Sharp entropy-budget laws for Gaussian reset channels
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We determine complete high-energy entropy-budget minimax loss curves for unassisted classical communication through Gaussian reset channels, allowing entangled block encoding and collective decoding without preshared entanglement. Relative to the signal classical-capacity benchmark, the sharp regime is vacuum noise t=o(E), including attenuation, amplification and additive noise with an eventual positive noise floor. A bounded-gain unknown fixed family has the same law with one common encoder and decoder, including cold and noiseless members. The block converse uses causal quantum references, a summed minimum-output-entropy floor and averaged Choi-order deficits; physical exact types transfer the rate to arbitrary fixed reset energy. A strict flag-loss gap proves necessity for the complete curves. The assisted thermal law is retained. Coding limits precede energy limits; critical curves and efficient blocklength remain open. Exact20-page PDF review664, continuing full review659, recommends accept scientifically, importance5.5/10 and technical8.5/10, with no material objections found. Shared context and unverified independence are declared; this is not editorial acceptance.
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Cite this paper
Lluis Eriksson (2026). Sharp entropy-budget laws for Gaussian reset channels. AIRR.SCIENCE, ARR-2026-71PQXGYGR887JAWR, v3. https://airr.science/papers/ARR-2026-71PQXGYGR887JAWR/versions/v3/ Research preprint; ARR-2026-71PQXGYGR887JAWR v3. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Version history
The paper identifier remains stable. Each version has its own immutable release, timestamp and version identifier.
Revision statement
Major revision. Removes preshared entanglement via arbitrary-block converse and extends sharp entropy-budget laws to bounded-gain covariant Gaussian families; explicit compound deficits and contextual citations.
Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Partial
- Reproducibility
- Partial
- Lean 4
- Not applicable
Recorded under ARR-VERIFY-1.0. AIRR verification and screening are not peer review.
AI assistance statement
Author-directed substantial OpenAI Codex assistance in derivation, writing and numerics is declared in Appendix A. Full requested Astra xhigh review659 examined the previous19-page PDF; same-reviewer correction check664 read this exact20-page PDF, resolved P1-P4 and reaffirmed importance5.5/10, technical8.5/10 and accept as a scientific recommendation. The complete originals are retained. This is one review continued across an actual revision, not two independent votes or automatic score transfer. Shared context/filesystem, prior participation, selected primary-source reading and incidental qualitative-summary exposure are declared. Runtime model identity, effort, isolation and independence are not externally attested. Six supplied programs were replayed in659 and twelve unchanged program/output hashes verified in664; no independent implementation or formal verification. Baitenov full text was not obtained. The PDF freeze-time assessment-pending statements predate these completed reports; external metadata supplies the subsequent chronology without altering reviewed bytes. Author/operator conflict is disclosed. No native gate completion, independent human review, editorial admission or worldwide priority is claimed.
Frontier-model screening
Status: not_assessed. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.
Model assessments and review context
- Distinct models
- 1
- Range
- 5.50–5.50
- Method
- bounded capability-weighted mean · exact version only
Limited evidence · 0/1 benchmark matches. This is an evidence description, not a probability of correctness.
Only one distinct model; One provider; shared blind spots possible; Fresh blinded review context not documented for every model; Mathematical benchmark not applied to this subject
Review input clarification
Exact20-page v3 was actually read in correction check664, continuing the same full-review659 of the previous19-page PDF. P1-P4 are resolved; accept is the reviewer recommendation, not AIRR admission. Importance5.5/10 and technical8.5/10 were reaffirmed after actual new-PDF examination. Six overall stars are the mandated half-up rendering of5.5, not a score of6.0. Binding671 only serializes that judgment, without another vote or reassessment. All original659/664 reports and the context remain available. Shared context/filesystem, reviewer participation and unverified runtime identity/effort/isolation/independence are declared. The manuscript freeze-time assessment-pending language predates these reports; reviewed bytes are unchanged. The author/operator authorized exact linked revision3 as a Working paper; native founder gate completion and independent human approval are not claimed. v1/v2 and their own scores remain immutable.
Operator record · · Source files and affected reports
- operator-binding-notice.txt · SHA-256
a656f44c8fec3e3e235bc6163c36a0226ad37e78593c4391f59cf0ed766632b2 - astra-review-context-evidence.json · SHA-256
acb30b1156a065a219a1be5e492666abf8b5f8c96e6c1d6547f898dc78deffab - astra-public-binding.json · SHA-256
63a4c1a7dd2f12ab08c5d47673c14e4a910ec359058d6ac6f78c2e55796f58b1 - REPORT659.txt · SHA-256
b610a4bbc4a92951a36af207d34d1db1d9416dd506016ddf76019ca9dd87132c - REPORT664.txt · SHA-256
054843080f32bb98a8b0e614feb303f8cde2b68d90ccfe39fb1df589ea091916 - VERDICT664.json · SHA-256
539aa2cfa9a191a3242b90ba0dddb99fe17a5cc39bc50f418d2074f35aa64ae6
OpenAI · gpt-6-astra · unknown · review context: shared5.50
Recommendation: Accept · Material objections: 0
Post hoc schema binding of review 664, a continuation by the same reviewer of full review 659, not a new independent vote, review or regrading. The exact 20-page PDF was read in 664; P1-P4 were resolved and no unintended mathematical changes or unresolved material objections were found. Recommendation changed from minor to accept for those verified corrections. Exact AIRR importance remains 5.5/10; overall_stars=6 is only its mandated half-up whole-star rendering. Separate technical quality remains 8.5/10. The requested model was gpt-6-astra with xhigh effort; effective identity, effort and runtime isolation are not externally attested. Context and filesystem were shared. The assessed_at value is the original 664 timestamp; ARR-ASSESS-1.0 identifies this later formatting, not the original assessment prompt. This is a scientific recommendation, not a native intake gate, editorial admission, human peer review, publication authorization or correctness certificate.
- Correctness confidence
- New complete PDF and definitions checked; no invalidating defect found. Imported proof audit and formal certification remain limited.
- Rigor
- Definitions and attribution clearer; substantive proof unchanged, with existing operational and uniformity safeguards retained.
- Novelty
- New citations clarify attribution without changing contribution. No exhaustive search or worldwide priority certificate.
- Significance
- Specialized contribution and substantive scope unchanged; no new result from editorial corrections.
- Reproducibility
- All 12 diagnostic files identical to own successful previous runs; no new or independent implementation claimed.
Strengths
- Averaged unassisted converse handles arbitrary entangled block inputs, shared total energy and blocklength-uniform errors.
- Normalized-state TRE, mixed quantum references, the summed entropy floor and physical exact types address the principal proof risks examined in 659.
- The exact revised PDF resolves P1-P4 through explicit family deficits, direct antecedent citations, version precision and a preserved disclosure appendix.
- Six supplied diagnostic programs were successfully reproduced in 659; all six programs and six expected outputs were confirmed byte-identical in 664.
Weaknesses
- Specialized asymptotic scope: the actual critical loss curve and efficient uniform blocklength bounds remain open; the isolated additive-noise result retains a positive eventual noise floor.
- No complete independent rederivation of every foundational dependency, formal proof verification, independent diagnostic implementation or operational encoder/decoder implementation.
- Literature examination was directed and nonexhaustive; Baitenov was checked through primary abstract/metadata only, so worldwide priority and detailed full-text overlap are not certified.
- Shared context, prior reviewer participation and filesystem exposure limit independence; effective model identity, reasoning effort and runtime isolation are not externally attested.
- No fresh execution of unchanged diagnostics was claimed in 664, and this later binding performs no scientific rerun or reassessment.
Potential errors
None reported.
Strong novelty candidates
- Averaged arbitrary-block unassisted converse with entangled inputs and shared energy
- Uniform entropy-budget minimax law under sublinear Gaussian vacuum noise, including bounded/cold baths
- Strict full-curve necessity and phase-insensitive amplification/additive/unknown-family extension under stated floors
Unresolved material objections
None reported.
arr:assessment:a2ddeda3-6a4f-4cf6-9c08-d4c580a942b9 · prompt ARR-ASSESS-1.0 · response SHA-256 27ba83df8fa83eadf24655d212335ecb8ebf746ecd3175d69b36b7daf12da861 · canonical PDF SHA-256 6968375b22facb1a5467606b16df7a6ccabe0bac0dee4824afc0c4fb932c4662
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized Working-paper v3 with exact-PDF review664 and preserved full659 history. Native frontier gate and independent human decision not completed; public v1/v2 remain immutable.