract": "This replacement restores the corrected Morse-Bott revision that was previously placed on another public record and adds an erratum delimiting its valid scope. The original manuscript used one symbol for both total loop holonomy and per-link angle, losing factors of L in the covariant symbol and metric. It also contained an incorrect sine identity, Fourier labels and normal-bundle statements that fail independently, and a determinant convention that double-counted the Faddeev-Popov factor. The replacement withdraws the claims that hypothesis (H1) was discharged and that (H-FACT) by itself replaced (H2); it records the resulting dependency loop with ai.viXra:2602.0033. What remains is a qualitative fixed-volume positivity statement, conditional quantitative implications under explicitly named hypotheses, and numerical evidence in the tested finite-volume case. The numerical checks printed in the historical revision are treated as author-reported evidence because the cited companion verifier is not present in the audited package. No unconditional continuum or infinite-volume mass-gap theorem is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0035", "abstract_url": "https://www.ai.vixra.org/abs/2602.0035", "first_submitted_at": "2026-02-08T14:26:38+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-31T23:13:34+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0035-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T14:26:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0035v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-31T23:13:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0035v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "053107800c2b81f2f6649016f095f748146acf5af073eea0a7776ab7da575db8", "canonical_bytes": 1046815 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:8f110611-e9e9-49b7-9d40-c081ad5e193a", "version_id": "arr:version:220989b2-7cd9-4b1b-8dc1-df26aa7ac4e0", "id": "ARR-2026-4F24313TF996VSTG", "version": "v1", "record_type": "research_paper", "title": "Geodesic Convexity and Structural Limits of Curvature Methods for the Yang-Mills Mass Gap on the Lattice", "abstract": "This replacement withdraws the global orbit-space Ricci lower bound and the spectral-gap corollaries derived from it. The printed proof of Theorem 3.1 traces O'Neill's horizontal sectional-curvature identity as though the total-space Ricci tensor contained only horizontal directions. The correct trace also subtracts the mixed horizontal-vertical sectional curvatures. For the bi-invariant product metric these terms are nonnegative before subtraction, so the omitted contribution has the unfavorable sign; the manuscript does not prove that the positive O'Neill term dominates it. Accordingly Theorem 3.1 is not established, rather than asserted false, and Corollaries 3.2-3.3 are withdrawn. The correction also separates a finite-dimensional orbit-space statement from later RCD results formulated for a different measure and operator, and records the broken dependency on a version of ai.viXra:2602.0035 that was not present in its public record. The local geodesic-convexity results and the independently stated structural obstruction are retained only within their stated scope.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0036", "abstract_url": "https://www.ai.vixra.org/abs/2602.0036", "first_submitted_at": "2026-02-08T13:06:34+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-31T23:08:44+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0036-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T13:06:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0036v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T07:39:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0036v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-31T23:08:44+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0036v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7e86eb7ba4e3ac1d79345632d20140b4b5fc8407fb9f55a171ec2bf79dd0b12f", "canonical_bytes": 941611 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:1694601b-0960-4e45-9ed2-4437466f0fde", "version_id": "arr:version:67d19282-6936-40a0-a491-3c16d940add4", "id": "ARR-2026-0PJHG1P2B09S2SXM", "version": "v1", "record_type": "research_paper", "title": "Zero-Momentum Propagator Bound in a Simplified Gribov-Zwanziger Lattice Measure", "abstract": "This replacement corrects the title and headline scope while preserving public version 2 in full. For the simplified quadratic Gribov-Zwanziger lattice measure defined in the manuscript, the zero-momentum propagator obeys the stated volume-uniform bound and its thermodynamic-limit value is computed. Finiteness of D(0) is only the necessary condition identified in Definition 4: it does not by itself prove exponential clustering, a transfer-operator spectral gap, a mass gap for the simplified measure, or a mass gap for Wilson Yang-Mills theory. The former title's phrases \"Mass Gap\" and \"A Non-Perturbative Proof\" are withdrawn. No continuum-limit or Clay-problem conclusion is claimed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0038", "abstract_url": "https://www.ai.vixra.org/abs/2602.0038", "first_submitted_at": "2026-02-08T11:01:58+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-31T23:14:38+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0038-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-08T11:01:58+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0038v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-06T08:05:29+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0038v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-31T23:14:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0038v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4bcadc2d4a5ea32c5a56c12d9ca6952fbb24e8c8fcceea868b1a40b0ad70260e", "canonical_bytes": 487089 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:f6f19177-6702-49f8-91a1-89f4ec972676", "version_id": "arr:version:2ff85117-0f4e-4018-95ea-8ea820fec916", "id": "ARR-2026-7PY68QESR297W938", "version": "v1", "record_type": "research_paper", "title": "Gradient Flow Monotonicity and the Yang-Mills Mass Gap: A Conditional Reduction via Spectral Methods", "abstract": "We establish a conditional reduction of the Yang-Mills mass gap problem to a concrete spectral inequality involving the gradient flow. Main result (informal): for pure SU(N) Yang-Mills theory, if the gradient flow beta-function satisfies a uniform strict asymptotic freedom condition |beta_GF(g)| >= delta g^3 for large g, and a Tauberian regularity condition holds for the spectral density, then: in d = 3 the theory has a mass gap Delta > 0; in d = 4 the infrared trace anomaly vanishes, a_IR = 0, ruling out a conformal infrared fixed point -- combined with the phase exclusion of the companion paper, this reduces the mass gap to explicit spectral conditions. However, the spectral argument is marginal in d = 4 and requires additional non-perturbative input. The proof uses a spectral representation of the gradient flow energy E(t) with the monotonicity identity R'(t) = -2 Var_t(lambda) <= 0, the Komargodski-Schwimmer a-theorem, and a gradient flow Poincare inequality connecting functional inequalities to exponential clustering. We verify all perturbative inputs: the free-field calibration gives R_free(t) = 2/t in d = 4 and the one-loop correction has the correct sign. We identify the indefiniteness of the Weitzenbock curvature term as the precise technical barrier in d = 4. v2 (no v1 numbered statement is changed): the fixed-measure spectral representation is retagged as an explicit hypothesis (H0) for the nonlinear interacting flow (equivalent to complete monotonicity of E(t), proven only for the linearized flow; the status table is retagged accordingly); an unresolved citation is repaired; the Holley-Stroock route claimed in v1 to give the Poincare inequality unconditionally at finite beta is corrected (its constant is exponential in the volume, so the L-uniform statement remains conditional outside the two controlled regimes); the a_IR = 0 phase classification behind the d = 3 mass-gap corollary is retagged as imported physical input; the Karamata attribution is replaced by the elementary direct bound actually used; and a verification suite adds numerical evidence: exact spectral machinery, lattice free-field calibration, the quantified d = 3 vs d = 4 dichotomy on synthetic spectral densities, and a first in-framework SU(2) Wilson-flow Monte Carlo diagnostic (8^4, beta = 2.4: c(t) = t^2 rises 42 percent across the measured window and R(t) < 2/t pointwise, i.e. beta_GF < 0 throughout -- numerical support for Hypothesis B' in a controlled lattice window, evidence not proof).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-07", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0020", "abstract_url": "https://www.ai.vixra.org/abs/2602.0020", "first_submitted_at": "2026-02-07T16:50:59+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T22:38:06+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0020-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-07T16:50:59+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0020v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T22:38:06+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0020v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f32229a6096148e70b31db77a4584aa0bbc6ff5266d0cbd8baa61332110b3233", "canonical_bytes": 390482 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2f9f7146-7f31-4d63-9f1f-277affdce317", "version_id": "arr:version:909ef1ac-1f1f-42a5-b8f9-b3be10b891f3", "id": "ARR-2026-1FKXRMCZSH9NHSY7", "version": "v1", "record_type": "research_paper", "title": "Yang-Mills Existence and Mass Gap: A Framework via Anomaly Algebra, Gradient-Flow Spectral Methods, and Quantum Information", "abstract": "We present a rigorous framework for the Yang-Mills mass gap problem, combining three independent lines of argument that reinforce each other. Result A (Unconditional): a new MaxEnt Clustering-Recovery Bridge -- for lattice gauge states with finite correlation length xi, in the polymer/Kotecky-Preiss regime made precise in Section 5, the Petz recovery fidelity satisfies 1 - F <= C e^{-r/xi}, proved via maximum-entropy truncation on gauge-invariant algebras, a convergent polymer expansion, and the Fawzi-Renner theorem. Result B (unconditional on the lattice, conditional for all couplings): for SU(N) lattice gauge theory (T=0, theta=0, d=3+1, N >= 2), the algebraic phase exclusion, using the projective commutation relation of 1-form symmetry operators, excludes the trivially gapped symmetric phase (v2: given the imported lattice realization of the symmetry pair); combined with Perron-Frobenius non-degeneracy and Gauss-law constraints, this forces confinement at strong coupling; the extension to all couplings relies on Hypothesis 1.1 (absence of a bulk phase transition), supported but not proven. Under Hypothesis 1.1 the uniform lattice mass gap holds for all lattice spacings. Result C (Conditional): under the same hypothesis, the continuum limit exists as a Euclidean QFT satisfying all Osterwalder-Schrader axioms with mass gap. Result D: the gradient flow reduction (developed in the companion ai.viXra:2602.0020). v2 (no v1 numbered statement is changed): the exact lattice realization of the commuting projective 1-form pair is made an explicit imported input, and a new remark records the Perron-Frobenius tension that forces this framing -- at finite volume, PF uniqueness plus exact commutation of both generators would contradict the projective relation outright, so the magnetic operator commutes with H only up to defect terms (verified numerically: toric code, exact pair with 4-fold degenerate ground state; Z2 gauge theory with electric term, unique ground state with both string commutators nonzero); the Result-D naming collision is resolved (the d = 2+1 theorem is now Result E); an unresolved citation is repaired; the epsilon-powers in the MaxEnt bridge are harmonized; and a replication report is added: the 7-qubit Z2 table is reproduced digit for digit, the Z3 table is reproduced digit for digit after a documented g <-> 1/g erratum between the v1 script and table, and the torus finite-size-scaling table could not be reproduced from the printed conventions and is downgraded to archival status (no framework result depends on it). v2 is presented in condensed form: every v1 numbered statement is preserved with the same numbering; detailed proofs and the full computational listing remain in the v1 PDF as the archival source.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-02-07", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2602.0021", "abstract_url": "https://www.ai.vixra.org/abs/2602.0021", "first_submitted_at": "2026-02-07T16:49:07+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T23:07:10+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2602.0021-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-02-07T16:49:07+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0021v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T23:07:10+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2602.0021v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "19ea135c085b5afa9f74ee898dac7ecc6fa6af975a553ac342b1ceecd4a54ec4", "canonical_bytes": 427982 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:f83ec351-7833-41ce-a46b-7931edd89b0d", "version_id": "arr:version:c96d6292-0089-4c51-88df-d68216a34d45", "id": "ARR-2026-7R7V1N2Y1K877A8T", "version": "v1", "record_type": "research_paper", "title": "Algebraic Entropy and Conditional Mutual Information in a Tiny Gauge-Invariant Truncated Hilbert Space: A Reproducible Toy-Model Study with Effective Mixing Hamiltonians", "abstract": "We present a reproducible pipeline to compute region algebraic entropies and conditional mutual informations (CMI) in a tiny truncated Hilbert space (here dim = 8) indexed by discrete fusion-like descriptors desc = (x, mu) on L = 4 cells. To generate nontrivial ground states within the descriptor-labeled subspace, we introduce an effective Hermitian mixing Hamiltonian based on a weighted k-nearest-neighbor (kNN) graph Laplacian over configuration labels. Across a parameter sweep, we identify a strong-mixing regime where the participation ratio approaches dim (consistent with Laplacian-dominated ground states on connected graphs) and algebraic CMI diagnostics become extremely small (down to 10^{-6} and below) for the chosen algebraic factorization, while region algebraic entropies remain O(1) and exhibit near-quantized values ~ n log 2. We stress that the mixing term is an ansatz used to probe information-theoretic diagnostics and is not claimed to coincide with a Kogut-Susskind plaquette operator. v2 (no v1 number is changed): the reproducibility gap of v1 is repaired -- v1's pipeline loaded an unshipped basis file (descs.pkl) that was never specified, so the v1 dataset was not regenerable from the paper; v2 prints a canonical self-contained basis whose pipeline reproduces every structural finding, keeping v1's Table 1 as an archival dataset; two empirical observations are upgraded to proved statements -- the descriptor-to-key map is injective, making S_alg a genuine von Neumann entropy of a sector (center-type) decomposition, and in the strong-mixing limit the ground state converges to the uniform superposition where the quantization S_alg = n log 2 and the vanishing of both CMIs are exact; the additional experiments recommended in v1 (Haar baseline, kNN ablations, finer t_mix grid) are executed -- the Haar median of I_sum is 0.39, five to six orders of magnitude above the strong-mixing point, so the small-CMI regime is nontrivial; and the verification suite is fully self-contained (no Drive dependencies).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-28", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0115", "abstract_url": "https://www.ai.vixra.org/abs/2601.0115", "first_submitted_at": "2026-01-28T08:43:53+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-07-31T23:16:43+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0115-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-28T08:43:53+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0115v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T22:07:41+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0115v2.pdf" }, { "version": "v3", "submitted_at": "2026-07-31T23:16:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0115v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "7e32a880d7fb3d91a64c9c3ede8ea605b480e003ea0693749675fc39ce037546", "canonical_bytes": 489546 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:3a1269e2-d492-4fe3-bb97-fafdd374184d", "version_id": "arr:version:2539b27a-d8e6-40dd-b5f7-68012b75a211", "id": "ARR-2026-1T29MY5N4J9ZHVQ5", "version": "v1", "record_type": "research_paper", "title": "Conditional Mutual Information and Petz Recovery in a Z2 Lattice Gauge Ground State", "abstract": "We study approximate quantum Markov structure in a Z2 lattice gauge ground state using the conditional mutual information (CMI) I(A:C|B(w)) and the performance of Petz recovery across a family of tripartitions (A, B(w), C) parameterized by a buffer width w. We consider a 2x4 plaquette lattice with open boundaries and qubits on links, restricted to a gauge-invariant (Gauss-law) physical sector, at coupling g = 1.0. For each w we compute reduced density matrices, the entropies entering the CMI, and a Petz-recovered state sigma_ABC = (id_A (x) R^Petz_{B->BC})(rho_AB), reporting fidelity F(rho_ABC, sigma_ABC) via the recovery error E_rec(w) = -log F. The Overleaf project includes the plot, a formatted table, raw CSV outputs, and a hash-based manifest; the appendix typesets raw artifacts. We also report numerical cross-checks (dense vs. low-rank method agreement and trace stability) to support validity. v2 (no v1 number is changed): the star-operator definition is corrected -- with the Hamiltonian convention used here (single-link Z terms), the Gauss stars must be G_s = prod Z_l; v1's printed prod X_l anticommutes with the Z_l terms of H (the code used the consistent convention: an independent reconstruction from the manifest alone reproduces the CSV ground energy to 7x10^{-15} and every CMI of Table 1 to machine precision); two interpretive remarks are added -- the CMI rise at w = 2 tracks the shrinking traced-out complement (|D|: 8 -> 2 -> 0), so the profile is not a shielding-decay curve, and the w = 2 ~ w = 3 plateau is the buffer-saturation identity of the companion 2601.0050 (v2); the apparent Petz-over-CMI excess at w = 1 (E_rec > I) is shown to be the delta = 10^{-6} regularization floor -- regenerating with delta = 10^{-12} restores E_rec <= I at every w in the regenerated dataset; and a verification suite replicates the full pipeline from the manifest data alone.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-27", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0111", "abstract_url": "https://www.ai.vixra.org/abs/2601.0111", "first_submitted_at": "2026-01-27T17:45:18+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T21:44:34+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0111-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-27T17:45:18+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0111v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T21:44:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0111v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3811ec104d7c37e0cdc9484e0ddbe935e9a6a48edd66c605ee3082fbc9eb6288", "canonical_bytes": 382792 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:fd008f62-fb5f-4d10-864d-e0f5da9b9c76", "version_id": "arr:version:af8d2666-99b1-41d9-a1c2-bfc42da6e195", "id": "ARR-2026-7X027P5YTZ9M88CK", "version": "v1", "record_type": "research_paper", "title": "Program A: Semi-Infinite Conditional Mutual Information in the 1D TFIM (iMPS)", "abstract": "We study an information-theoretic notion of locality -- approximate quantum Markov behavior -- via the conditional mutual information (CMI) I(A:C|B(w)) in a semi-infinite geometry of the 1D transverse-field Ising model (TFIM). Using infinite matrix product states (iMPS), we compute I(A:C|B(w)) as a function of the collar width w separating two semi-infinite regions. In a representative gapped point (h = 1.5), we observe clean exponential decay and a rapid plateau of the local effective-length estimator, yielding an early-decay length xi_rec^(early) comparable to the iMPS transfer-matrix correlation length xi_corr. Near criticality (h = 1.005), the local estimator increases throughout the accessible range, indicating a pre-asymptotic regime; we therefore report a fixed-window effective length and a window-sensitivity range as a systematic uncertainty. All generated assets used here (two JSONL data streams, the figure, and the LaTeX table snippet) are included in the Overleaf project. v2 (no v1 number is changed): Appendix A is repaired (in v1 the data-source filenames were typeset in math mode and the near-critical entry was missing entirely); Table 1 is re-typeset (collided columns in v1); the Colab scripts of Appendix B are shipped as runnable files in the series repository rather than as listings; series positioning is added -- this paper is a numerical instantiation of the A-CMI hypothesis of the contract note ai.viXra:2601.0066 in a semi-infinite 1D geometry; and an independent verification suite (free fermions via Jordan-Wigner, no tensor networks) reproduces the gapped point of Table 1 exactly (xi_rec^(early) = 1.149 on the main window, window sensitivity [1.149, 1.158], both matching v1 digit for digit), verifies the operational identity I = 2 S_cut - S(B(w)) to 10^{-11}, and reproduces the rising near-critical xi_local(w); a TeNPy cross-check reproduces the free-fermion I(w) pointwise to 5x10^{-5} relative.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-24", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0099", "abstract_url": "https://www.ai.vixra.org/abs/2601.0099", "first_submitted_at": "2026-01-24T17:02:20+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T21:05:26+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0099-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-24T17:02:20+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0099v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T21:05:26+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0099v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "3eea0d998b2fd48bc98e37d2a074334da38aa69e3eee1e5d42fdcf6cbb9b2cfc", "canonical_bytes": 353925 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:a3e292c2-6163-4cb1-8ebd-feb5e0140680", "version_id": "arr:version:0f062324-807d-49a3-9761-4d03c61f5550", "id": "ARR-2026-53WA9C4RB39JRRXF", "version": "v1", "record_type": "research_paper", "title": "RIP-U and the ω = 0 Obstruction in Davies Dynamics: Upper Envelopes, Witness Floors, and Falsification Protocols for Separation-Dependent Decoherence Rates", "abstract": "We isolate the dynamic hinge in typed separation-to-rate-to-power pipelines within the Davies (weak-coupling, Markovian) setting in finite dimension. First, we formulate an upper-envelope statement (RIP-U): under an explicit factorized bath-correlation envelope with separation-dependent amplitude f(epsilon) and integrable time profile, Fourier-transformed Davies rates inherit an O(f(epsilon)) envelope. Under additional regularity assumptions preventing trivial degeneracies, this yields a worst-case bound kappa_up(epsilon) <= C f(epsilon) for the instantaneous relative loss rate of a coherence-like functional. Second, we isolate a structural obstruction to lower-envelope statements: we prove an exact identity for the omega = 0 contribution to the Davies Dirichlet form, E^(0)sigma(O) = (gamma(0)/2) ||[S(0),O]||^2{2,sigma}, and derive a witness mechanism showing how omega = 0 channels can enforce a non-vanishing dissipation contribution for suitable observable families. We emphasize directionality: RIP-U (upper) does not imply a positive lower envelope kappa_down(epsilon) without additional family-qualified input. All assumptions are explicit and accompanied by falsification routes. v2 (no v1 number is changed): two v1 assumptions are upgraded to proved statements in their canonical instances -- Delta-MONO holds unconditionally for the energy pinching (Davies covariance plus data processing), and a sufficient bridge with an explicit constant is proved; the cross-reference labels are repaired (in v1 every assumption and theorem was typeset as \"Definition x.y\"); Table 1 is re-typeset (overlapping text in v1); the omega = 0 identity is placed within the corrected Bohr-channel decomposition of the companion 2601.0023 (it is exactly the omega = 0 sector, and the plain-commutator form provably fails at omega != 0); and a verification suite reproduces every proved item numerically, including the identity at machine precision and an explicit family with kappa_down much smaller than kappa_up under the same envelope.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0064", "abstract_url": "https://www.ai.vixra.org/abs/2601.0064", "first_submitted_at": "2026-01-17T19:05:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T19:25:29+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0064-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-17T19:05:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0064v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T19:25:29+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0064v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "45fe63280b6079729eebe7b5ddf6bc7eda2679c42fefc9331deb8718a89e1cb5", "canonical_bytes": 343124 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:775fdc37-7adb-478d-8b74-81e425ec1d78", "version_id": "arr:version:97cd391c-aa5b-49ed-8b38-be566a296885", "id": "ARR-2026-3QBZE3EYPV8Y6RPX", "version": "v1", "record_type": "research_paper", "title": "Split-Regularized Recoverability in Type III AQFT: Conditional Expectations, Split-Dependent CMI, and an Audit-Friendly Recoverability Contract", "abstract": "Local algebras in relativistic quantum field theory are typically Type III, so reduced density matrices and von Neumann entropies are not available without additional structure. We give a B-minimal, audit-friendly interface for recoverability in Type III AQFT: we fix a collar geometry and a split datum N (an intermediate Type I factor) and define (i) a split-regularized conditional mutual information (CMI) and (ii) a Bures-fidelity-based recovery error for normal states. We isolate, as explicit assumptions, the two hard bridges needed for an exponential recoverability statement in Type III: (a) existence of an omega_0-preserving conditional expectation onto N (a Takesaki-type condition) and (b) an FR-type inequality in the fixed split implementation. We prove a conditional theorem: if split-regularized CMI decays exponentially in the collar width and an FR-type inequality holds in that split, then recoverability error decays exponentially, with constants tracked explicitly. This paper makes no Clay mass-gap claim and does not invoke von Neumann entropy on Type III algebras without split regularization. v2 (no v1 number is changed): the cross-reference labels are repaired (in v1 every assumption and theorem was typeset as \"Definition x.y\") and Table 1 is re-typeset; a direction slip in the recovery candidate is corrected -- under CE the GNS-adjoint of the conditional expectation is provably the inclusion iota: N into M, so the operational candidate aligned with the recovery task is the predual of the conditional expectation itself; the finite-dimensional reduction is proved rather than remarked, including the equivalence of the two split-regularized CMI definitions and c_FR = 1 in the fixed conventions; a constructive instance of CE with product reference state is proved; series positioning is added; and a verification suite instantiates the entire contract end to end in the Type I regime (gapped transverse-field Ising collar: CMI decay with alpha ~ 1.06, Petz-type reconstruction satisfying E_rec <= I^(N) at every width in the generated dataset, and the omega_0-adjoint identity E^# = iota at machine precision).", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0065", "abstract_url": "https://www.ai.vixra.org/abs/2601.0065", "first_submitted_at": "2026-01-17T18:43:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T19:47:43+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0065-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-17T18:43:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0065v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T19:47:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0065v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8eaf5dcd2084bc89ac167b6d6be1b84f45d323fad7b5e31f14b4d0dd9cb04768", "canonical_bytes": 318169 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:902b8918-1eb4-47a0-b3e7-494ab6094a92", "version_id": "arr:version:0beec367-4819-49de-933a-4753669993e8", "id": "ARR-2026-4G5E4HG7NM8YGB7S", "version": "v1", "record_type": "research_paper", "title": "Typed Pipeline for Recoverability-Rate-Power Links: A Contract Paper with a Closed Recoverability Lane and Falsification Criteria", "abstract": "We present an audit-friendly logical contract for a multi-layer program connecting (i) static locality/Markovness, (ii) recoverability bounds, (iii) separation-dependent dissipation rates, and (iv) thermodynamic maintenance power. Each interface is typed with explicit quantifiers, tagged as [PROVED]/[IMPORTED]/[ASSUMED]/[CONJECTURED], and paired with falsification routes. We do not claim a proof of the Clay Yang-Mills mass gap; we separate a Clay (closed-Hamiltonian) track from an operational (open-system/maintenance) track. As a fully closed lane inside this paper, we prove that an exponential conditional mutual information (CMI) decay hypothesis implies exponential recoverability via an imported Fawzi-Renner inequality, with fidelity conventions fixed explicitly. v2 (no v1 number is changed): the cross-reference labels are repaired (in v1 every assumption, lemma, theorem, remark and corollary was typeset as \"Definition x.y\") and Tables 1 and 2 are re-typeset; the constant-alignment step of Appendix A is executed rather than prescribed -- in the locked conventions (squared fidelity, E_rec = -log F) the Fawzi-Renner import yields c_FR = 1 exactly; the deferred interfaces of Appendix B are now concrete series papers and are cited as such (the Type III interface is ai.viXra:2601.0065, the Davies/RIP-U dynamics note is ai.viXra:2601.0064, the benchmark infrastructure lives in the series repository); the BATO-LAW upgrade path of Appendix C records the partial progress of ai.viXra:2601.0031; and a verification suite instantiates everything instantiable: the closed recoverability lane end to end on a gapped transverse-field Ising collar (I ~ 0.20 e^{-1.06 w}, E_rec <= I at every width in the generated dataset, full 1 - F <= E_rec <= c_FR K e^{-alpha epsilon} chain), the exact-Markov example at machine precision, and the dephasing example with an explicit kappa_up/kappa_down spread of two orders of magnitude illustrating the directionality golden rule.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0066", "abstract_url": "https://www.ai.vixra.org/abs/2601.0066", "first_submitted_at": "2026-01-17T18:30:12+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T20:13:04+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0066-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-17T18:30:12+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0066v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T20:13:04+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0066v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "ded20a40e5090439d85d2cbf07af4c0c16d89a2d48e96b59360319a0deff747e", "canonical_bytes": 318994 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:ddc0dce2-8e11-4388-9c44-03fc0f372f08", "version_id": "arr:version:9c32692b-98a6-4eab-8989-3ca6b170ae9c", "id": "ARR-2026-6XR3EE53GH8E49RH", "version": "v1", "record_type": "research_paper", "title": "Cmi-Based Recoverability Versus Wilson-Loop Diagnostics in Z2 Lattice Gauge Theory (2+1D): Exact Diagonalization Benchmark on Small Open Lattices", "abstract": "We provide a finite-size benchmark testing whether a CMI-based recoverability proxy correlates with Wilson-loop confinement diagnostics in Z2 lattice gauge theory in 2+1 dimensions, computing ground states by sparse exact diagonalization on 2x2 and 2x3 open lattices (link qubits, Gauss-law penalty verified by ~ 1) and evaluating entropic quantities by pure-state Schmidt/SVD. We state a conditional bridge from a spatial area law to an operational \"information horizon\" via explicit hypotheses (H1)-(H4), with two recovery-length conventions (absolute, and normalized by the boundary prefactor Sigma_B(w) = |dB(w)| log 2). v2 (no v1 number is changed) adds a structural lemma that v1's own Table 1 was exhibiting unnoticed: for a pure global state, when the collar saturates (B = (A u C)^c) purity forces I(A:C|B) = I(A:C|empty) -- this is exactly why v1's Table 1 shows I(w=2) = I(w=0) = 0.4992999 to seven digits; the saturated row carries no buffer information, and the informative range of that benchmark is w in {0, 1}. v2 also anchors the non-monotonicity of CMI under collar enlargement as geometry-dependent (v1's wall geometry shows growth at w=0 to 1; a BFS-patch geometry on the same states decays monotonically -- there is no data-processing theorem in that direction); cross-links the CMI benchmark to the Petz-error twin on the same lattices (densified n = 8 sweep: Spearman rank-trend +1.00, permutation p = 1e-4, against both 1/sigma_eff and the inverse spectral gap -- so, as in the twin, confinement specificity is unresolved at these sizes); harmonizes the fidelity convention (v1 correctly uses root fidelity with I >= -2 log f, equivalent to the companions' squared-convention I >= -log F); removes an internal phase label leaked into v1's Section 1 title and a duplicated heading; and adds series positioning and a regenerable verification suite. The conditional proposition and its hypotheses are unchanged.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0050", "abstract_url": "https://www.ai.vixra.org/abs/2601.0050", "first_submitted_at": "2026-01-14T20:46:34+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T18:08:54+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0050-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-14T20:46:34+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0050v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T18:08:54+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0050v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "aa5673e79cd8263bbc03fce13aee9b2f3ae6c41aeaead53ac7637803bd761c8e", "canonical_bytes": 396367 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:49f7c16b-a8c9-4c36-8d25-2e3675d2d79c", "version_id": "arr:version:4995e8af-146f-48f4-b2b8-6704241d6683", "id": "ARR-2026-29YZ0PQA699GV8T9", "version": "v1", "record_type": "research_paper", "title": "Petz Recoverability Versus Wilson-Loop Diagnostics in 2+1D Z2 Lattice Gauge Theory: Benchmarks by Exact Diagonalization and Tensor-Network Ladders", "abstract": "We provide reproducible finite-size benchmarks testing whether a Petz-type recoverability proxy correlates with Wilson-loop confinement diagnostics in Z2 lattice gauge theory in 2+1 dimensions: an exact-diagonalization benchmark on 2x2 and 2x3 plaquette lattices (Gauss penalty, ~ 1 verified), and TeNPy DMRG ladders 2xL, L in {4, 6, 8}, chi_max = 96, with a warm-start bond-dimension stability check (chi = 96 to 192 stable to all shown digits). In the tensor-network part, E_rec is reported as a function of contiguous buffer size |B| in MPS site ordering (a declared proxy), not the BFS collar of the ED part. v2 (no v1 number is changed): the broken Appendix A.1 of v1 -- whose published PDF literally prints \"Missing file\" where the ED reproduction script should appear -- is repaired by pointing to the series repository, where that script and a full verification suite for the ED benchmark already live with the companion paper; internal working titles leaked throughout v1's scripts and captions are removed; the MPS-ordering proxy is sharpened with new evidence -- on an exact Z2 ladder the geometric admissible buffer decays cleanly (5e-4 to 3e-8) while the contiguous-ordering proxy starts orders of magnitude higher and saturates, and a from-scratch DMRG replication (reduced chi, Lx = 4) reproduces both the trend direction of the money plots and v1's own buffer inversion E_rec(|B|=2) > E_rec(|B|=1), confirming it as a property of the contiguous proxy rather than a numerical accident; the confinement-vs-gap degeneracy established for the ED twin applies verbatim to the ladder money plots and is now stated; and series positioning is added. All conclusions remain finite-size benchmark statements.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-14", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0051", "abstract_url": "https://www.ai.vixra.org/abs/2601.0051", "first_submitted_at": "2026-01-14T20:03:27+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T18:33:10+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0051-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-14T20:03:27+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0051v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T18:33:10+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0051v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "f10520e4d78d1ea5c12e6b6893aa692981c1f05dd93911f18b64e01444d94186", "canonical_bytes": 1042431 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:536f4da0-48fe-48c8-8d51-7d30a1297f71", "version_id": "arr:version:abbc7721-d5ae-4dd0-8934-ccd07eec1e72", "id": "ARR-2026-2KDX6T0J7Y9348TM", "version": "v1", "record_type": "research_paper", "title": "Petz Recoverability Versus Wilson-Loop Diagnostics in Z2 Lattice Gauge Theory (2+1D): Exact Diagonalization Benchmark on Small Open Lattices", "abstract": "SUPERSEDED BY AI.VIXRA:2601.0051V2 FOR THE CONSOLIDATED BENCHMARK. This replacement preserves public version 2 and makes the series relation explicit. The exact-diagonalization benchmark remains a valid finite-size component, but the successor is the authoritative combined source because it retains that benchmark and adds tensor-network ladder calculations and further scope controls. The reported Petz/Wilson rank alignment is not a confinement-specific or thermodynamic theorem: absolute recovery errors remain prescription dependent, and an equally strong spectral-gap covariate leaves confinement specificity unresolved at the tested sizes. The preserved version 2 follows the two-page notice unchanged.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0047", "abstract_url": "https://www.ai.vixra.org/abs/2601.0047", "first_submitted_at": "2026-01-13T21:46:46+00:00", "latest_declared_version": "v3", "latest_submitted_at": "2026-08-01T08:40:56+00:00", "mirrored_version": "v3", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0047-v3.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-13T21:46:46+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0047v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T17:45:47+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0047v2.pdf" }, { "version": "v3", "submitted_at": "2026-08-01T08:40:56+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0047v3.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a4779474c2ff4b967f463ee93dd0f1e829eaa193e0f6cb3e2d7cd961d888e43c", "canonical_bytes": 563912 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:eb19e3b6-394d-4a82-be5f-4858cac6c9fb", "version_id": "arr:version:f75fc5a5-1e2e-476a-a944-294ce8ac6b5e", "id": "ARR-2026-7B37HVCEAD9A1BWQ", "version": "v1", "record_type": "research_paper", "title": "Recoverability Geometry: Distances and Embeddings from Quantum Markov Data — Definitions, Diagnostics, and a Reconstruction Protocol", "abstract": "We propose an operational route from recoverability data to effective geometry. Given a tripartition A-B(w)-C and a collar width w, we consider a Petz-type recoverability error E_rec(w) defined via fidelity and extracted from a fixed collaring rule (A, C, w) -> B(w). We define distance-like functionals from the minimal buffer needed to suppress E_rec(w) below a threshold, and from exponential fit scales when such a regime exists; these are organized into a (generally non-metric) dissimilarity matrix on coarse regions, symmetrized when needed, and embedded via multidimensional scaling or diffusion maps. The paper emphasizes precise definitions (collaring rule, symmetrization, censoring below numerical floors) and falsifiable diagnostics (approximate triangle inequalities, robustness to thresholds and regularization). A minimal control experiment in the 1D transverse-field Ising model illustrates the pipeline and the growth of a recoverability length near criticality. v2 (definitions unchanged) adds: a regenerable suite replacing the \"representative run\" of v1 -- the control table is regenerated from scratch, its g = 0.5 row is flagged as unstable by the paper's own fit-window policy, and a three-point-fit caveat is stated; the first in-model test of the tracking conjecture -- from the same ground states, xi_rec/xi_corr in {0.98, 0.53, 0.52} across regimes, same order of magnitude throughout; a first numerical illustration of the embedding machinery (four coarse regions, MDS recovering the chain order exactly, triangle violations bounded by discretization), which also surfaces an operational lesson: tracing out the region between B(w) and C fakes separation and inverts monotonicity, so the separation condition of the collaring rule is essential, and profiles below the separating width are not admissible; the observation that the fixed-|A|,|C|/traced-environment design of the control is precisely the fixed-target protocol that resolves the |C|-shrinkage confound identified in the companion d_eff notes; and series positioning.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0043", "abstract_url": "https://www.ai.vixra.org/abs/2601.0043", "first_submitted_at": "2026-01-13T12:50:18+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T16:21:06+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0043-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-13T12:50:18+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0043v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T16:21:06+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0043v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "04b9c5ce59ad3513ef2c3d4ca7810b616dceb265b36a82b2fe807a3ea301c0ec", "canonical_bytes": 317167 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:96118901-3580-4375-a9d8-fb7c70c1f377", "version_id": "arr:version:feac72a5-f40c-4d0b-b986-69039335fa17", "id": "ARR-2026-4P264G2DC08DTTKP", "version": "v1", "record_type": "research_paper", "title": "Recoverability Length Scales and Wilson Loops in Lattice Gauge Theories: Protocol, Definitions, and Conjectural Links to Confinement Diagnostics", "abstract": "We propose a numerical protocol and falsifiable conjectures relating quantum-information recoverability measures to confinement diagnostics in lattice gauge theories. For a tripartition A-B-C and collar width w, we define a Petz-type recovery error E_rec(w) and extract a recoverability length from threshold and fit criteria. Since gauge constraints obstruct naive factorization, the protocol is formulated in an extended-Hilbert-space (EHS) prescription by default, with an algebraic (gauge-invariant) variant outlined together with its subtleties (centers, sectors). We conjecture that E_rec(w) decays exponentially in gapped phases and that its scale tracks confinement scales set by Wilson loops. v2 executes the testbed that v1 only specified: on a Z2 ladder of four plaquettes (14 links, Gauss law enforced exactly, = 1 to 1e-6), the suite computes E_rec(w) and Wilson decay on the same ground states across five couplings. Findings: the pipeline runs end to end; xi_rec is identifiable at three of five couplings and nearly coupling-independent (0.21-0.31, spread x1.4), while the Wilson decay length varies strongly (0.38-6.9, spread x8.6): no tracking at ladder level. Because height-one ladders degenerate area and perimeter, the Wilson scale there is not a pure confinement scale, so this first dataset is inconclusive-but-cautionary for the tracking conjecture rather than a falsification -- and it sharpens the requirement: a genuine 2D lattice is needed. v2 further flags the TFIM control row shared with the companion framework note as unstable under regeneration, and adds series positioning. No v1 definition is changed.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0044", "abstract_url": "https://www.ai.vixra.org/abs/2601.0044", "first_submitted_at": "2026-01-13T12:46:11+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T16:44:35+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0044-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-13T12:46:11+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0044v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T16:44:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0044v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "eca9afd4f5df2fecc27e96f83476f47c770ccb59be92c53f0207626728ee7c6e", "canonical_bytes": 308755 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:b1822c95-aae7-430a-a58a-01cc77da8b4f", "version_id": "arr:version:73416dd0-959e-49b6-b12b-7e384bf24703", "id": "ARR-2026-5HG8P9BAQ78C5AB2", "version": "v1", "record_type": "research_paper", "title": "Petz Recoverability in AQFT via Conditional Expectations: A Framework and a Conditional Exponential Recovery Bound", "abstract": "We formulate an operational notion of recoverability in algebraic quantum field theory for type III local von Neumann algebras. Fixing a faithful normal KMS reference state and assuming a state-preserving conditional expectation, we define the recovery channel and, working in a fixed split implementation for each separation r, we assume (i) exponential decay of split-implemented conditional mutual information and (ii) a CMI-to-recovery inequality. Under these explicit bridge assumptions we obtain a conditional exponential recoverability bound E_rec(r) <= g(C1 e^(-m r)). v2 corrects the duality underlying the construction: v1 defined the Petz-type channel as the \"Accardi-Cecchini adjoint\" via the pairing omega(Z R(X)) = omega(eps(Z) X) and \"proved\" finite-dimensional consistency with the standard Petz map; that identity is false in general (the printed proof contains an invalid cyclicity step; numerically the identity fails at order 1e-1 on random faithful states, holding only in commuting/product situations). The correct statement, proved and machine-verified here, is that the standard Petz map is the trace-predual of the generalized (Accardi-Cecchini) conditional expectation; accordingly, v2 defines the recovery channel in Schrodinger picture as precomposition with the conditional expectation. This also repairs a type/direction error in v1's recovered-state definition, whose corrected form (omega restricted to AB, composed with the normal extension of id_A tensor eps) reproduces the standard Petz reconstruction exactly in finite dimensions. We further relabel v1's finite-dimensional map as the generalized conditional expectation (its Takesaki module property fails generically -- verified), record that for a true state-preserving conditional expectation the recovery is the CE-pullback, and add series positioning: this note is the AQFT capstone announced by the companions, its split-implemented CMI is one of three compatible regularizations in the series, and the numerical program deferred by v1 has since been executed. The main theorem is unchanged: a conditional framework statement isolating the missing bridge assumptions.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-13", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0046", "abstract_url": "https://www.ai.vixra.org/abs/2601.0046", "first_submitted_at": "2026-01-13T05:25:36+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T17:09:22+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0046-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-13T05:25:36+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0046v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T17:09:22+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0046v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "9ad398242e2a32158dcc4f5213078ee31dace22e1e3e0b4108338ed45d1c9532", "canonical_bytes": 272641 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:148f2d97-bfa6-4998-89f0-b27be13637cf", "version_id": "arr:version:8a8246c9-ff57-46a0-ae14-50fb74301b27", "id": "ARR-2026-0MHWPSFFX696C8KW", "version": "v1", "record_type": "research_paper", "title": "Finite-Size Scaling of Petz Recovery Length in the TFIM: Threshold-dependent Operational Exponents from Exact Diagonalization", "abstract": "We study finite-size scaling of an operational recovery length extracted from Petz-map recovery in the transverse-field Ising chain. For a tripartition A-B-C with a collar B of width w, we define E_Petz(w) = -log F (squared Uhlmann fidelity), E_best(w) = min over w' <= w of E_Petz(w'), and the effective recovery distance d_eff(epsilon), with log-linear interpolation. Using exact diagonalization at hz = 0, beta = 12, |A| = 2 for N in {9, 10, 11, 12}, we analyze the peak height d_max(epsilon; N) = max over hx of d_eff in a censoring-free threshold regime, finding that the finite-window data are well summarized by descriptive power-law fits d_max(epsilon; N) ~ N^kappa(epsilon) with, e.g., kappa(3e-3) of about 0.44 and kappa(5e-3) of about 0.26, and a pseudocritical drift of the peak location with a threshold-dependent effective exponent nu_eff -- reported as operational quantities, not universal estimates. v2 adds (no v1 number is changed) two mandatory caveats, both quantified by a regenerable suite that reproduces v1's Table 1 exactly: (i) a |C|-shrinkage/growth confound -- the off-critical baseline d_eff(hx = 0.80; N) also grows with N at fixed thresholds, so the raw peak growth conflates critical physics with tripartition geometry; the cleaner object is the critical enhancement Delta(N) = peak - baseline, which still grows with N (e.g. 0.42 to 0.74 over N = 9, 10 at epsilon = 3e-3), so the critical signal survives baseline subtraction while kappa(epsilon) from raw peaks must be read as geometry-contaminated; (ii) functional-form indistinguishability -- over the accessible sub-octave in N, power-law, logarithmic and linear fits of the peak height have R^2 spreads below 0.01, and kappa itself shifts strongly with the fit window; the correct reading of kappa(epsilon) is a descriptive summary, not an established power law. Series positioning and a verification suite are included.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0040", "abstract_url": "https://www.ai.vixra.org/abs/2601.0040", "first_submitted_at": "2026-01-12T06:23:09+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T15:18:12+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0040-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-12T06:23:09+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0040v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T15:18:12+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0040v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "ce0cb7bd4fbd89acad818c30e5cf38554b2bf7230f748c290a484f77fb24bb2f", "canonical_bytes": 539867 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:5bd15612-2d88-43a0-9d37-8d0c0452744b", "version_id": "arr:version:41a66dde-2f98-4e57-9659-53b3e9e88261", "id": "ARR-2026-2VT5B14BC88EG9TD", "version": "v1", "record_type": "research_paper", "title": "Operational Signatures of Criticality from Petz Recovery: Collar-length Requirements in TFIM Exact Diagonalization", "abstract": "We study whether recovery-based operational distances exhibit a distinctive finite-size signature near quantum criticality. For a tripartition A-B-C of a 1D chain with a collar B of width w separating A from C, we compute a Petz-based reconstructed state and the recovery error E_Petz(w) = -log F (squared Uhlmann fidelity), and define an effective recovery distance d_eff(epsilon) as the minimal collar width achieving error below epsilon, stabilized by E_best(w) = min over w' <= w of E_Petz(w') and reported with explicit censoring. Using exact diagonalization of the transverse-field Ising chain at N = 11 with |A| = 2, we sweep hx across the critical region at hz = 0 and compare to a longitudinally perturbed control hz = 0.5: pronounced growth and extensive censoring of d_eff(epsilon) appear in the critical region at low temperature, while the control remains comparatively featureless; an extended-collar spot-check yields d_eff(1e-3) of about 7.6-7.7 at beta = 12 near hx in {0.96, 1.00}. v2 adds (no v1 result is changed): an explicit |C|-shrinkage caveat -- at fixed N, growing w also shrinks C, so the absolute scale of d_eff near w_max conflates buffer growth with a shrinking reconstruction target, while fixed-geometry comparisons across hx (the criticality signature) are unaffected; a window-relativity remark (epsilon, beta, N jointly set what is resolvable: at smaller N the beta = 12, epsilon = 1e-3 window censors even off-critical points, consistent with v1's own zoom); delivery of v1's \"future work\" item: a CMI-based distance computed on the same sweep shows the same criticality signature at its own threshold (CMI decays about half as fast as the Petz error, cf. 2601.0035); series positioning; and a fully regenerable verification suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-12", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0038", "abstract_url": "https://www.ai.vixra.org/abs/2601.0038", "first_submitted_at": "2026-01-12T01:13:42+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T14:43:48+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0038-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-12T01:13:42+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0038v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T14:43:48+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0038v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "58782baf185626e05f705f787b6fbdaad98cb34a62bd7a7f6a8d77149ca01660", "canonical_bytes": 419126 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:8300d47f-42a9-494f-a06c-8ba5bfac9ea9", "version_id": "arr:version:3da3b71c-4315-42e4-b693-40c15df81d9d", "id": "ARR-2026-4303A7YGN9957T0V", "version": "v1", "record_type": "research_paper", "title": "Emergent Information Distance from Petz Recovery: Temperature and Perturbation Dependence in TFIM Exact Diagonalization", "abstract": "We define an operational notion of effective distance from approximate quantum state recovery. Given a tripartition A-B-C with B a collar of width w separating A from C, we compute a Petz recovery reconstruction error E_Petz(w) = -log F(rho_ABC, rho_Petz(w)) (squared Uhlmann fidelity) and define an emergent distance d_eff(epsilon) as the minimal collar width such that the best-achieved error up to w falls below a threshold epsilon. Using exact diagonalization for the transverse-field Ising chain at N = 11, hx = 1.05, |A| = 2, we find that d_eff(1e-3) grows strongly with inverse temperature beta in the unperturbed case (hz = 0), from 1.00 at beta = 0.5 to 3.57 at beta = 5.0, while remaining near-minimal in the longitudinally perturbed case (hz = 0.5), close to 1.0 across the same range. We also introduce a discrete curvature diagnostic based on second differences of log E_Petz(w) on a pre-floor window, reported only when identifiable. v2 (no v1 number is changed): the garbled reproducibility paragraph of v1 is replaced by a real, regenerable verification suite, which reproduces the beta-sweep to two decimals already at N = 9 (d_eff = 1.00, 1.00, 1.51, 2.11, 2.82, 3.55 vs 3.57 at N = 11; mu_prefloor endpoints 8.44 to 1.35 vs 1.33; PSD-projection sensitivity 3.3e-8 vs about 3e-8) -- independently confirming the finite-size robustness of the appendix; the mild |C|-shrinkage caveat is stated with cross-references to its quantified analysis in the companions; and series positioning is added.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0042", "abstract_url": "https://www.ai.vixra.org/abs/2601.0042", "first_submitted_at": "2026-01-11T14:41:55+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T15:57:50+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0042-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-11T14:41:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0042v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T15:57:50+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0042v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d222a2a8997bbd11927273063173e838a32833e6d269dafdb3a074a911ea5af3", "canonical_bytes": 606068 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:ab937c6b-cf31-4dd7-abe7-67e2628fcf8c", "version_id": "arr:version:4b86b734-21c9-4ca6-be20-4673bae71d87", "id": "ARR-2026-5BJDY6QKSH9QBTQS", "version": "v1", "record_type": "research_paper", "title": "Modular Recovery from Split Inclusions: A B-minimal Bridge from QFT Collar Geometry to Approximate State Reconstruction", "abstract": "In algebraic quantum field theory (AQFT), local algebras are typically Type III factors, so density matrices and von Neumann entropies are unavailable for bounded regions. We formulate a B-minimal continuum analog of the lattice \"collar => Markovness => recovery\" mechanism by combining: (i) the split property as the mathematical replacement of a buffer (collar), (ii) Araki relative entropy to define a split-regularized conditional mutual information I^N(A:C|B) relative to fixed Type I interpolating data N, and (iii) modular/twirled Petz recovery as an explicit candidate recovery channel. Assuming an FR-type recoverability inequality in the fixed-split setting, we obtain quantitative recovery bounds in a fidelity-based error metric (purified distance). We conclude with a conditional holographic remark. v2 corrects the fidelity-convention factor in the assumed FR-type inequality: with the squared (Bures/Uhlmann-squared) convention used throughout, the importable finite-dimensional motivation gives -log F <= I, not -log F <= I/2; v1's half-form is strictly stronger than its motivation and is refuted as a finite-dimensional anchor on 40/40 random tripartite states (the corrected form holds on 40/40) -- the same factor-2 correction applied in 2512.0101 v2 and 2601.0020 v2. The recovery theorem's constant changes by sqrt(2); the exponent is unaffected. v2 further adds series positioning, a compatibility remark with the split-regularized CMI of 2601.0020, a concrete demonstration that I^N can be negative for unfavorable split data -- nonnegativity of I^N is part of the good-split-data regime, not automatic -- and a finite-dimensional verification suite for every checkable ingredient of the dictionary.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0034", "abstract_url": "https://www.ai.vixra.org/abs/2601.0034", "first_submitted_at": "2026-01-11T09:52:52+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T13:15:01+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0034-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-11T09:52:52+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0034v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T13:15:01+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0034v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4abff7f5961f8b5fab943467c9e8a96232efeadd36f8641e60e834464f5527b3", "canonical_bytes": 246842 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:f856699a-479c-45a8-9ca1-824e33b46bd3", "version_id": "arr:version:9642547c-7b2e-4a6a-9bf9-84acaf0fe220", "id": "ARR-2026-7RASMSMHWW8PM9S8", "version": "v1", "record_type": "research_paper", "title": "A Non-Gaussian Clustering-Recovery Bridge via Conditional Mutual Information: Interacting Gibbs States, Explicit Petz Benchmarks, and a Conditional Link to Entanglement Wedge Reconstruction", "abstract": "We present a quantitative clustering-recovery bridge for interacting quantum many-body systems that is intrinsically non-Gaussian, organized around conditional mutual information (CMI). For a geometric tripartition A-B-C in which B is a collar of width w separating A from C, an exponential geometric Markov bound I(A:C|B) <= K e^(-alpha w) implies exponentially accurate recovery of rho_ABC from rho_AB in the theorem-facing metric -log F, by combining the Fawzi-Renner inequality with an elementary conversion to fidelity error bounds. We obtain a proved interacting lane (shielded small-region geometry, arbitrary temperature) by invoking recent local Markovness results for finite-range lattice Gibbs states. Numerically, we benchmark the mechanism in the transverse-field Ising chain with longitudinal field, comparing integrable (hz = 0) and non-integrable (hz = 0.5) regimes, and evaluate the explicit Petz recovery map with a censored log-plotting and fit protocol. v2 corrects the Fawzi-Renner factor under the squared-fidelity convention used throughout (-log F <= I, not I/2; fourth occurrence of this correction in the series), with a substantive empirical consequence: v1's headline \"mild overshoot\" of Petz over the FR scale (r of about 1.23-1.26 in the non-integrable, low-temperature, minimal-collar regime, including rotated and twirled controls) was measured against the incorrect half scale; against the corrected scale the overshoot disappears entirely (r of about 0.62), and the v1 conclusion of \"a genuine gap between explicit Petz-type constructions and the existential optimal-recovery scale\" is withdrawn. The corrected conclusion is stronger: explicit Petz satisfies the FR scale throughout the dataset, with at least about 40 percent margin even at the hardest point. A fully regenerable verification suite reproduces the pipeline from scratch. Finally, we state a conditional application to entanglement wedge reconstruction, separating proved information-theoretic content from bulk-boundary interface assumptions.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-11", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0035", "abstract_url": "https://www.ai.vixra.org/abs/2601.0035", "first_submitted_at": "2026-01-11T08:26:27+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T13:44:55+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0035-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-11T08:26:27+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0035v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T13:44:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0035v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a1baeb63193badb0883ed8b518e2b005ce27a572a00786b9d5e5baeaf877325b", "canonical_bytes": 381200 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:64eb2238-b393-4baa-b211-73de790235d9", "version_id": "arr:version:dd9c9f9a-b483-49e9-9819-ebda52ecf291", "id": "ARR-2026-34XCH3HCWK9ENB44", "version": "v1", "record_type": "research_paper", "title": "From Static Recoverability to Maintenance Power: A Typed Pipeline with ω = 0 Obstructions", "abstract": "We study when geometric separation in gapped quantum systems yields a genuine reduction in thermodynamic resources required to maintain coherence against uncontrolled open-system dynamics. Our analysis separates three layers. First, in a regularized Gaussian split regime motivated by algebraic QFT, we state an explicit static reconstruction bound: collar suppression of vacuum cross-correlations enables approximate state recovery via a conditional-reattachment covariance rule with fidelity error controlled by a cross-block recovery norm. Second, we show why static recoverability does not automatically imply suppression of dynamical decay rates: fixed-point structure and Bohr-zero (omega = 0) channels can generate obstructions invisible to static clustering alone. We formalize this using an exact omega = 0 Dirichlet identity and implement finite-size commutator-witness diagnostics in the transverse-field Ising chain, finding no evidence of a size-independent omega = 0 floor in that benchmark regime for tested sizes. Third, we give an autocontained finite-dimensional core linking coherence loss to incremental maintenance power under an explicit battery-assisted thermal-operations model with paired strategies, and we state a typed rate-inheritance hypothesis identifying precisely what additional dynamical input is required to propagate collar suppression into power suppression. We conclude with a Type III blueprint. v2 corrects two points and adds verification: (i) the recovery rule of the static layer is conditional reattachment -- not the Petz map for correlated Gaussian references (aligned with 2601.0007 v2 and 2512.0060 v2), with an explicit admissibility hypothesis; (ii) the v1 work-cost bookkeeping (its Eq. (25)) carried a sign error -- the work cost is the battery free-energy decrease -- which made v1's one-step work lemma false as printed (random energy-conserving unitaries violate it in 57/100 draws) while its own proof chain and everything downstream hold verbatim with the corrected sign; this is the same error class repaired in 2512.0061 v2. v2 further adds a GNS/KMS convention bridge to the companion witness papers, series positioning, an updated status of the rate-inheritance hypothesis, and a verification suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-10", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0031", "abstract_url": "https://www.ai.vixra.org/abs/2601.0031", "first_submitted_at": "2026-01-10T16:50:51+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T12:40:49+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0031-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-10T16:50:51+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0031v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T12:40:49+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0031v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "98e052292f88e60652571551f05346173da6b70d85f0c57468911716be944c70", "canonical_bytes": 370647 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:881e94bd-ae71-48d3-b1df-eb768a4e689a", "version_id": "arr:version:54f7359e-eb04-4dac-a678-0b605100fd79", "id": "ARR-2026-483TABVBKH939V3Q", "version": "v1", "record_type": "research_paper", "title": "Operational Influence Proxies in a TFIM Surrogate: Non-Monotonicity and a Controlled ω = 0 Witness Floor Mechanism", "abstract": "We study spatial influence detection in a transverse-field Ising chain (TFIM) subjected to localized Markovian noise. Using an operational one-site trace-distance influence proxy computed from TEBD combined with Monte Carlo wavefunction (MCWF) sampling, we test whether remote dissipation produces an identifiable nonzero asymptotic influence offset (a \"floor\") as a function of separation epsilon. Uncertainties are estimated by trajectory bootstrap and model selection is performed between exponential decay and exponential-plus-offset forms using both BIC and the finite-sample corrected criterion AICc. In the TFIM surrogate regimes explored, we find no robustly identifiable floor for both dephasing and amplitude-damping channels; instead, the influence proxy is non-monotone in separation, consistent with coherent finite-size structure superimposed on average attenuation. To demonstrate that floors can exist as a controlled mechanism independent of fragile spatial fits, we present a Davies/witness stress test: for nonzero zero-frequency bath weight gamma(0) > 0, a commutator witness yields a strictly positive lower bound on an effective decay envelope. Exact-diagonalization calculations show this lower bound is robust to enlarging the observable support and to variations in inverse temperature. v2 adds: a synthetic-injection power analysis showing that over the sampled one-octave window epsilon in [16,32] with n = 5 points, a constant floor is nearly degenerate with a slow exponential -- AICc essentially never detects a floor and even BIC requires D0 ~ 30 sigma -- so \"no identifiable floor\" is in part a design limitation, now stated as such; a fully declared exact-diagonalization benchmark for the witness (v1 did not record its ED parameters), regenerable from scratch by the shipped suite; a null case showing the witness switches off (kappa_min ~ 1e-29) for couplings with vanishing omega = 0 component; an invariant-subspace caveat for the envelope interpretation; and series cross-references.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0022", "abstract_url": "https://www.ai.vixra.org/abs/2601.0022", "first_submitted_at": "2026-01-08T22:09:15+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T10:46:14+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0022-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-08T22:09:15+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0022v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T10:46:14+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0022v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c3b1194c683a1d525119f19f51152f4f89ae71a2eeb866ab72a42bfbc5ece0fc", "canonical_bytes": 697244 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e996058a-4636-48f1-b534-5abf70224f33", "version_id": "arr:version:8cf008a4-ea76-407f-93c5-299b9d3b652d", "id": "ARR-2026-79JR2RMHHP93RVAD", "version": "v1", "record_type": "research_paper", "title": "Finite-Dimensional Davies Interface Lemmas and TFIM Witness Tests for Separation-Dependent Decoherence Rate Envelopes", "abstract": "We develop a finite-dimensional technical core for relating separation to effective decoherence-rate envelopes in Davies-type open-system dynamics. We work with energy pinching Delta and quantify coherence by C(rho) = S(rho||Delta[rho]). We import a maintenance inequality P_extra(rho) >= k_B T dC_loss(rho) -- in the corrected operational sense of its source (paired strategies against efficient/free baselines, 2512.0061 v2) -- as an external input. On the operator side we prove: (i) an exact omega = 0 Dirichlet identity yielding a witness-based lower bound on instantaneous decay envelopes, (ii) a Bohr-channel Dirichlet decomposition for a single-channel Davies generator under quantum detailed balance -- corrected in v2: the v1 form (1/2) sum_w gamma(w) ||[S(w),O]||^2 is false as an identity (numerical deviations of order 20%); the exact form is sum_w gamma(w) e^(beta w/2) Re , which reduces to (i) at omega = 0 and is nonnegative pairwise in +-omega -- and (iii) envelope suppression lemmata under infrared exclusion and quasi-local spectral tails, reproved in v2: the v1 proofs used a KMS submultiplicativity step that is false in general (a one-qubit counterexample saturates the corrected constant); the corrected constants carry c_sigma^2 = (lambda_max/lambda_min)^(1/2) and sup_w gamma(w)e^(beta w/2), and the e^(-2 eps/xi) exponent survives via a new positivity-pinning argument: for S = S_near + delta S_tail and far-supported O, detailed balance at every delta forces E_delta(O) = delta^2 E_tail(O) exactly. Consequently Lemma 4.13's v1 claim of a lambda_min-free prefactor is downgraded to a quadratically improved dependence. On the state side we give an asymptotic linearization on Bohr-block perturbations with fixed diagonal, yielding a direction-dependent effective decay rate. Finite-size TFIM witness diagnostics are provided, and every corrected statement is verified to machine precision by the shipped suite.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0023", "abstract_url": "https://www.ai.vixra.org/abs/2601.0023", "first_submitted_at": "2026-01-08T22:07:05+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T11:58:08+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0023-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-08T22:07:05+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0023v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T11:58:08+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0023v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "871fcced1cf481047c650541f2d1285388f8708a67bb3c32c6d997fce932a819", "canonical_bytes": 642098 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:31c0daea-f95f-4e51-b660-a8395bcce8a0", "version_id": "arr:version:42db9a26-5cb3-4f18-b5c5-b0de8491a605", "id": "ARR-2026-1HR3DENYAZ9S8VCR", "version": "v1", "record_type": "research_paper", "title": "Geometric Markov Bounds and Rate Inheritance Modulo Fixed Points: A Scalar Entropic Interface from Static Locality to Davies Dynamics", "abstract": "We propose an entropic interface between locality, recoverability, and dynamical decay rates across a geometric collar. The central scalar invariant is the conditional mutual information (CMI) I_rho(A:C|B), where B is a buffer separating A and C. In finite dimension (Type I algebras), the Fawzi-Renner theorem implies that small CMI yields a quantitative recovery channel acting on B. We formulate a volume-uniform geometric Markov bound with a boundary prefactor, I_rhoLambda(A:C|B) <= sigma(dB) g(w), and summarize recent literature inputs establishing exponential CMI decay in shielded/high-temperature regimes. On the dynamical side, we formulate a Rate Inheritance Principle (RIP) for Davies/KMS-symmetric generators: static Markovness across the collar constrains decay rates on the fast sector F-perp modulo the fixed-point algebra F = ker L (the omega = 0 floor), with a dynamical input stated as a Poincare inequality for a local collar Dirichlet form. The only remaining nontrivial link is isolated as an explicit Dirichlet comparison assumption. We verify a diagonal (classical) heat-bath comparison and derive a diagonal subsector corollary with an explicit transfer coefficient. Finally, we define a split reduction datum and a split-regularized CMI target quantity for an AQFT lift and include finite-size illustrations/diagnostics. v2 corrects two points and adds verification: (i) the Fawzi-Renner factor under the squared-fidelity convention is -log F, not -2 log F (as in the companion 2512.0101 v2), so the geometric recovery bound reads 1 - F <= sigma(dB) g(w); (ii) the v1 bulk-collar comparison for diagonal heat-bath observables is false as stated -- exact-enumeration counterexamples are exhibited -- and is replaced by a proved version with the collar extension taken on the enlarged neighborhood B^(+2r) (commuting-projection argument). A full verification suite (exact enumeration, N = 9 Ising-Z) ships with the paper, checking the corrected comparison (0 violations), the transfer constants, the exact vanishing of CMI for the 1D Markov field, and the corrected FR factor on random tripartite states. Throughout, the target RIP theorem remains conditional on the bulk-collar comparison assumption; the diagonal heat-bath result verifies only a corrected commuting-subsector comparison, and also exhibits a 1D degeneracy of the transfer constant.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-08", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0020", "abstract_url": "https://www.ai.vixra.org/abs/2601.0020", "first_submitted_at": "2026-01-08T00:26:07+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T09:50:00+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0020-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-08T00:26:07+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0020v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T09:50:00+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0020v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "46e37a6a0954b9dca2c32dfe409b4ecb6ade9db4d6c7e0a249b24fe44cb10356", "canonical_bytes": 700270 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:1753461b-c954-413d-8020-5146c4c93afd", "version_id": "arr:version:7c720513-1e40-4c71-9f31-a44b47da5023", "id": "ARR-2026-0QAD31QJAM84YR08", "version": "v1", "record_type": "research_paper", "title": "Quantitative Recovery Bounds from Vacuum Clustering in Finite-Mode Gaussian States (A Regularized CCR Blueprint Motivated by Split Inclusions)", "abstract": "We prove a quantitative clustering—recovery bound for centered quasi-free (Gaussian) states in a finite-mode bosonic CCR (Weyl) setting. Motivated by split inclusions in algebraic quantum field theory, we work in a regularized framework where Gaussian states are parametrized by finite covariance matrices and a recovery map admits an explicit covariance block formula. Using a perturbative Gaussian fidelity input and explicit coercivity bounds for inverse covariances, we control the recovery error in terms of a vacuum cross-correlation factor, a cross-correlation perturbation parameter, and a recovery-error matrix norm ||DeltaGamma||_HS with an explicit quadratic+quartic structure. In a distinguished class (Family A, X = X0), this reduces to a bound in terms of the cross-block error ||Delta12||_HS. We include ancillary numerical sanity checks verifying the perturbative regime, a collar-envelope decay model, a dimension sweep n1 = n2 in {1,2,3}, and phase-diagram checks of the perturbative domain. v2 adds: a collar-suppressed recovery corollary making the \"clustering suppresses recovery error\" mechanism a single displayed inequality; an upgraded discussion of the fidelity constants (the local coefficient 1/8 is shown numerically to be a directional benchmark, not a uniform bound, and an empirical constant is certified on the sampled domain); an independent verification suite in pure NumPy/SciPy implementing the Banchi—Braunstein—Pirandola fidelity formula with closed-form anchors, with all proved inequalities tested on random draws (zero violations); positioning remarks relative to the companion notes 2512.0060 and 2512.0101; and, aligning with 2512.0060 v2, corrected Petz-identification language (the recovery rule is conditional reattachment, with Petz agreement only in the factorized case) plus an explicit admissibility hypothesis for the recovered covariance.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2026-01-02", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2601.0007", "abstract_url": "https://www.ai.vixra.org/abs/2601.0007", "first_submitted_at": "2026-01-02T13:26:10+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T08:56:03+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2601.0007-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2026-01-02T13:26:10+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0007v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T08:56:03+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2601.0007v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "75f27c0c27b4607152ed67e704fbec55269e11896ed2f465105c06d244706195", "canonical_bytes": 1426286 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:82b187f9-cac3-4ca6-9465-31fe00b4cc0d", "version_id": "arr:version:c43faf25-1f21-40c2-89c2-b9877d351eb7", "id": "ARR-2025-42P63ZKJP39JK98S", "version": "v1", "record_type": "research_paper", "title": "Refix-Path Bell Transport on Ibm Quantum Hardware: High-Resolution Replication, Comparative Geometry Dependence, and Stress Tests of a Static—Dynamic Link", "abstract": "This note reports a replicated, high-resolution Bell-transport experiment on IBM Quantum superconducting hardware using a prefix-path protocol that controls spatial heterogeneity across transport lengths. A single physical qubit chain is fixed and increasing transport length L is realized via prefixes of that chain, so that L changes depth while keeping qubits nested rather than switching to different qubit subsets. We reconstruct the Bell-state fidelity F(L) from Pauli correlators E_XX, E_YY, E_ZZ and apply a minimal drift correction using interleaved full-Phi+ control blocks. Beyond a single-chain sweep, we perform a comparative geometry test across three disjoint physical chains on the same backend: the effective decay scale differs significantly across chains (with >10 sigma separations under fit uncertainties), providing operational evidence that the transport decay scale is geometry-dependent under fixed compilation constraints. Motivated by the Rate Inheritance Principle (RIP) framing, we also investigate whether a phase-sensitive static correlation metric measured on idle chains can predict dynamical transport decay. A curated three-chain set exhibits an ordering agreement between a static Ramsey-X nearest-neighbor covariance metric and the transport decay scales mu measured on the same chains; however, scale-up studies over n=18 randomly sampled chains and a preregistered out-of-sample prediction test do not show statistically significant monotone association under permutation testing. We interpret the static—dynamic ordering agreement as conditional and geometry-specific, while the geometry dependence of dynamical decay is robust. v2 adds: a fitting-choice caveat with a synthetically validated re-analysis pipeline for future variant tables, a power bound showing the negative preregistered test excludes a strong device-wide static—dynamic law (from published quantities alone), an all-lengths rate proxy specification, small-sample and estimator caveats, context references, and an offline re-analysis script with documented schema for a future data revision.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-31", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0105", "abstract_url": "https://www.ai.vixra.org/abs/2512.0105", "first_submitted_at": "2025-12-31T20:11:52+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T07:16:09+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0105-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-31T20:11:52+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0105v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T07:16:09+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0105v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "c922f39ba8a043df8fb92b1fd58718efbabfe1af43ac312b8f735671991457bd", "canonical_bytes": 831061 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:59fd4f44-6298-4b42-8e20-de423108e80b", "version_id": "arr:version:e92c1889-aabd-4a13-9f40-8a30bd62bab7", "id": "ARR-2025-2SZN7M8RMR9D18W8", "version": "v1", "record_type": "research_paper", "title": "Heat Kernel Methods and the Sign of Induced Gravity: Resolving Conventions via the Laplacian—Lichnerowicz Identity", "abstract": "We derive the local one-loop contribution proportional to the scalar curvature R in the Euclidean effective action obtained by integrating out matter fields on a curved background. Using a Schwinger proper-time cutoff epsilon = Lambda^(-2) and the Seeley—DeWitt coefficient a_1, we extract the quadratically divergent term multiplying int d^4x sqrt(g) R. We fix a single Euclidean convention for the Einstein—Hilbert action, state an explicit Laplacian convention, and write the Laplacian—Lichnerowicz identity in a sign-robust form so that the fermionic contribution is unambiguous. We provide a unified bookkeeping coefficient A_1^(eff), and hence an induced Newton coupling G_ind via comparison with the Euclidean Einstein—Hilbert action. We also include the minimal gauge+ghost package in background Feynman gauge, a species table, and a reproducible verification suite. v2 adds: the equivalence of the species table with the classic counting 1/G_ind = (Lambda^2/12pi)(N_0 + 2N_(1/2) - 4N_1), gauge- and scheme-dependence caveats for the vector sector, a Weyl/Majorana caveat, corrected Wick-rotation wording, and an exact-spectrum numerical verification of every a_1 entry against closed-form spectra on S^4.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-31", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0102", "abstract_url": "https://www.ai.vixra.org/abs/2512.0102", "first_submitted_at": "2025-12-31T01:35:33+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T06:40:10+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0102-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-31T01:35:33+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0102v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T06:40:10+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0102v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "6d0c308e2dda03d1d3c4758ad464b39f7075b7c26de2a8b2379660c9dc7376e4", "canonical_bytes": 292300 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:d5c00e7f-e3e1-4d64-8c41-e09d64bd8e36", "version_id": "arr:version:997fd655-522d-4682-9517-3323a4922f2b", "id": "ARR-2025-6NR077ZRZ19NJ8RG", "version": "v1", "record_type": "research_paper", "title": "Beyond Gaussianity: Extending the Clustering-Recovery Bridge", "abstract": "We formulate a non-Gaussian, finite-volume and uniform-in-Lambda version of the Clustering-Recovery bridge for interacting lattice systems. We introduce an explicit collar geometry, a CMI formulation via Fawzi-Renner, and an operational (Heisenberg-picture) quasi-locality strengthening for the recovery map. Version 2 corrects one identity: v1's \"CMI as relative entropy\" equation equated I(A:C|B) with the relative entropy to the normalized Markov-product state; the exact identity holds for the unnormalized product M = exp(log rho_AB + log rho_BC - log rho_B), and the normalized version underestimates the CMI by -log Z >= 0 (Z <= 1 by Lieb's triple-matrix inequality). We also fix the Fawzi-Renner factor: with the squared-fidelity convention used throughout, the bound is I(A:C|B) >= -log F (not -2 log F). All numerical claims of v1 (Petz slope table; prefactor-slope trade-off; crossover w*=3) have been independently reproduced from scratch by a NumPy-only verification script that ships with this paper.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-31", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0101", "abstract_url": "https://www.ai.vixra.org/abs/2512.0101", "first_submitted_at": "2025-12-31T01:06:02+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T06:24:25+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0101-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-31T01:06:02+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0101v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T06:24:25+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0101v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "deccb8bc94753f1dd39565fd6033782d99aef7f10414a406080a50a3d0ead463", "canonical_bytes": 324112 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:cd2d6537-139a-414d-8ca1-6c0bede2c5bf", "version_id": "arr:version:7f782ec5-a0fb-49db-bcb3-8b37ed02113f", "id": "ARR-2025-6D5NJKE4WT856RS8", "version": "v1", "record_type": "research_paper", "title": "Technical Appendix: Heat Kernel, Fermions, and the Sign of Induced Gravity (Sign Conventions Fixed; Laplacian/lichnerowicz Hinge Made Explicit)", "abstract": "We derive the local contribution proportional to the scalar curvature R in the Euclidean one-loop effective action obtained by integrating out matter fields on a curved background. Using a Schwinger cutoff epsilon = Lambda^{-2} and the Seeley-DeWitt coefficient a1, we extract the quadratically divergent term multiplying the integral of sqrt(g) R. We fix a single Euclidean convention for the Einstein-Hilbert action, state an explicit Laplacian convention, and write the Lichnerowicz/Weitzenbock identity in a sign-robust form so that the fermionic contribution is unambiguous. We provide a unified bookkeeping coefficient A1_eff such that W_R^total = -(A1_eff / 32 pi^2) Lambda^2 integral sqrt(g) R, and hence an induced Newton constant G_ind via comparison with the Euclidean Einstein-Hilbert action. We include the minimal gauge+ghost package in background Feynman gauge, a species table, and a reproducible symbolic check of every entry.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-27", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0091", "abstract_url": "https://www.ai.vixra.org/abs/2512.0091", "first_submitted_at": "2025-12-27T17:26:11+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T05:50:16+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0091-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-27T17:26:11+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0091v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T05:50:16+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0091v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Relativity and Cosmology" ], "subjects": [ "Relativity and Cosmology" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "db0b2aa950d5be9473fca427fcb66408393b158abe34e2c2f578556f52328775", "canonical_bytes": 288885 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:94d9eb37-ac50-4cfb-b409-f30f89867194", "version_id": "arr:version:0ba15b47-63f0-464f-8694-886f90fa1c39", "id": "ARR-2025-4MV7NKFB2G9KXV82", "version": "v1", "record_type": "research_paper", "title": "The Maintenance Constraint: How Resource Boundaries Shape Cognitive Availability", "abstract": "Cognitive systems are resource-limited, but \"resource limitation\" is often invoked without distinguishing one-shot costs (forming a representation) from sustained costs (keeping it usable under noise). We argue that the availability of internal state features for control, integration, and report is constrained by their maintainability under finite budgets. As a technical anchor we cite a companion preprint deriving an operational maintenance inequality in explicit thermodynamic control models: incremental maintenance power has a non-arbitrary lower bound tied to dynamical fragility (in its corrected form, against efficient baselines, with an unconditional entropy-production floor beneath). This motivates an operational cut: a feasibility boundary separating maintainable from unmaintainable state features. We develop an auditable bridge argument (maintainability to stability to availability), propose a neutrality-friendly principle of maintenance-feasibility bias, and show how it can be incorporated into active inference (the Free-Energy Principle) as a maintenance penalty or constraint, aligning secondarily with Global Workspace accounts of access stability. We address objections and offer falsifiable predictions for synthetic agents and neuromorphic systems, plus an explicitly exploratory psychophysics subsection framed in terms of reportability and stability rather than phenomenology. We do not propose collapse mechanisms, do not derive the Born rule, and make no claims about phenomenological consciousness.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-24", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0084", "abstract_url": "https://www.ai.vixra.org/abs/2512.0084", "first_submitted_at": "2025-12-24T22:34:15+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T05:45:54+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0084-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-24T22:34:15+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0084v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T05:45:54+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0084v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mind Science" ], "subjects": [ "Mind Science" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "5f82531a3404c7b3bb9fae52b549174b961413014cdff0289fc037828cb4b9d5", "canonical_bytes": 231957 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:4abf7242-44df-442e-a80a-039938e0c57f", "version_id": "arr:version:143d6b49-f172-419a-9798-44aa288402bd", "id": "ARR-2025-2AQXS44H6Z8GQAG2", "version": "v1", "record_type": "research_paper", "title": "Geometry, Membranes, and Life as a Resource Boundary: A Correct-by-Construction Operational Pipeline from Static Suppression to Maintenance Costs", "abstract": "We present a logically explicit operational program connecting three themes: geometry as suppressibility of cross-region influence, membranes as engineered interfaces implementing that suppressibility, and life as sustained maintenance of internal organization under finite resources. The program composes: (i) a law-grade thermodynamic inequality relating incremental maintenance power to the instantaneous loss rate of an organization functional, imported in its corrected operational hierarchy; (ii) a static geometric suppression layer in which cross-interface leakage admits an envelope f(eps) ~ poly(m eps) e^{-m eps} (with K_nu(m eps) as a canonical representative in massive homogeneous models); and (iii) a dynamical hinge (the Rate Inheritance Principle, RIP) connecting static suppression to separation-dependent effective dynamical rates. This version distinguishes upper and lower rate envelopes kappa_up(eps) and kappa_down(eps) to avoid sign/quantifier errors -- a distinction now vindicated by the companion series -- separates a law-grade Delta-track (energy pinching) from a conditional biology-grade E-track (general conditional expectations), and adds two interface anchors: a recoverability layer via conditional mutual information (CMI) and the Fawzi-Renner guarantee, and a minimal Davies interface lemma showing how correlator envelopes imply Davies-rate upper envelopes (supporting RIP-U microscopically in standard weak-coupling settings). A concrete electrical testbed using membrane-embedded spin probes is proposed to measure dephasing-rate envelopes and detect near-zero-frequency floors that create a resource horizon. A dependency and falsification matrix makes the logical structure audit-friendly.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-24", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0085", "abstract_url": "https://www.ai.vixra.org/abs/2512.0085", "first_submitted_at": "2025-12-24T22:30:35+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T05:47:22+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0085-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-24T22:30:35+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0085v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T05:47:22+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0085v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "64146659ff96cd3261b55c37093df439deb061625a11f869712ae01c0c3f6c01", "canonical_bytes": 310394 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:294a5258-ba85-463e-ab55-8ebc46290e0c", "version_id": "arr:version:6131aad7-638e-4cfe-81e6-fe74081767f7", "id": "ARR-2025-199995HEM58RZAPN", "version": "v1", "record_type": "research_paper", "title": "Operational Coherence Maintenance and the Quantum-Classical Boundary: Formal Definitions, Falsifiable Protocols, and an Outlook for Cognitive Systems", "abstract": "Maintaining quantum coherence against uncontrolled open-system dynamics is a control task with unavoidable thermodynamic cost. In a finite-dimensional setting with battery-assisted thermal operations at bath temperature T, we present the corrected operational hierarchy for maintenance power: an unconditional lower bound P_min(rho) >= k_B T sigma(rho) with sigma(rho) the entropy production rate of the target (proved in the appendix); the coherence-power bound P_min >= k_B T Cdot_loss(rho) under diagonal contraction; and incremental (extra) power bounds relative to thermodynamically efficient population-maintenance baselines, which become assumption-free exactly when the pinched target is stationary -- e.g. under pure dephasing, the very dissipator used in this paper's numerical protocol. Here C(rho) = S(rho||Delta[rho]) is relative-entropy coherence to energy pinching and Cdot_loss(rho) := -d/dt C(rho_t)|_{t=0}. These statements are operational, observer-independent, and geometry-free. We then present the Rate Inheritance Principle (RIP) as the falsifiable dynamical bridge between static clustering and decoherence rates, with its status: weak form a lemma under explicit hypotheses; strong form derived, with a frequency-resolved squared-amplitude exponent, in an exactly solvable quasi-free local-sink class; failure through near-zero Bohr-frequency channels realized within the secular Davies class. We provide falsifiable protocols distinguishing one-shot work from sustained maintenance power, including a numerical stress test (distance-independent influence floor without an interface vs collar-induced suppression) in a transverse-field Ising chain with remote dephasing. Finally, an explicitly speculative Outlook connects the resource boundary to the Free-Energy Principle for resource-limited agents, at a methodological (non-phenomenological) level.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-23", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0081", "abstract_url": "https://www.ai.vixra.org/abs/2512.0081", "first_submitted_at": "2025-12-23T10:38:28+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-05T05:44:24+00:00", "mirrored_version": "v1", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0081-v1.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-23T10:38:28+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0081v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-05T05:44:24+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0081v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "4d2b2443bda740859f18a78e17b00490263e5dbb5dce6ecfdd93ed253340840b", "canonical_bytes": 530940 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:2d45e482-53c0-4b2a-b922-d51611965bcc", "version_id": "arr:version:5e8aca29-0e28-4823-80bf-70ea67b0177f", "id": "ARR-2025-1D8QJ84MY09CNBJ8", "version": "v1", "record_type": "research_paper", "title": "Stress Testing the Rate Inheritance Principle: Spectral Decoherence Rates and an Operational Resource Horizon", "abstract": "In gapped quantum many-body systems, static correlations decay exponentially with distance. A common heuristic expectation is that this geometric suppression carries over to dynamical decoherence rates induced by local environments; this expectation has been isolated as the Rate Inheritance Principle (RIP). We stress test RIP in a fully specified Davies-type Markovian setting: a gapped transverse-field Ising chain weakly coupled to a thermal bosonic bath through a strictly local operator. RIP is formulated operatorially through two spectral envelopes of the Dirichlet form on operators supported at distance eps from the coupling region: a ceiling kappa_sup(eps) (v1's envelope) and a floor kappa_perp(eps) (smallest nonzero rate, new in v2 — the quantity a maintenance no-go actually needs; v1's inference from ceiling saturation to a power floor was a non sequitur and is corrected here). Numerically, rate inheritance remains conditional: for energy-exchange-dominated coupling the ceiling decreases with separation, while for near-zero-Bohr-frequency coupling it saturates — and, more importantly for the no-go, the projected floor also persists in that regime. Version 2 adds the diagnostic that the series' methodology demands: the near-zero-frequency Bohr components of the local coupling are strongly delocalized at finite size (about 90 percent of their weight beyond the coupling site), so the saturation is established within the Davies model class, whose secular construction is nonlocal; the exactly solvable local-sink model of the companion paper shows genuine geometric suppression, and the two results bracket the physics. Combined with the corrected maintenance bounds of the companion work theorem, a persistent projected spectral floor yields a quadratic-proxy resource horizon; the corresponding relative-entropy no-go is stated with its required uniform-Cdot_loss / MLSI-type hypothesis explicit.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0070", "abstract_url": "https://www.ai.vixra.org/abs/2512.0070", "first_submitted_at": "2025-12-19T18:38:28+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T16:52:43+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0070-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-19T18:38:28+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0070v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T16:52:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0070v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "d17233949d5fef496c7f5c73d2fe3da138cc803d550d5a19cf98af8771501e6d", "canonical_bytes": 328933 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:239355f7-f6d6-405c-bf13-940d1b80518a", "version_id": "arr:version:b6d44571-c74f-41a7-bee6-e0f00bae37ce", "id": "ARR-2025-13JDAZFXPP81EBY4", "version": "v1", "record_type": "research_paper", "title": "Operational Coherence Maintenance: Proven Results, Conditional Interfaces, and Open Dynamical Gaps", "abstract": "Maintaining quantum coherence against uncontrolled open-system dynamics is an operational control task with unavoidable thermodynamic cost. In finite dimensions, explicit lower bounds on the minimal power required to stabilize coherence can be derived under standard Markovian assumptions, independently of geometric or field-theoretic structure. At the same time, static correlations in gapped systems are geometrically suppressed, raising the question of how such suppression influences dynamical decoherence rates and, consequently, coherence-maintenance power. Bridging the two domains requires dynamical input that static clustering alone does not provide.This note introduces no new technical results. It provides a logical closure of the program by separating (i) results proven without additional structure, (ii) conditional interfaces, and (iii) dynamical hypotheses — and, new in this version, it updates the status of the central hinge. In v1, rate inheritance — the relation between static correlation envelopes and effective decoherence rates — was identified as the unique unresolved hinge. Since then it has been partially resolved in both directions anticipated by v1's scenario analysis: it is now a derived, frequency-resolved law in an exactly solvable quasi-free local-sink class (2512.0064 v2), and the failure scenario through near-zero-frequency channels has been realized within the Davies model class, with the persistent floor computed and the secular nonlocality of that construction quantified (2512.0070 v2). The imported maintenance bound is restated in its corrected v2 form (2512.0061 v2), whose v1 formulation was vacuous. The framework's design goal — robustness under partial refutation — has thus been exercised in practice, twice.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0071", "abstract_url": "https://www.ai.vixra.org/abs/2512.0071", "first_submitted_at": "2025-12-19T18:31:21+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T17:25:11+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0071-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-19T18:31:21+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0071v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T17:25:11+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0071v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "a162065564b23b7dc1a79f4336ff22c724c66a8259fd3792ee3ab89c560ba062", "canonical_bytes": 249511 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:a243fc1b-439a-45dd-be5c-cb35bab74bd0", "version_id": "arr:version:66932fd4-7c13-4a35-ad45-8ab666e3a72f", "id": "ARR-2025-528FY1PGWT8QEVWQ", "version": "v1", "record_type": "research_paper", "title": "The Rate Inheritance Principle: From Static Correlations to Dynamical Decoherence Rates", "abstract": "In gapped open quantum systems with localized couplings, static correlations across an operational interface of width eps are exponentially suppressed by the mass gap. Independently, the energetic cost of maintaining quantum coherence is governed by the rate at which coherence is lost under uncontrolled dynamics. The Rate Inheritance Principle (RIP) is the hypothesis connecting the two: effective coherence-loss rates inherit the suppression envelope of static correlations across the interface. We distinguish a weak upper-envelope form — stated here as a short proved lemma under explicit integrability hypotheses — from a stronger envelope-class conjecture, and we record what is now known: the strong form is derived, with a frequency-resolved exponent, in an exactly solvable quasi-free local-sink class, where the rate inherits the square of the static amplitude envelope, kappa(eps) proportional to e^(-2 q(omega_b) eps) — confirming the squared-envelope caveat anticipated in v1 — and it fails through near-zero-frequency channels within the secular Davies model class, whose delocalized jump operators sustain a persistent rate floor. Version 1's surrogate decay-curve evidence is withdrawn: it belonged to the uncontrolled proxy class whose failure mode was exposed by the critical-point control of the companion paper, and it is replaced here by the exact Liouvillian-rapidity evidence. Failure modes (now including secular delocalization), a proxy-validated falsification protocol, and the conditional operational consequences for the quantum-classical resource boundary are stated with explicit scope.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0072", "abstract_url": "https://www.ai.vixra.org/abs/2512.0072", "first_submitted_at": "2025-12-19T18:23:38+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T17:26:43+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0072-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-19T18:23:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0072v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T17:26:43+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0072v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "8eba17b544a16854847bc54d74c5d53c4454e52bf1557617a3b8028182274b56", "canonical_bytes": 316870 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:03c70b98-cc65-404a-bfe1-a0df042ce11b", "version_id": "arr:version:2bc714b6-4af4-43b1-aac8-f22b9b66f8bb", "id": "ARR-2025-03RW5SHK35815BZR", "version": "v1", "record_type": "research_paper", "title": "Finite-Dimensional Davies Interface Lemmas and TFIM Witness Tests for the Heisenberg Cut as a Resource Boundary", "abstract": "SUPERSEDED BY AI.VIXRA:2601.0023V2. This replacement preserves public version 1 and adds an explicit correction and supersession record. The exact omega=0 statements and witness mechanism of version 1 stand unchanged, and Proposition 4.4 survives with a repaired proof. What is superseded is the false general plain-commutator Bohr decomposition, the suppression proof route using a false KMS submultiplicativity bound, the associated constants and claim of avoiding an inverse-smallest-eigenvalue factor, and the inline listing. ai.viXra:2601.0023v2 supplies the exact general decomposition, corrected c_sigma-dependent bounds, pinning identity, explicit hypotheses and verification suite. No thermodynamic, continuum or universal resource-boundary theorem follows from the finite tests. The preserved version 1 follows the two-page notice unchanged.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-19", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0073", "abstract_url": "https://www.ai.vixra.org/abs/2512.0073", "first_submitted_at": "2025-12-19T17:44:57+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-08-01T08:38:55+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0073-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-19T17:44:57+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0073v1.pdf" }, { "version": "v2", "submitted_at": "2026-08-01T08:38:55+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0073v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "11cc85a3fe09efaac11fe7721c338eb2ad5998c9c31aa9972a074f8b4851708c", "canonical_bytes": 947931 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:37127244-0b60-4683-bd80-544021314a7c", "version_id": "arr:version:d2d07e19-8efc-4d1c-ae8f-4d06d526af5a", "id": "ARR-2025-1Q29S482V08T1VV0", "version": "v1", "record_type": "research_paper", "title": "The Heisenberg Cut as a Resource Boundary: An Operational Outlook from Coherence Maintenance Costs", "abstract": "We revisit the proposal that the Heisenberg cut is best understood operationally, as a resource boundary: a superposition counts as effectively classical for an agent once the power required to maintain its coherence against decoherence, P_extra >= k_B T Cdot_loss, exceeds that agent's budget. Version 1 supported the key dynamical ingredient — the rate-inheritance hypothesis, that decoherence rates transmitted through a gapped buffer of width eps are suppressed as poly(eps) e^(-m eps) — with a windowed numerical proxy on a transverse-field Ising chain. Two things change in this revision. First, rate inheritance is now derived in an exactly solvable quasi-free model and verified against exact Liouvillian rapidities: for a probe mode of renormalized sub-gap frequency omega_b coupled through a Kitaev buffer to a Markovian loss, the exact Liouvillian rapidity obeys kappa(eps) proportional to e^(-2 q(omega_b) eps) with cosh q(omega) = (mu^2 + 4 - omega^2)/(4 mu), verified to four decimal places over ten decades of kappa; the exponent is the squared (amplitude^2) one, resolving Remark 8.1 of v1, and it closes continuously at the band edge. Second, the central numerical evidence of v1 (its Fig. 1) is withdrawn: an exact critical-point control shows that the co-moving-window proxy decays faster when the gap is removed, so what it measured was arrival kinematics, not gap physics. We identify the mechanism with photonic-band-gap suppression of emission and evanescent atom-photon bound states, restate carefully what is imported versus what is new, derive a logarithmic law for the resource cost of coherence lifetime, note that the protected object is a sub-gap subalgebra rather than a spatial region, and state the interacting-buffer conjecture that would take rate inheritance beyond the quasi-free class. The non-claims of v1 stand unchanged: nothing here derives the Born rule or selects single outcomes.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0064", "abstract_url": "https://www.ai.vixra.org/abs/2512.0064", "first_submitted_at": "2025-12-17T19:09:08+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T16:52:40+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0064-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-17T19:09:08+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0064v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T16:52:40+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0064v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Quantum Physics" ], "subjects": [ "Quantum Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "923f3f37f923649fba6e830da97452e3dc8cf666358f950cdac110711ea2a3b9", "canonical_bytes": 376340 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:f0ebf41d-df69-44aa-a35e-befea3f5956c", "version_id": "arr:version:c00b5c6e-2dff-4b76-b28b-343645cb4f1f", "id": "ARR-2025-7GXFT1VQV98JNA6Q", "version": "v1", "record_type": "research_paper", "title": "Clustering, Recovery, and Locality in Algebraic Quantum Field Theory: Quantitative Bounds via Split Inclusions and Modular Theory", "abstract": "We prove that exponential clustering of vacuum correlations enables approximate reconstruction of global quasi-free states from local data in algebraic quantum field theory. The reconstruction is an explicit Gaussian procedure — conditional reattachment through the vacuum's regression structure — which coincides with the output of the Petz recovery map when the reference state factorizes across the split, but not in general: for a pure reference the Petz map returns the reference itself for every input, and version 1 of this paper incorrectly identified the two. For quasi-free states of a massive scalar field satisfying natural constraints, including a symplectic-gap (mixedness) condition on the reference state and an admissibility (no-steering) condition on the split geometry, we prove 1 - F <= C(d,kappa) / [eps^2 (1 - (eta_vac + delta)^2/eps)^2] * ||Delta12||_HS^2, where Delta12 is the reconstruction error, eta_vac <~ e^(-mr) is the vacuum correlation factor, delta controls cross-correlation perturbations, and C(d,kappa) = C_k(6+C_k)/(16 min(c1,c2)^2) with C_k = (1+kappa)^2/(kappa(kappa+2)) determined by the symplectic gap kappa > 0. A finite-rank corollary with explicit factor 2n recovers physical intuition. All counterexamples and bounds are verified by an exact truncated-Fock numerical suite distributed with the paper. Applications to holographic reconstruction are discussed.Version 2 makes three corrections to v1: (i) the reconstruction map of v1's Proposition 2.14 is not the Petz map — its \"marginal preservation\" step fails for correlated references — and the main theorem is restated for the reconstruction procedure the proof actually controls; (ii) the simplified constant is corrected (3/8 to 7/16 in the strongly mixed limit); (iii) a symplectic-gap hypothesis is added to the Gaussian fidelity lemma, shown necessary by an explicit counterexample.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-17", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0060", "abstract_url": "https://www.ai.vixra.org/abs/2512.0060", "first_submitted_at": "2025-12-17T02:23:22+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T16:52:36+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0060-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-17T02:23:22+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0060v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T16:52:36+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0060v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Mathematical Physics" ], "subjects": [ "Mathematical Physics" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "fc87d35d6258539c4c660b7bf271736fc3658efcc19f35d7cb02ae9c848b481b", "canonical_bytes": 514597 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] }, { "schema_version": "1.3", "record_id": "arr:record:e660f23c-e696-4464-8abf-98e8b8ad0867", "version_id": "arr:version:981ae9a5-ea9c-4155-9565-2227c98fdcc2", "id": "ARR-2025-76C3S3SSMP8HJ8NF", "version": "v1", "record_type": "research_paper", "title": "The Conditional Maintenance Work Theorem: Operational Power Lower Bounds from Energy Pinching and a Split-Inclusion Blueprint for Type III AQFT", "abstract": "We derive operational lower bounds on the minimal thermodynamic power required to maintain quantum coherence against uncontrolled open-system dynamics. Work is defined as the consumption of non-equilibrium free energy stored in an explicit battery at bath temperature T, namely W := F_W(sigma_W) - F_W(sigma'_W) with F_W(sigma) = k_B T S(sigma||gamma_W), and allowed controls are battery-assisted thermal operations implemented by energy-conserving global unitaries. Coherence is quantified as a relative entropy to a conditional expectation, C_E(rho) := S(rho||E[rho]). Our main proved results are: (i) an unconditional maintenance bound P_min(rho) >= k_B T sigma(rho), where sigma(rho) >= 0 is the entropy production rate of the target under the uncontrolled semigroup (Spohn), which splits via the pinching Pythagorean identity as sigma = F_diag + C_loss; (ii) the coherence-power bound P_min >= k_B T C_loss(rho) under a diagonal-contraction hypothesis satisfied by Davies generators; and (iii) extra-power bounds for coherence stabilization relative to thermodynamically efficient population-maintenance baselines — version 1's \"assumption-free\" paired-infimum formulation is shown to be vacuous (the unlinked-pairs infimum is minus infinity), and the corrected statement is genuinely assumption-free precisely when the pinched target is stationary (e.g. pure dephasing), where the baseline is free. We further provide a conditional extension to general conditional expectations and a Type III split blueprint, with external geometric inputs encoded as explicit two-sided interface assumptions. All finite-dimensional claims are verified by an exact numerical suite distributed with the paper. These results provide an operational resource criterion for quantum-to-classical behavior, not a collapse theory.Version 2 corrects a sign error in the work definition and in the final step of v1's Appendix A, replaces v1's vacuous extra-power definition, and strengthens the main bound to an unconditional entropy-production form.", "authors": [ { "name": "Lluis Eriksson", "affiliation": "Independent researcher" } ], "date": "2025-12-16", "status": "archived", "archival_source": { "archive": "ai.vixra", "identifier": "2512.0061", "abstract_url": "https://www.ai.vixra.org/abs/2512.0061", "first_submitted_at": "2025-12-16T22:14:29+00:00", "latest_declared_version": "v2", "latest_submitted_at": "2026-07-04T16:52:38+00:00", "mirrored_version": "v2", "mirror_pdf_url": "https://github.com/arr-research/arr-research.github.io/releases/download/AIVIXRA-LATEST-2026-08-30/ai-vixra-2512.0061-v2.pdf", "mirror_release_url": "https://github.com/arr-research/arr-research.github.io/releases/tag/AIVIXRA-LATEST-2026-08-30", "versions": [ { "version": "v1", "submitted_at": "2025-12-16T22:14:29+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0061v1.pdf" }, { "version": "v2", "submitted_at": "2026-07-04T16:52:38+00:00", "pdf_url": "https://www.ai.vixra.org/pdf/2512.0061v2.pdf" } ] }, "licenses": { "manuscript": "LicenseRef-Author-Retained", "metadata": "CC0-1.0", "code": [], "data": [] }, "source_of_truth": "external_pdf", "keywords": [ "Thermodynamics and Energy" ], "subjects": [ "Thermodynamics and Energy" ], "deposit": { "depositor_name": "Lluis Eriksson", "relationship": "author", "deposit_authorized": true, "third_party_material_disclosed": false, "terms_version": "ARR-HISTORICAL-IMPORT-1.0" }, "integrity": { "algorithm": "sha256", "manifest": "MANIFEST.sha256", "canonical_sha256": "1efa158fa87afe14617dd19d5247dcc29a8a8e4c3eaebf939664cf81d739511b", "canonical_bytes": 383771 }, "ai_assistance": { "used": true, "statement": "Historical import from ai.vixra, an AI-assisted e-print archive. ARR has not normalized or independently verified the original manuscript's model-use disclosure; the author remains responsible for its contents." }, "screening": { "protocol": "ARR-SCREEN-1.0", "status": "not_assessed", "critical_objections_unresolved": 0, "human_signoff": true, "evaluators": [] }, "verification": { "protocol": "ARR-HISTORICAL-IMPORT-1.0", "bibliography": "not_assessed", "source_integrity": "pass", "reproducibility": "not_assessed", "lean4": "not_assessed", "report": "VERIFICATION.md" }, "editorial": { "decision": "historical_import", "signed_by": "Lluis Eriksson", "conflicts": [ "author_is_founder_editor" ], "statement": "Author-authorized historical import. ARR verified file retrieval and integrity only; it did not perform the current hostile frontier-model admission audit, peer review, novelty review, or correctness certification." }, "latest_version": "v1", "version_count": 1, "versions": [ { "version": "v1", "publication_state": "pending", "release_tag": null, "source_snapshot_available": true } ] } ]