Research paperScreenedARR-2026-54Q3HMFJ0Z8CZB4T · v1 · 2026-09-05

Polynomial vertex reduction and optimal stability at balanced inertia (4,4)

Lluis Eriksson

Admitted after checks by named AI models and editor approval. Not peer reviewed. Screening record

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.

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v1 · 2026-09-05

Lluis Eriksson (2026). Polynomial vertex reduction and optimal stability at balanced inertia (4,4). AIRR.SCIENCE, ARR-2026-54Q3HMFJ0Z8CZB4T, v1. https://airr.science/papers/ARR-2026-54Q3HMFJ0Z8CZB4T/versions/v1/

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Verification record

Frontier-model screening
Pass · 1 models
Source integrity
Pass
Bibliographic integrity
Partial
Reproducibility
Pass
Lean 4
Not applicable

Recorded under ARR-VERIFY-1.0. AIRR verification and screening are not peer review.

AI assistance 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.

Frontier-model screening

Status: pass. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.

  • gpt-6-astraOpenAI · pass
Longitudinal frontier-model record

Model assessments and review context

Read the scale and limits
4.02 / 10.00Strong
Distinct models
2
Range
3.78–4.10
Method
bounded capability-weighted mean · exact version only

Limited evidence · 1/2 benchmark matches. This is an evidence description, not a probability of correctness.

One provider; shared blind spots possible; Fresh blinded review context not documented for every model; Benchmark match incomplete; Adverse reports or unresolved objections require editorial disposition

Score calculation and evidence

Unweighted mean: 3.94. Policy: AIRR-RATING-1.0. Method and limits.

ModelOriginal scoreWeightBasis
OpenAI · gpt-6-astra4.102.904Exact evidenced model and effort
OpenAI · gpt-5.6-sol3.781.000No evidenced exact benchmark configuration

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Review input clarification

The earlier review packet omitted public mathematical certificate inputs, including witnesses_N4.json, optimal_constant_N4_d8.json and balanced_four_certificate.json. The original missing-file objections concern that incomplete packet; these files are present in the public repository. Both original reassessments resumed after a service usage interruption. Their native reports, verification records and execution logs are now preserved separately, and the restored-source assessments contribute through the normal rating policy. Any remaining scientific findings and execution limits are recorded in those reports. Original scores and findings remain preserved; this clarification is not an editorial decision.

Operator record · · Source files and affected reports

OpenAI · gpt-5.6-sol · High · unknown · review context: unknown3.78

Recommendation: Minor Revision · Material objections: 0

This exact 8-page PDF gives a valid polyhedral reduction of the balanced stability problem and a well-supported evaluation at N=4. I checked the ordered-simplex geometry, product-edge hyperplane cuts, convex vertex reduction, Horn formulation, dimension-independent lower obstruction, boundary sharpness sequence, and concavity-based contact classification. Independent executions reconstructed 89 vertices and 8,752 Littlewood-Richardson/Horn triples, verified the 4/7 primal and dual certificates, and checked the four zero-contact vertices plus the positive midpoint gap. No unresolved material objection was found. Minor revision reflects an obsolete source/PDF-check path and an externally imported all-dimension antecedent that could not be fetched in this environment, not a detected flaw in the new proofs.

Correctness confidence
The finite reduction, 4/7 vertex bound, Horn obstruction, sharp perturbation, and four-point contact classification are mutually consistent and independently replayed exactly.
Rigor
The paper separates imported Horn sufficiency from new arguments, proves the cell geometry and cut construction, and handles compact-boundary versus exact-stratum quantifiers carefully.
Novelty
The O(N^5) rational program-count reduction and exact balanced-(4,4) coefficient/contact set appear substantive. Priority remains a bounded-search claim, not an established universal negative result.
Significance
The result solves a concrete next multiplicity and gives a reusable finite reduction, but it does not control Horn-program size, polynomial total time, or a general closed formula for N.
Reproducibility
Five standard-library replays and the exploratory LP run passed, reproducing 89 vertices, 8,752 Horn triples, exact certificates, and contact slacks. The separate PDF checker has an unavailable legacy path.

Strengths

  • Lemma 1 gives an explicit pyramid-over-product description of every ordered-simplex cell, with counts V_N and L_N that agree algebraically and in the independent geometry replay through N=8.
  • Lemma 2 correctly lists all new vertices from cutting product cells by q(a)=q(b); the O(N^5) claim is explicitly limited to the number of rational Horn programs rather than their size or total running time.
  • The N=4 forward bound uses only feasible rational common spectra at every cut vertex, so it does not depend on trusting the exploratory optimizer; Horn sufficiency and convexity then cover the compact domain.
  • Lemma 3's two-row Horn inequality and min-max bounds give the exact boundary cost 3/2, and the b_eta sandwich correctly proves optimality within every fixed exact-inertia stratum.
  • The contact proof is strong: 85 vertices have certified positive slack, only four have exact zero gap, cell incidence leaves two candidate segments, and the verified midpoint gap 7/16 excludes both interiors by concavity.

Weaknesses

  • The reverse inequality, positivity used in Theorem A, and all-dimension one-spike endpoint cost are imported from ARR-2026-24M24KDPZK8HDBQ9. Its direct PDF was inaccessible here, although base-dimension endpoint costs are covered by exact dual certificates.
  • The public-code correspondence checker expects ../pdfs/commutator.pdf and separate QA renders, neither manifest-listed in this packet. The restored public-code/paper.pdf was verified byte-identical to the canonical PDF but was not substituted into that missing path.
  • The exploratory certified_constant.py passed under NumPy 2.3.5 and SciPy 1.17.0, not the exact declared NumPy 2.5.1 and SciPy 1.18.0. The proof-critical standard-library certificate replays are unaffected.
  • The equality classification depends on exact finite incidence and witness tables rather than a compact hand-verifiable enumeration printed in the PDF; the supplied independent replay substantially mitigates this dependence.

Potential errors

  • Theorem A's assertion that the optimal coefficient is positive relies on the imported prior positive balanced stability bound. The rational finite-minimum argument itself is sound once that antecedent is granted.
  • A cut-edge enumeration could fail if product edges or cell overlaps were mishandled. The explicit proof accounts for fixed-factor product edges, and two independent implementations produced the same 89 vertices; no omitted vertex was found.
  • Zero padding yields only kappa_d<=kappa_8, not general equality. The manuscript uses this direction for the forward bound and separately invokes lower bounds at contact points, so I found no illicit invariance step.

Strong novelty candidates

  • An explicit rational O(N^5) reduction from the continuous balanced stability problem to finitely many Horn linear programs.
  • The exact optimal forward coefficient 4/7 for balanced inertia (4,4), uniformly in the number of ambient zeros.
  • The complete four-point equality locus on the compact spectral closure and strictness throughout the exact inertia stratum.

Unresolved material objections

None reported.

arr:assessment:fcd65ef6-a625-42c5-949a-9519cc8610df · prompt ARR-ASSESS-1.0 · runtime identity: OpenAI gpt-5.6-sol · reasoning effort: high · basis: operator verified ui · evidence SHA-256 b6a20a5406e416e5509f29d523ec21f17b71909ad9937491e9e77a8a04888fdd · response SHA-256 c5d076d68791b5c28265288799aaf2fab8ca5f83c7b126467380a54657c5b9c2 · canonical PDF SHA-256 c4e21f587ecaafe4aa01e7b638e3f23b90263bfe77970a924b48625afbc52901

OpenAI · gpt-6-astra · High · unknown · review context: unknown4.10

Recommendation: Accept · Material objections: 0

All eight pages of the exact PDF were inspected. The polynomial vertex reduction and the sharp 4/7 bound are supported by the written geometry and by executed exact certificates, including 778,928 original Horn checks and 787,680 contact checks. The four-point equality locus survives the midpoint and ambient-dimension arguments. No unresolved material mathematical objection was found. The main limits are specialized significance, bounded novelty verification, and an optional build-layout checker that cannot run from this packet. This is a referee assessment, not an editorial decision.

Correctness confidence
Theorems A-C survive the cell-geometry, Horn-sign, boundary, and contact-hull checks. Executed all five mathematical replays and regenerated the 48 exact LP certificates. The imported reverse bound and positive general bound were checked in the hash-matched antecedent.
Rigor
Lemmas 1-2 supply complete vertices and edges, not sampled spectra. Convexity is restricted correctly to the ordered chamber. Lemma 3 and the perturbation avoid unjustified zero-padding invariance; the midpoint witness and concavity exclude every candidate contact segment.
Novelty
The O(N^5) count of exact Horn programs and the 4/7 coefficient with four contacts are credible specific advances over the inspected antecedent. Horn sufficiency and convex polyhedral reduction are established tools. No exhaustive priority search was performed.
Significance
A useful general finite reduction plus a sharp next-multiplicity result. Its complexity claim counts programs only; it gives neither polynomial total running time nor a general interior cost formula. This supports a strong specialized contribution, not a field-transforming claim.
Reproducibility
89-vertex, LR, 48 primal-dual, and contact replays succeeded; proposal regeneration also succeeded with exact replay. The optional PDF/build correspondence checker fails at an excluded path. Actual NumPy/SciPy differ from preparation pins, documented in the verification record.

Strengths

  • Theorem A, pp.3-5: the step-coordinate face dimension p+q-2 gives the claimed vertices and base-edge rule. Product edges and transverse cuts yield V_N^2+2V_N L_N candidates; D_* is affine on each resulting cell.
  • Theorem A, p.5: positive rationality follows from rational finite LP optima and the antecedent positive stability bound. Mixing a minimizing boundary pair with u keeps the ambient dimension fixed and proves exact-stratum optimality by continuity.
  • Theorem B, pp.5-6: regenerated all 8,752 Horn triples. The 89 ordered rational witnesses pass 778,928 inequalities; 48 separate primal-dual certificates reconstruct 152 dual terms and give coefficient 4/7.
  • Lemma 3, p.6: (I,J,K)=((1,3),(1,d-1),(2,d-1)) is admissible. Applying it to -F and adding s_2>=b_2, s_4>=a_4 gives the all-dimensional lower bound. At (A,B), cost 3/2 and D_*=7/4 match the witness.
  • Theorem C, p.7: 85 vertices have strictly positive witness gap, minimum 1/7. Exact incidence leaves only two segments; midpoint cost 25/16 and gap 7/16 exclude both interiors by concavity. Padding can only increase the gap; the four endpoint costs remain exact.
  • Antecedent PDF SHA-256 15b54435c01a4972af77db0277c7f99fc21afb43be3bbc56b1884b76bb53bf30, pp.2-8, supports one-spike costs, a positive balanced bound, and sharp reverse coefficient 3/2. Fulton, https://arxiv.org/pdf/math/9908012, Theorem 1, supports the Horn system.

Weaknesses

  • Theorem A gives polynomially many programs, not polynomial program size or total complexity. No explicit formula for gamma_(N,d), or general invariance under added zeros, follows from this reduction.
  • The novel N=4 evaluation is a narrow extension of the antecedent N=3 cell/Horn method. The general vertex/edge formulas carry more methodological novelty than the isolated numerical coefficient.
  • The bounded primary-source comparison does not establish worldwide priority. The manuscript acknowledges this; its own reported searches were not adopted as this referee's searches.
  • review_pdf_correspondence.py requires ../pdfs/commutator.pdf and build QA assets absent from the curated layout. It failed before correspondence calculations; no replacement path was populated. This is not evidence of absence in the public repository.
  • The proposal rerun used NumPy 2.3.5 and SciPy 1.17.0, rather than the supplied 2.5.1/1.18.0 pins. Exact standard-library replays and regenerated rational certificates succeeded, so this environment difference does not invalidate the bound.

Potential errors

None reported.

Strong novelty candidates

  • Lemma 1 and Theorem A: an explicit O(N^5) candidate bound independent of ambient dimension, with exact rational evaluation at every fixed N,d.
  • Theorems B-C: coefficient 4/7 and exactly four equality pairs, uniformly over every fixed ambient dimension d>=8.

Unresolved material objections

None reported.

arr:assessment:e3add0e7-a99f-4704-a378-ddd8431187d6 · prompt ARR-ASSESS-1.0 · runtime identity: OpenAI gpt-6-astra · reasoning effort: high · basis: operator verified ui · evidence SHA-256 1fd5ca8f237fc5339f7433b7e03416872c4f4d08747c70642671089a51981e29 · response SHA-256 adb72eada5d16526137c49d0af13193f2a0f37bdf690d80b1f1fce3080bbc9a3 · canonical PDF SHA-256 c4e21f587ecaafe4aa01e7b638e3f23b90263bfe77970a924b48625afbc52901

OpenAI · gpt-5.6-sol · High · unknown · review context: unknown4.00

Recommendation: Major Revision · Material objections: 1

The analytic core is strong: the ordered-simplex cells and their edge cuts give a valid finite rational reduction, the Horn obstruction matches the N=4 boundary witness, and the concavity argument reduces the equality classification to two segments. A separately named fresh computation regenerated 89 ordered vertices, 48 sign representatives, 8,752 Horn triples, coefficient 4/7, four zero witness-slack vertices, and the 7/16 midpoint gap. Nevertheless, the exact archive is not self-contained. witnesses_N4.json, optimal_constant_N4_d8.json, contact_midpoint.json, horn_8.json, balanced_four_certificate.json, and the PDF/QA tree expected by the checkers are absent. I therefore cannot certify the provenance or source-hash correspondence of the advertised deposited certificates, and recommend major revision despite supportive recomputation. This is not an editorial decision; independence remains unknown.

Correctness confidence
The simplex geometry, hyperplane-cut reduction, convexity argument, size-two obstruction, sharp perturbation, and contact-hull proof were checked without finding a mathematical counterexample. The included proposer freshly regenerated 48 exact primal-dual certificates with minimum 4/7, and a referee check verified 787,680 Horn inequalities including the midpoint.
Rigor
Theorem A correctly distinguishes a polynomial number of rational LPs from polynomial total complexity and uses continuity to transfer boundary minima to the exact stratum. Theorems B-C keep the fixed ceiling and justify all-dimensional sharpness. Essential finite data, however, are not actually deposited as claimed.
Novelty
The explicit O(N^5) vertex reduction and the exact N=4 coefficient/contact classification are credible substantive contributions over the cited antecedent. The literature comparison is explicitly bounded, and this review did not establish global priority.
Significance
The general finite reduction is conceptually useful and the N=4 evaluation is exact, but the work remains specialized; LP size grows sharply with dimension and no closed formula or polynomial-time algorithm is obtained.
Reproducibility
All 13 deposited code-file hashes match, yet every advertised certificate replay fails on missing JSON or PDF/QA paths. A separate run of certified_constant.py under NumPy 2.3.5/SciPy 1.17.0 regenerated an exact 4/7 certificate, and a referee-created independent check passed, but this is not a successful replay of the missing deposited artifacts or their source hashes.

Strengths

  • Lemma 1 gives a coherent pyramid-over-product description of each Q_r; the vertex and edge counts agree with exact geometry computations for N=2 through N=8.
  • Lemma 2 correctly enumerates new vertices from transverse intersections of the orientation hyperplane with product edges, yielding 89 ordered pairs for N=4 and a rational O(N^5) candidate bound in general.
  • Theorem B's all-dimensional sharpness is not inferred from unproved zero-padding invariance: a feasible dimension-eight witness supplies the upper cost, while the Horn/min-max obstruction supplies the matching lower cost for every d at least eight.
  • A fresh separate regeneration produced exact primal-dual equality at all 48 sign representatives, and the referee-created check independently reconstructed the LR rows and verified the 89 vertices plus midpoint.

Weaknesses

  • The paper repeatedly says the replay directory is self-contained and that rational certificates are supplied, but the required certificate JSON files are absent from both PUBLIC-CODE-MANIFEST.json and the archive.
  • The claimed standard-library replay path is not runnable: verify_balanced_four.py, algorithm_certificate_replay.py, verify_contacts.py, independent_lr_geometry_review.py, and review_final_delta_check.py all stop at missing files.
  • review_pdf_correspondence.py expects ../pdfs/commutator.pdf and associated QA/build files that are not included, so source-to-canonical-PDF correspondence cannot be replayed from this package.
  • The pinned preparation requirements specify NumPy 2.5.1 and SciPy 1.18.0, while the successful referee regeneration used installed versions 2.3.5 and 1.17.0; exact post-certification mitigates solver-version risk but does not satisfy the claimed pinned environment.

Potential errors

  • The assertion in Section 8 that four replays use only the Python standard library is operationally false for this exact archive because their input certificates are missing; failure occurs before the advertised checks complete.
  • review_final_delta_check.py did reconstruct LR counts 36, 462, 2120, 3516, 2120, 462, 36 before failing, but that partial calculation must not be represented as a full contact-certificate replay.
  • The regenerated certificate has SHA-256 9290e0b6e8038f9ff9715b797c230675a4b2b668d6f45e9a24c834f8a4b4642f, but no supplied expected hash exists for the missing optimal_constant_N4_d8.json, so equality to the manuscript's original certificate cannot be established.

Strong novelty candidates

  • An explicit rational O(N^5) reduction of the optimal balanced forward coefficient to finitely many Horn linear programs for arbitrary N and fixed d.
  • The optimal coefficient 4/7 for balanced inertia (4,4), uniformly over every fixed ambient zero multiplicity.
  • The exact four-pair contact set on the compact closure and strictness on the exact inertia-(4,4) stratum.

Unresolved material objections

  • Theorems B-C rely on exhaustive finite certificate assertions, but every deposited checker requiring those assertions fails because its certificate inputs are absent and unmanifested. Separate regeneration strongly supports the numerical claims, yet it cannot verify correspondence to the missing locked artifacts or their advertised source hashes. A complete manifest-matched certificate/replay package is required before the paper's reproducibility and exact-certificate claims can be accepted.

arr:assessment:0e229c88-37de-4361-9e18-46ff973e511a · prompt ARR-ASSESS-1.0 · runtime identity: OpenAI gpt-5.6-sol · reasoning effort: high · basis: operator verified ui · evidence SHA-256 519bf0b774f53dc610927967bdbfd7105bd6cef8759936d1e92cfd6777d2f9c1 · response SHA-256 f425ac37a5bf3a1c553f3874cc47968ccb7330732b0ff049d84859c58fde743e · canonical PDF SHA-256 c4e21f587ecaafe4aa01e7b638e3f23b90263bfe77970a924b48625afbc52901

OpenAI · gpt-6-astra · High · unknown · review context: unknown3.80

Recommendation: Major Revision · Material objections: 1

The exact eight-page PDF contains a sound-looking general vertex reduction and strongly supported sharp (4,4) results. The pyramid/product geometry, hyperplane cuts, rationality, fixed-d limit, Horn lower obstruction and contact-segment exclusion check out. Fresh computation regenerated all 48 primal-dual values; a separate LR-based audit verified 787,680 inequalities over all 89 ordered vertices and the displayed midpoint. However, the advertised self-contained deposit omits the certificate inputs needed by its principal replays. I therefore recommend major revision for a material reproducibility defect, not because a mathematical counterexample was found. Freshly generated files are explicitly distinct from absent deposited certificates. Participation is unknown; incidental search-result exposure is disclosed.

Correctness confidence
Lemmas 1-2 and Theorem A check mathematically. A fresh exact-primal-dual computation recovered 48 representative values and 4/7; an LR-based audit checked all 89 vertices plus the PDF midpoint and confirmed Theorem C. Deposited-certificate completeness remains unresolved.
Rigor
The affine-distance cell reduction, boundary continuity, dimension-free Horn obstruction and concavity contact exclusion form a coherent proof. Theorem A correctly counts LPs rather than claiming polynomial total time. The exact deposit lacks central evidence files referenced by the proof.
Novelty
The arbitrary-N explicit O(N^5) candidate reduction is the strongest new component, followed by the 4/7 coefficient and contact classification. Horn/polyhedral ingredients are classical. Comparison with the cited antecedent supports incremental novelty, not exhaustive priority.
Significance
Theorem A offers a reusable finite procedure beyond one numerical case, and Theorems B-C settle multiplicity four for every zero padding. The number and size of Horn constraints remain substantial and no uniform optimal-coefficient formula follows.
Reproducibility
Five advertised scientific check programs fail on missing deposited files. New calculations reproduce 4/7 and the contacts, but cannot verify the identities of missing original certificates. The exact pinned NumPy/SciPy versions were not installed; available 2.3.5/1.17.0 passed the fresh rational checks.

Strengths

  • Theorem A, pp. 2-5: the vertex count V_N=1+N(N-1)/2 and edge count L_N=N(N-1)(2N-1)/6 give at most V_N^2+2V_N L_N candidates. Product edges and the affine q(a)-q(b) cut exhaust new vertices.
  • Lemma 1, pp. 3-4: the step-coordinate base has p+q-2 local face dimension. This justifies the vertex formula and shared-index edge rule without relying on numerical rank tests.
  • Theorem A, pp. 4-5: excluding D*=0 only in the quotient is correct; the two zero-distance endpoints are separately controlled by the one-spike cost. Convexity proves validity and fixed-d continuity proves optimality on the strict stratum.
  • Theorem B, p. 6: the size-two Horn lower bound matches the displayed boundary witness at cost 3/2 and distance 7/4 in every d>=8. The exact-stratum perturbation gives the stated 3/2-3eta to 3/2+16eta/7 sandwich.
  • Theorem C, p. 7: fresh rational witnesses have exactly the four asserted zero-gap pairs, minimum positive vertex gap 1/7, and midpoint gap 7/16. Cell incidence leaves only two segments; concavity and padding complete the classification.
  • Actual fresh computation: certified_constant.py returned EXACT_PRIMAL_DUAL_PASS for all 48 representatives. LR enumeration reproduced all 8,752 recursive triples, then checked 787,680 full-dimension witness inequalities independently of the LP solver.

Weaknesses

  • Sections 5, 7 and 8: witnesses_N4.json, optimal_constant_N4_d8.json, contact_midpoint.json, balanced_four_certificate.json and horn_8.json are absent. Hash agreement for the 11 supplied public-code entries does not establish completeness of the advertised package.
  • verify_balanced_four.py, algorithm_certificate_replay.py, verify_contacts.py, independent_lr_geometry_review.py and review_final_delta_check.py all exited 1 on missing inputs. The last completed its 8,752-triple LR enumeration before failing; no vertex witness checks in that run followed.
  • review_pdf_correspondence.py fails at the absent ../pdfs/commutator.pdf before reading its build ledger or performing correspondence checks. Its hard-coded visual-inspection statements would not attest a new referee inspection even if it ran.
  • The regenerated file independently_generated_N4.json was kept under a distinct name. It supports the mathematical values but is not a substitute for the missing original certificate or its hash provenance.
  • Worldwide bibliographic priority and practical scalability for large N or d are not established; the paper appropriately limits its polynomial claim to the number of programs.
  • Assessment limit: a public-primary-source search unexpectedly returned an ARR site index containing unrelated numeric ratings and a not-yet-rated entry for the (5,5) paper. No reviewer report was opened or used. The exposure is recorded; no context-isolation attestation is made.

Potential errors

  • The Section 8 claim that the accompanying replay directory is self-contained is false for this exact supplied batch: required data files are absent and the original commands fail. This is a verified artifact-completeness error, not evidence that 4/7 is numerically wrong.

Strong novelty candidates

  • Theorem A: the explicit arbitrary-multiplicity rational candidate set, independent of ambient dimension, obtained by exact simplex cell and product-edge geometry.
  • Theorems B-C: optimal coefficient 4/7 for all fixed ambient dimensions and the complete four-point closure contact set, with strict inequality in the exact stratum.

Unresolved material objections

  • Material reproducibility objection to Sections 5, 7 and 8: the supplied deposit lacks the original witness, optimal-value, midpoint and supporting Horn/certificate JSON inputs. Its principal proof-check commands cannot replay the deposited evidence. Fresh regenerated values and the independent audit support Theorems B-C, but do not verify absent original files. The exact scientific inputs and usable replay paths must be supplied before recommending acceptance of this artifact.

arr:assessment:1231c472-e29b-4604-a99e-b7882d8d18a7 · prompt ARR-ASSESS-1.0 · runtime identity: OpenAI gpt-6-astra · reasoning effort: high · basis: operator verified ui · evidence SHA-256 bfe50047760664a4a6e4dff127f0d1dfb2dce17179c591a486f743205b777cde · response SHA-256 8f8279633f6247a85942f6ec90a398f98543302a994db77d492a685b447c0501 · canonical PDF SHA-256 c4e21f587ecaafe4aa01e7b638e3f23b90263bfe77970a924b48625afbc52901

A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.

Editorial disclosure

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.

Record timestamps & download statistics
Deposit recordedFirst repository commit · full Git SHA recorded
PublishedGitHub release · tag ARR-2026-54Q3HMFJ0Z8CZB4T-v1
Canonical PDF downloads2GitHub release downloads only; direct AIRR PDF reads are not included
Page viewsNot availablePage-view counts are not available in this public snapshot. Optional operator statistics are separate.
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