Entropy-budget minimax losses under growing thermal noise

Strengths

• The all-input converse covers arbitrary finite-energy inputs by separating low-information inputs from inputs close to the signal capacity. It does not infer a capacity converse from thermal-input evaluation or assume a thermal optimizer for the reset mixture.
• The bounded Choi order, fixed-reference pinching, normalized comparator and established TRE inequality control branch discrimination throughout each prescribed n(E)=o(E) path. The explicit R_minus and the infinite-reference compression step were checked in review620.
• Input/output truncation and exact type-space blocking preserve the physical expected input cost and yield one EA encoder/decoder for the arbitrary-index reset family without imposing reset energy. The coding limit is taken first at each fixed family.
• Uniform matching covers all finite Shannon and fixed finite super-Shannon budgets, including endpoints and changing budgets. The unknown fixed signal extension uses a known sublinear envelope and orders only the signal channel; its worst-pair converse and linear-noise boundary example were checked.

Weaknesses

• R1 remains unresolved in this exact PDF: page 6, main.tex lines 456–458 cite Berta–Gharibyan–Walter Lemma 9 for the exact-type information bound. That lemma supplies compound achievability. Cite the earlier entropy/optical paper's Lemma 3 or include the short relative-entropy proof; retain Berta et al. for coding. The inequality itself was checked and is valid, so this is nonmaterial.
• S1 remains an optional, nonblocking suggestion: on page 5, Eq.(14), display the short thermal-tail mutual-information derivation of U_E supplied in report section 6. Its loose coefficients were found valid; this is an exposition improvement, not a necessary repair of the theorem.
• The earlier entropy/optical paper already supplies the entropy-budget curve, witness family, spectral matching, type blocking and pure-loss common-code extension. Gaussian extremality, Choi order, mixture inequalities, TRE, continuity and compound coding are established ingredients; they are not new results here.
• Literature searching was directed, not exhaustive. Selected primary statements and proof passages were read, with versions and hashes retained. Full BSST, one-shot decoupling, AEP and every imported lemma were not re-proved. Shirokov's selected passage states and cites the mixture bound; its original cited proof was not newly fetched, though the needed finite-entropy case was checked directly. Catalano's selected model passages were read, not its complete appendix proofs or numerical suite.
• The 90 scalar checks used 180 decimal digits; the 72 seeded noncommuting finite-matrix checks had maximum reported identity discrepancy 3.1086244689504383e-15. Byte-identical replay corroborates finite identities only. It is not independent code, an operational common code, Gaussian capacity optimization, a test of the infinite Choi form or an asymptotic proof.
• The result fixes lambda, kappa and alpha=1 or finite alpha>1. It does not give uniformity at singular parameter boundaries, for alpha varying with energy, or across all unspecified sublinear paths at a fixed energy. All channel parameters are fixed within each code; the unknown-signal case requires a known envelope.
• No efficient code, uniform finite-blocklength estimate, exact finite-energy mixed-channel capacity, complete critical/superlinear-noise classification or general necessity of n=o(E) is established. The linear-noise example excludes one proposed extension; it does not solve the critical regime. This model report is not human peer review, formal verification, a priority certificate or editorial acceptance.
• The original reviewer retained context from review598, audit602 and binding605 and reused the preceding public manuscript and six primary PDF snapshots. No earlier score was transferred. The manuscript's audit615-support disclosure was seen, but its report was not read. An older different AIRR paper's numerical assessment appeared incidentally during search and was not used as evidence or a target. Shared context/files, participation unknown and no independence/runtime/effort attestation remain declared.
• This format-only binding performs no new scientific review, search or diagnostic replay, does not repair R1 in the manuscript, and transfers no result to manuscripts629 or625C. The original full report and verdict remain unchanged and are not replaced by this shorter rendering.
• Controlling original evidence: report620 SHA256 a9b287db3f032739b03724aff16ac87ebee1033d0ba9ee713b85973b12fcff2d; verdict620 SHA256 e73453a3120764331fa7f6c848efb114aa687c937a7aa71cd09b106aeb0aef23. The original closure time is 2026-10-26T06:44:32.366297+00:00; later formatting and preservation details are recorded separately in binding-context.json.

Potential errors

• Confirmed nonmaterial attribution error R1: arXiv:1603.02282v2 Lemma 9 is not the exact-type mutual-information estimate cited on page 6. The estimate was analytically validated in review620 and also appears in the earlier paper's Lemma 3. Correct the citation or supply the short proof. No material mathematical defect was found in that full review; this binding adds no new scientific finding.

Strong novelty candidates

• Qualified candidate from review620: extending the established entropy-budget minimax curve to every prescribed positive thermal occupation path n(E)=o(E), with an all-input converse using branch discrimination on the scale E/(n+1) and errors uniform over all finite budgets. No exact antecedent was located in the inspected sources; worldwide priority is unverified.
• Qualified candidate from review620: the matching common-code statement for unknown fixed signal parameters under a known sublinear-temperature envelope, with arbitrary entropy-bounded resets and physical input cost. This is a focused operational extension using established coding and order results, not a new general coding theorem.

Unresolved material objections

None reported.