Support and quantum-reference activation of classical channels
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
For an arbitrary finite classical channel K, we characterize when quantum side information prevents strict relative-entropy contraction. The complete equal-reference Umegaki coefficient equals one if and only if the Doeblin common-component coefficient d(K)=sum_y min_i K(y|i) vanishes. Positive d(K) gives the known upper 1-d(K). For the converse, one channel-independent family of faithful separable classical-quantum hypotheses, with reference dimension equal to the input alphabet size, admits channel-dependent binary readouts whose input, output and measured relative entropies tend to log 2. Explicit scalar bounds make this convergence uniform over all zero-Doeblin channels with a fixed input alphabet, even as supports and output cardinalities vary. For symmetric channels we additionally determine exact SLD, minimal chi-square, triangular, BKM and Umegaki coefficients: (n-1)lambda^2/[1+(n-2)lambda]. Every two-symbol restriction retains its ordinary classical coefficient, exposing the failure of classical binary-support reduction. Conditioning, rare events and parameter-dependent effects remain essential costs. Certified asymmetric examples, failed numerical selectors and regularizer counterexamples are retained. No capacity advantage, robust implementation, minimal reference dimension or worldwide priority is claimed.
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Cite this paper
Lluis Eriksson (2026). Support and quantum-reference activation of classical channels. AIRR.SCIENCE, ARR-2026-564FZ70CSN83KACD, v2. https://airr.science/papers/ARR-2026-564FZ70CSN83KACD/versions/v2/ Research preprint; ARR-2026-564FZ70CSN83KACD v2. Not peer reviewed by AIRR.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. Extends symmetric-channel activation to an arbitrary finite-classical-channel support criterion with a uniform binary witness, full exact-PDF assessment and documented correction.
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
Exact corrected15-page PDF1155 SHA256 5cf3e9a66c6d86063d68b92bb0494bb5186a73506da60935819ff9d0265be361. One complete scientific judgment1148 of exact predecessor203d0c2fde218e4de67fc54852129bdc70a8352336f68e4222e0a01e551c8288, followed by a limited correction check1156: importanceAIRR7.0/10, globalMillennium6.7/10, technicalquality8.8/10. The three judgments are distinct and not averaged.1156verifies the sole phrase limiting the inactive eigenvalue to n>=3; all other14pages are pixelidentical, general support section byteidentical. It explicitly applies the SAME judgment to this exact correctedPDF, without a new full review, score recalculation or additional vote. The original minor_revision and O1 remain intact; O1 is resolved by the separate delta, with O2-O5 retained. No confirmed unresolved material mathematical objection. Uniformity is over finite zero-Doeblin classical channels at fixed input size and with adaptive effects; no uniformity in dimension, precision, uncertain supports or conditioning, fixedeffect, robust implementation, minimal reference or capacity advantage. Known Doeblin upper, classical scrambling and tools are prior. Priority remains open and Lee-Makur2024 fulltext uninspected. Requested GPT-6 Astra xhigh; effective identity/effort/isolation/statisticalindependence unattested. OpenAI Codex substantially assisted derivation,writing,numerics and review; involved context952andcontinuations and shared filesystem reused, not fresh/blind/independenthuman evidence. Componentaudits and bounded replays are not additional votes. All reports,originalobjections,adverses,incidents and manifests are preserved. Founder-authorship/native exactPDFpermission recorded. Working paper only, not Accepted or peer reviewed; two-distinct-identified-model admission gate remains incomplete. Later CQ1152 is outside this manuscript and receives no score here. The pending-assessment sentence retained in the frozen manuscript originated before review1148. The public evidence now consists of full1148 on PDF203d... plus limited corrective1156 on PDF5cf3...; this is not a newly repeated full review of the corrected PDF.
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
- 6.70–6.70
- 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
Exact v2 PDF5cf3e9a66c6d86063d68b92bb0494bb5186a73506da60935819ff9d0265be361: one full judgment1148 of PDF203d..., followed by limited O1 correction1156 and format-only1159. Not a new full review, regrade or extra vote. Distinct judgments importanceAIRR7.0,globalMillennium6.7,technical8.8 are unchanged, not averaged or correctness probabilities. Original minor_revision/O1 and its resolution remain visible alongside O2-O5 and all incidents. Requested Astra xhigh; effective model identity,effort,isolation,independence unattested. Substantial Codex involvement, reused context and sharedfilesystem; not fresh/blind or human peer review. Known upper/tools prior, priority open and Lee-Makur fulltext uninspected. Uniformity only fixedn/adaptiveeffects; rareevents,conditioning,variablemarginal/preparation and quantum inputdenominator are costs. No capacity,robust implementation,minimalreference or optimalresource claim. The frozenPDF assessment-pending sentence is historical; evidence is full1148 plus limited1156. Full operator-context and exact report/delta/binding hashes are linked below. Working paper only, not Accepted; twoidentified-model admissiongate incomplete. LaterCQ1152 is outside this PDF.
Operator record · · Source files and affected reports
- operator-context1158.txt · SHA-256
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a00ba996be7defcd9230f34fb0398fd9673cbf521907a8a3c28a39911aba5c1c - DELTA1156.txt · SHA-256
1b5dbe0aa81552187232d0fe7ab544ec0fecc0a819ec509be89b79a1a439ce0d - DELTA1156.json · SHA-256
1bbed28e2e969e375440f5d2759a4b68d80efc70f567e75925923f47d3203d46 - BINDING1159.json · SHA-256
df827c270c220025841cd32438a4a6e320ffea7f00edfe882168d8ebc6ba8d71 - model-response.json · SHA-256
5bec9a9cb2c35f5d9a269f52d51dd8d623ff111133e1ccf78826a2b5351bcb21
OpenAI · unknown · involved in manuscript · review context: unknown6.70
Recommendation: Accept · Material objections: 0
Serialization only of the same judgment 1148 (2026-10-27T23:48:25Z UTC), with its limited corrective continuation 1156 (2026-10-27T23:55:15Z UTC). The full review concerned PDF 203d...; 1156 verified the sole O1 wording correction and binds that judgment to this exact v2 PDF. No new full review, scientific reading, controls, grading or additional vote occurred in 1159. Original minor_revision is preserved: O1 is resolved; accept serializes the already documented recommendation to publish within declared scope, not editorial acceptance. O2–O5 remain reservations. Importance 7.0/10, global Millennium 6.7/10 (7 stars), technical quality 8.8/10 and all five criteria 4/5 are unchanged, distinct judgments, not an average or correctness probability. OpenAI Codex participated in the project; shared context from 952 through 1128/1137/1148/1156 and shared filesystem, prior-score exposure and possible bias persist. GPT-6 Astra xhigh was requested only; effective identity, effort, isolation and independence are unattested; no fresh/blind or human review is claimed. The PDF §8 phrase about a still-required full assessment is historical: evidence is full 1148 plus limited delta 1156. assessed_at dates this serialization; ARR-ASSESS-1.0 is only the later format. Full original reports and all objections accompany the binding.
- Correctness confidence
- Original 1148 basis, unchanged: General arguments reconstructed and pertinent adverse checks without confirmed material error. One minor scalar-domain flaw; no independent expert/formal guarantee. Historical O1 is resolved by 1156; this is not a rerating.
- Rigor
- Original 1148 basis, unchanged: Arbitrary-reference upper, active supports, restricted inverse, minimum branch and uniform bounds justified. No transfer to all Petz, fixed reference floors or optimal resources.
- Novelty
- Original 1148 basis, unchanged: Complete support criterion and uniform realization are substantive candidates relative to selected primary passages. Definitions, upper and tools prior; worldwide priority and incomplete source coverage remain open.
- Significance
- Original 1148 basis, unchanged: A structural classification across finite classical channels gives a precise side-information distinction. Specialized significance without established robust operational gain.
- Reproducibility
- Original 1148 basis, unchanged: Complete source packet,12bounded replays, own exact/high-precision checks and all failures retained. Shared context and inherited libraries are not independent or formal verification; not every archived script rerun.
Strengths
- Original 1148 finding, unchanged: Complete support criterion for every finite classical channel n>=2.
- Original 1148 finding, unchanged: Explicit faithful separable preparation independentK and binary measured positive limit uniform in zero-DoeblinK at fixedn.
- Original 1148 finding, unchanged: Named exact symmetric coefficients and binary-input distinction integrated consistently.
- Original 1148 finding, unchanged: Analytical branch/root control with no minimum-row-weight dependence and adverse-case retention.
Weaknesses
- O1 — historical minor scalar-domain error, p.6: The displayed inactive-output scalar eprime>0 is not true for all n2 parameters, though the corresponding eigenmode has multiplicity zero. Evidence: n2,alpha=beta1/4,epsilon1,delta1/2 satisfies stated conditions and active determinant1/32>0, but eprime=2alpha-epsilon=-1/2. It did not refute the states, fixed scaling or Theorem 6.1. Resolution recorded in 1156: the same sentence now says "only for n>=3" before "inactive eigenvalue". The original objection and original minor_revision remain in the source report; no formulas, controls or Section 6 changed.
- O2 — moderate novelty/evidence reservation; pp.1,2,15. open bibliographic uncertainty. Priority and absence of a covering prior theorem are not certified; tools and known upper are prior. Evidence: Directed selected primary reading only. Lee–Makur2024 full text and entire order/Doeblin-curve proof bodies uninspected; new Hirche2610.03706 selected hierarchy not a literal covering iff. Preserve: Retain limitations and appropriate attribution; do not claim worldwide priority from this audit.
- O3 — moderate operational scope limitation; pp.7,8,11,12,13. properly delimited in manuscript; preserve publicly. Uniform inK at fixedn does not mean fixed effect, uniform precision, robustness to uncertain zeros or uniformity inn. Evidence: Effects dependK,k, marginal/preparation vary, condition~4k2^k, rareq and vanishing trace distance. Quantum input denominator remains. Preserve: Keep limits in summaries; no capacity, small one-shot error, robust implementation or optimal copy cost inference.
- O4 — moderate provenance limitation; pp.14. declared; remains a limit on evidence. Effective identity/effort/isolation and statistical independence unattested; prior participation, context and score exposure/shared filesystem real. Evidence: Same reused task context and dependent reports/code; no fresh/blind or independent-library claim. Preserve: Preserve provenance and all earlier evidence; no automatic AI penalty or duplicate-current-vote representation.
- O5 — minor access and reproduction scope; pp.14. local packet verified; remote current supplement not checked. Internal dossier IDs and predecessor link do not themselves certify public access to current exact supplement or full-campaign replay. Evidence: 12bounded checkers executed; all original inputs authenticated; not every archived script or platform. Preserve: Accompany any public exactPDF with full report, current supplement, adverses and manifests; describe bounded scope.
Potential errors
- Original 1148 uncertainty, unchanged: An unidentified covering prior theorem or proof error remains possible despite inspection.
- Original 1148 uncertainty, unchanged: Bibliographic and verification limitations do not establish correctness probability or worldwide priority.
- Historical I1–I2: the first TeX read preceded the initial 312-file integrity completion (subsequently all passed). Truncated display was recovered; failed README.md lookup was corrected to README.txt. No input was changed or review restarted.
- Historical I3: the own equality-case checker had a chained-tolerance bug; Do-Di=7.784e-259 at 260 digits versus intended tolerance 1e-210. Split comparisons retained the same cases, parameters and tolerance. Initial failures, diagnosis, initial and repaired code remain in 1148; no scientific checker was rerun in 1159.
- Historical I4: replacement-channel Do=-4.7039e-262 was a numerical residual; exact value zero. It remains visible, not presented as physical negative divergence.
- Historical I5: first 1134 flagged protocol failure; 1136 Unicode/float-stochasticity/script-reconstruction, negative residual, selector and scale falsifiers; and 1126 malformed-output narrative correction remain preserved. No adverse case is removed by this projection.
- Historical I6/O4: previous scores were exposed and original narratives accessible; shared involved context, dependent code and reports give no fresh/blind, isolated, human, independent-library or statistically independent review guarantee. No runtime model or effort evidence is supplied.
- Original reproduction limits: 12 bounded checkers plus stated own exact/high-precision checks, not every archived script/platform; inherited integer libraries and diagnostics are not independent interval implementation or universal numerical proof. Full source packet authentication does not mean every historical line was read.
- O2/O3/O5 remain: directed partial primary reading, Lee–Makur 2024 full text uninspected, priority open; fixed-n/adaptive-effect/exact-support/rare-event/conditioning and quantum-input-denominator limitations; remote current-supplement access not validated by 1148 or 1159. No capacity, robust experiment or optimal cost claim follows.
- Binding limitation: 1156 was a limited O1 delta check, not a second full assessment of the corrected PDF. This serialization adds no scientific evidence. The historical §8 assessment-pending sentence is contextualized, not silently edited. Working-paper status and model-identification gates are not converted into editorial acceptance.
Strong novelty candidates
- Original 1148 candidate, unchanged: complete support criterion for every finite classical channel (n>=2), with the distinctions and known upper/tools attribution in the full report. Worldwide priority is not certified.
- Original 1148 candidate, unchanged: channel-independent faithful separable preparation and an adaptive binary measured positive-limit realization, uniform over zero-Doeblin channels only at fixed n. No uniformity in n, fixed measurement, robust experiment or optimal resource claim.
Unresolved material objections
None reported.
arr:assessment:6f909c5d-b419-4a38-82be-638845055ff1 · prompt ARR-ASSESS-1.0 · response SHA-256 751c11bbd41021d91e9c3501dfe0bce42a3c2429fa12e619084c077b6e0af20f · canonical PDF SHA-256 5cf3e9a66c6d86063d68b92bb0494bb5186a73506da60935819ff9d0265be361
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Exact corrected15-page PDF1155 SHA256 5cf3e9a66c6d86063d68b92bb0494bb5186a73506da60935819ff9d0265be361. One complete scientific judgment1148 of exact predecessor203d0c2fde218e4de67fc54852129bdc70a8352336f68e4222e0a01e551c8288, followed by a limited correction check1156: importanceAIRR7.0/10, globalMillennium6.7/10, technicalquality8.8/10. The three judgments are distinct and not averaged.1156verifies the sole phrase limiting the inactive eigenvalue to n>=3; all other14pages are pixelidentical, general support section byteidentical. It explicitly applies the SAME judgment to this exact correctedPDF, without a new full review, score recalculation or additional vote. The original minor_revision and O1 remain intact; O1 is resolved by the separate delta, with O2-O5 retained. No confirmed unresolved material mathematical objection. Uniformity is over finite zero-Doeblin classical channels at fixed input size and with adaptive effects; no uniformity in dimension, precision, uncertain supports or conditioning, fixedeffect, robust implementation, minimal reference or capacity advantage. Known Doeblin upper, classical scrambling and tools are prior. Priority remains open and Lee-Makur2024 fulltext uninspected. Requested GPT-6 Astra xhigh; effective identity/effort/isolation/statisticalindependence unattested. OpenAI Codex substantially assisted derivation,writing,numerics and review; involved context952andcontinuations and shared filesystem reused, not fresh/blind/independenthuman evidence. Componentaudits and bounded replays are not additional votes. All reports,originalobjections,adverses,incidents and manifests are preserved. Founder-authorship/native exactPDFpermission recorded. Working paper only, not Accepted or peer reviewed; two-distinct-identified-model admission gate remains incomplete. Later CQ1152 is outside this manuscript and receives no score here. The pending-assessment sentence retained in the frozen manuscript originated before review1148. The public evidence now consists of full1148 on PDF203d... plus limited corrective1156 on PDF5cf3...; this is not a newly repeated full review of the corrected PDF.