Quantum reference activation of classical symmetric channels

Strengths

• Exact universal upper and faithful sharp constructions for named quantities.
• All binary-input subchannels separated from complete quantum-reference behavior.
• Fixed-dimensional separable realization with binary measured entropy tending to a positive limit.
• Ordered limits, marginal equality, conditioning and nonuniformity costs explicitly stated.

Weaknesses

• O1 [moderate novelty/evidence reservation; PDF pp1,9,10,12]: Exact priority remains unresolved; known tools, classical coefficients and generic non-contraction cannot be sold as new. Status: open uncertainty explicitly retained. Primary passages checked; Lee–Makur2024 full formula/proof remains uninspected. Negative search is not a priority certificate.
• O2 [moderate only under operational extrapolation; PDF pp7,8,9,10]: Rare-event, conditioning and k-dependent measurement/marginal costs delimit operational relevance. Status: manuscript scope satisfies limitation; preserve in public summaries. Condition ~4k2^k, exponentially rare q, decreasing trace distance, varying preparation/common marginal/effect; quantum input denominator. No fixed effect, spectral floor, optimal resources, capacity or robust experimental advantage.
• O3 [minor clarity; PDF pp6]: State n>=3 at the start of Section5.1 before naming inactive eigenvalues. Status: optional clarification; Theorem5.1 already restricts n>=3. For n=2 these modes have zero multiplicity; no main theorem relies on treating them as physical eigenvalues.
• O4 [moderate verification provenance limitation; PDF pp11]: Shared context, dependent code/reports and unattested runtime cannot be represented as independent or blind review. Status: declared; remains an evidence limitation. Prior involvement/context reused, late curation correction and historical1126 correction preserved. No automatic numerical AI penalty.
• O5 [minor access/presentation; PDF pp11]: Keep a stable public link to exact supplement, complete reports and adverse results alongside the PDF. Status: local packet verified; remote publication not checked or performed. Internal dossier identifiers alone do not establish public inspectability. This is not a gap in the self-contained proofs.

Potential errors

• Unidentified covering prior theorem remains possible.
• Minor Section5.1 domain clarification O3.
• A general proof or archival verification error could remain despite bounded checks; no formal guarantee.
• I1 [preserved incident, not a newly detected theorem error]: Two frozen narratives contain another-artifact historical score despite overbroad initial dispatch. Notice and curated copies arrived after start; originals untouched. Narrative bodies had not been read then, but prior context already contained earlier judgments. Status: preserved and declared; no blind/withheld attestation or restart.
• I2 [preserved incident, not a newly detected theorem error]: SymPy structural equality rejected equivalent forms of the same rational expression. Fixed by simplifying their difference; same cases and mathematical assertion. Status: repaired with originals retained.
• I3 [preserved incident, not a newly detected theorem error]: SymPy Rational times mpmath matrix raised TypeError. Converted the same rational to mpmath representation at100digits; no parameter or criterion change. Status: repaired with originals retained.
• I4 [preserved incident, not a newly detected theorem error]: Long console reads truncated parts of1093/1100/1115; missing portions were recovered in bounded reads. Original files complete. Irrelevant search hits are not evidence. Status: resolved for declared reading scope.
• I5 [preserved incident, not a newly detected theorem error]: Archived first-control and final control1110 are valid byte-identical JSON, not preserved malformed output. Only script change is removal of unused except_placeholder=0. Old narrative kept as unsupported claim, not raw evidence. Status: correction verified; mathematical outputs unchanged.
• I6 [preserved incident, not a newly detected theorem error]: A Get-Content lookup tried input/CORRECTIONS1126.json; actual path is input/research/1126/CORRECTIONS1126.json. Tool reported missing file; rg located it and full read succeeded. No file written or scientific conclusion changed. Status: resolved.
• Verification scope from1128 is unchanged: seven bounded replays passed; all200research files were not read line by line; additional eleven2048-bit1115 cases were authenticated/read but not all rerun. Own100-digit checks are numerical, not interval certificates; the inherited interval library is not an independent implementation. No formal proof, independent expert guarantee or remote supplement publication validation was claimed.
• Adverse cases remain part of the same report and dossier: three nonseparating1096/1099 Umegaki pairs; small dimensional cases; n=3,k=3,4 below1/2; deterioration when n=k; changed regularizer; reversed Bernoulli orientation; replacing the effect by its limit gives zero divergence; polynomial delta changes the limiting retention. They are not excluded by selecting favorable finite certificates.

Strong novelty candidates

• Same1128 novelty candidate, priority open: exact complete coefficients for the classical symmetric family with arbitrary finite common quantum reference upper and faithful simplex sharpness for the named quantities; not a claim of all-Petz equality.
• Same1128 novelty candidate: contrast with every binary-input classical subchannel, whose quantum-reference amplification is absent. Classical formula and classical binary-support reduction are prior.
• Same1128 novelty candidate: fixed-dimensional separable CQ exclusion construction and binary readout retaining relative entropy with positive limit. States, common marginal and effect vary with k; conditioning and rare-event costs are essential.

Unresolved material objections

None reported.