Sharp reference-assisted contraction for the minimal quantum Fisher metric
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We derive a harmonic-weight contraction bound for random-unitary channels on pairs with the same uniform-twirl image. It applies to every operator-convex Petz divergence on faithful states and is uniform over finite quantum reference systems. For a qubit depolarizing channel with retained amplitude 0<lambda<1, we identify the exact complete equal-reference contraction coefficient of both the minimal quantum Fisher metric and the triangular Petz divergence: 3lambda^2/(1+2lambda). The lower bound uses an explicit qubit-qutrit ladder state, a partial-trace-zero tangent, and an ordered faithful regularization. Thus the general Petz upper bound is sharp as a bound uniform over that family. At lambda=1/2 it equals 3/8, compared with the ordinary value 1/4. This does not determine the relative-entropy or mutual-information coefficient. We include a finite rational triangular-divergence witness above 1/3, explain a limitation of scalar-centering proofs, and preserve failed auxiliary variance and numerical routes. The supplement is public and pinned to an immutable commit.
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Cite this paper
Lluis Eriksson (2026). Sharp reference-assisted contraction for the minimal quantum Fisher metric. AIRR.SCIENCE, ARR-2026-77DGRYDGXD8MDSY2, v1. https://airr.science/papers/ARR-2026-77DGRYDGXD8MDSY2/versions/v1/ Research preprint; ARR-2026-77DGRYDGXD8MDSY2 v1. Not peer reviewed by AIRR.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.
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
Review1006 is one completed full assessment of this exact eight-page PDF1005. Scientific importance4.30/10, global Millennium4.40/10 and technical quality8.60/10 are distinct judgments. The catalogue global score is4.4, not technical8.6. O1-O5 are resolved in1006 after actual current-PDF inspection and replay; the unchanged earlier998 report is historical evidence for a different PDF, not another vote or automatic score transfer. Requested GPT-6 Astra xhigh; effective model identity, effort, runtime isolation, blinding and independence are unattested. Shared filesystem and reused952/998 context are explicitly disclosed. Original recommendation recommends publication within the declared scope; this is not editorial acceptance or independent human peer review. The paper remains a Working paper, with the native distinct-identified-model admission gate incomplete. No grade is assigned to later997/1003/1011 candidates. The PDF assessment-pending wording and CHANGES1005 were frozen before the completed1006 report.
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
- 4.40–4.40
- 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
Review1006 is one completed full assessment of this exact eight-page PDF1005. Scientific importance4.30/10, global Millennium4.40/10 and technical quality8.60/10 are distinct judgments. The catalogue global score is4.4, not technical8.6. O1-O5 are resolved in1006 after actual current-PDF inspection and replay; the unchanged earlier998 report is historical evidence for a different PDF, not another vote or automatic score transfer. Requested GPT-6 Astra xhigh; effective model identity, effort, runtime isolation, blinding and independence are unattested. Shared filesystem and reused952/998 context are explicitly disclosed. Original recommendation recommends publication within the declared scope; this is not editorial acceptance or independent human peer review. The paper remains a Working paper, with the native distinct-identified-model admission gate incomplete. No grade is assigned to later997/1003/1011 candidates. The PDF assessment-pending wording and CHANGES1005 were frozen before the completed1006 report. Binding1010 is format-only serialization of the same1006 assessment, not another review, grade or vote. Native accept maps the original recommend_publication_with_declared_scope to a scientific recommendation; catalogue status stays working_paper and founder admission is incomplete. ARR-ASSESS-1.0 denotes the later serialization format; assessed_at denotes serialization time, while the actual original report was sealed2026-10-27T15:14:22.419803+00:00. See unchanged source report/verdict for original wording and all reasoning.
Operator record · · Source files and affected reports
- operator-context1009.txt · SHA-256
eb83ce0ea0eb24f872f0a16c643c393ba960a61a324b75db468178cde00de7fb - REVIEW1006.txt · SHA-256
b179331da60c87e842db4156280f9ac90430de85d4daa0a5e18073c9f4ce15eb - verdict1006.json · SHA-256
481786d96a45ca2b393b11cd569d3ee3605207b4db50ce09c9a9fba9a8cf5732 - PROVENANCE1006.json · SHA-256
c21789805a6bec0de7b0baa20d10dca8b0581fee6f99711d0fc5fdee6f6665ee - READINGS1006.json · SHA-256
205a2d68f8ba2ded7826e7f445164f45393711667c4409e6d252724383002399 - INCIDENTS1006.json · SHA-256
1cbe33573c615367b850f8adb6918c7e51d5fa3f73e896e8c91583883482b826 - REVIEW998.txt · SHA-256
a490d74c3b6b6c4f7cbace1898e55835845c7058d754b3fdaeb51319569fe855 - PUBLISHED-REVIEW-SCOPE1009.json · SHA-256
04b6ea00c4fd53f1a6c0c0913d4d8c630c90730e6d52dc3e9ca38bc77cbb5c6f - model-response.json · SHA-256
b799c714c171f3aa487cbd60da1f30a29d1ffe48387d0e0a2f801c270d156233 - BINDING1010.json · SHA-256
56003f63566337addf294548007fb11c130b36d5e39dc35abf90bd26065a91ea
OpenAI · unattested-effective-model; requested GPT-6 Astra xhigh via Codex · unknown · review context: unknown4.40
Recommendation: Accept · Material objections: 0
Serialización posterior1010 del MISMO informe1006, fechado2026-10-27T15:14:22.419803+00:00; no nueva revisión, nota ni voto. ARR-ASSESS-1.0 designa sólo este formato y assessed_at la serialización. 1006 recomienda publicar el PDF exacto1005 dentro de su alcance: O1–O5 resueltas, sin nuevas objeciones condicionantes. accept es esa recomendación científica, NO un estado Accepted ni decisión editorial. Global Millennium4,4/10 (Strong,4estrellas); importancia científica4,3/10; calidad técnica8,6/10: ejes distintos, sin promedio. La aportación especializada es la constante completa exacta y su construcción; el alcance e importancia amplios y la prioridad mundial no están acreditados. La calidad técnica se apoya en la cota universal, familia explícita, límites fieles ordenados y certificados racionales. Participación sustancial de OpenAI Codex en derivación/escritura/trabajo numérico declarada; contexto952/998 y filesystem compartidos. Se solicitó GPT-6 Astra xhigh; identidad/esfuerzo efectivos, aislamiento e independencia no atestados. El informe íntegro REVIEW1006.txt y BINDING1010.json deben acompañar esta proyección.998 pertenece al PDF995 anterior, no es otro voto sobre1005.
- Correctness confidence
- Current complete proof inspection, corrected hypotheses and public exact replay reveal no central error; no formal or attested independent verification.
- Rigor
- Declared finite-reference quantifiers and ordered boundary limits are covered; precision objections resolved. Compact proof and certificates remain a model-inspected argument, not formal verification.
- Novelty
- Specific exact coefficient and sharp family not identified in checked passages; tools are established and search remains directed and partial.
- Significance
- Clear specialized reference-assisted result; broader operational and entropy implications not demonstrated.
- Reproducibility
- Pinned public code, manifest and dependencies now available and replayed; inspectable evidence without an independently certified campaign or formal whole-corpus validation.
Strengths
- 1006 inspeccionó la prueba de la cota armónica para todos los generadores de Petz operator-convexos no afines, estados fieles, pesos positivos y referencias finitas, sin identificar un error invalidante.
- La familia qubit–qutrit y los límites ordenados muestran el supremo3lambda²/(1+2lambda) para SLD, chi-cuadrado mínimo y Petz triangular; la optimalidad uniforme no se atribuye a cada generador.
- 1006 verificó los21payloads congelados en C/D, los10artefactos locales sin cambios,13archivos públicos seleccionados y los3verificadores públicos. Reprodujo9identidades,9pares a75dígitos,2certificados racionales y4controles exactos focalizados.
- El suplemento está fijado al commit f0b3642b196b9de6d51b31cca49a69818522ee91, con manifiesto y dependencias. Las diferencias LF/CRLF y el README público distinto están declarados;998 permanece íntegro.
Weaknesses
- O1 RESUELTA en1005,p.7: el URI real fija el commit, el manifiesto y13archivos públicos coinciden, y3scripts descargados reproducen las salidas. Sólo se comprobaron las entradas pertinentes seleccionadas; no se avalan científicamente988 ni las extensiones posteriores.
- O2 RESUELTA en1005,pp.7–8: cita George–Tomamichelv3 y distingue base fija, coeficiente ordinario y completo restringido. Se contrastaron pasajes seleccionados; la prioridad mundial sigue sin establecerse.
- O3 RESUELTA en1005,p.5: ahora0<xi<1 garantiza autovalores positivos; el control exacto del límite de regularización pasa. El orden t→0,xi→0,e→0 permanece explícito.
- O4 RESUELTA en1005,pp.5–6: combinación convexa finita, pesos no negativos normalizados y eliminación de átomos de peso cero explícitos; el caso r=0 está bien definido.
- O5 RESUELTA, originalmente opcional, en1005,p.5: comparación ordinaria lambda² y1/4 frente a3/8 añadida y contrastada con Hiai–Ruskai para T=lambdaI.
- Las herramientas de representación, convexidad y cálculo espectral son conocidas. La búsqueda bibliográfica fue dirigida y parcial, con lecturas anteriores de998 reutilizadas; no certifica originalidad mundial.
- No se determinan el coeficiente completo de entropía relativa o información mutua, la dimensión mínima suficiente de referencia, la exactitud en dimensiones mayores ni aplicaciones operacionales amplias.
- El contexto952/998 y el filesystem se comparten, y hubo participación sustancial de Codex. Identidad/esfuerzo efectivos e independencia no están atestados. unknown no significa ausencia de participación ni revisión independiente.
- 998 evaluó otro PDF y1006 es la única evaluación actual.1010 sólo serializa1006. Las extensiones997/1003 no se leyeron ni evaluaron; nombres y hashes del listado público no constituyen revisión.
- La evaluación conserva incidentes de preparación PDF y diferencias esperadas de transporte. No hubo fallos matemáticos, discrepancias de hashes ni fallos en los tres verificadores públicos; el detalle íntegro permanece en el informe y registros1006.
Potential errors
- 1006 no identificó errores centrales ni nuevas objeciones condicionantes. Eso no constituye verificación formal ni arbitraje humano independiente; la inspección del modelo puede no detectar un error.
- Los diagnósticos finitos y la reproducción racional no reemplazan las pruebas universales y los argumentos de límite ordenado. No se afirma optimalidad a partir de optimizadores ni una campaña computacional exhaustiva.
- Un antecedente que cubra los mismos cuantificadores podría afectar la novedad; los pasajes consultados no certifican su ausencia en toda la literatura. La búsqueda y sus límites constan en READINGS1006.json.
- La optimalidad uniforme sobre Petz no fija la constante de cada generador; ordenar métricas no ordena sus cocientes. El resultado no debe trasladarse a BKM, entropía relativa, información mutua o extensiones posteriores sin prueba.
Strong novelty candidates
- Candidata provisional ya identificada por1006: constante completa exacta de qubit para SLD, chi-cuadrado mínimo y Petz triangular con familia qubit–qutrit que aproxima el supremo, junto a la cota armónica uniforme. Novedad mundial no certificada; no se cuenta la maquinaria conocida como aportación adicional.
Unresolved material objections
None reported.
arr:assessment:e9a7bc7f-dbdc-417a-9a5f-d9cffda31229 · prompt ARR-ASSESS-1.0 · response SHA-256 bb61c8cbd23134a03194533735f15a4594a882318ed6d0ab9fbd6e2db31cb932 · canonical PDF SHA-256 b4728f44f7af59809be26e0eba957336695ff34cfc3cb10c17fcfa06ffb93381
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Founder-authored exact author-authorized Working paper. Current full model report1006, earlier adverse report998 and context limits preserved. Native admission gate incomplete; no Accepted status or independent human peer review.