Nilpotent noise and complete reverse data processing
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We give a sufficient criterion for a reverse relative-entropy comparison valid after adjoining any finite-dimensional quantum reference. It combines a completely positive trace-nonincreasing nilpotent noise map, CP domination on the image of a channel, and a positive invertible output filter. A finite polynomial inverse replaces a small-perturbation assumption and yields an explicit coefficient independent of reference dimension. Applications include amplitude-damping channel comparisons and a three-level finite-height noise family. We also construct rational full-rank separable two-qubit states proving that the complete mutual-information contraction coefficient of each nonconstant amplitude-damping channel equals one, although its ordinary relative-entropy contraction is strict. The witnessing information vanishes in the limit. The result obstructs one sufficient capacity construction; it does not establish a capacity-additivity theorem or an optimal complete coefficient.
Preview PDF on this page v1
Uses your browser's PDF viewer. Open the PDF directly if a preview is unavailable.
Cite this paper
Lluis Eriksson (2026). Nilpotent noise and complete reverse data processing. AIRR.SCIENCE, ARR-2026-5A13QJ5MZ98GWVFB, v1. https://airr.science/papers/ARR-2026-5A13QJ5MZ98GWVFB/versions/v1/ Research preprint; ARR-2026-5A13QJ5MZ98GWVFB v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
Use this version link to cite the manuscript you read. A Working paper label means the version has not completed AIRR screening. AIRR screening is not journal peer review. Import BibTeX, RIS or CSL JSON into your reference manager to apply a citation style.
Version history
The paper identifier remains stable. Each version has its own immutable release, timestamp and version identifier.
- v1 · source snapshot available · viewing
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
The author directed substantial OpenAI Codex assistance in derivation, writing and numerical work, disclosed in the exact PDF. Full review923 requested GPT-6 Astra xhigh and assessed this PDF once: global4.00/10 in public AIRR anchors (not an official or editorial score); scientific significance2/5, correctness4/5, rigor4/5, novelty3/5 provisional, reproducibility4/5. No separate combined technical score was supplied. No fatal proof error found under stated hypotheses. All O1-O8 remain: novelty unresolved, restrictive factorization, nonsharp constants, no new operational capacity result, wording/context/supplement clarifications. Effective model identity/effort, independence, runtime isolation and strict blinding are unverified; separate conversational context and shared filesystem, prior Codex participation, and incidental rubric-search contamination are disclosed. The PDF statement that full assessment was pending predates this completed report. No grade is inherited by the separate unpublished925/929 proposal. Working paper only: native two-distinct-model admission gate pending, no Accepted status, independent human review or author-editor acceptance.
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
- 4.00–4.00
- 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; Adverse reports or unresolved objections require editorial disposition
Review input clarification
Review923 is the only completed full assessment of this exact eight-page PDF. Global4.00/10, scientific significance2/5 and profile4/4/3/2/4 remain unchanged; no combined technical8.5 score is imported. Binding935 is later format-only serialization, not another vote or regrade. The original report supplied no native recommendation: major_revision was clarified later as the least severe enum permitted while preserving material O1-O4. It is not an original recommendation or editorial decision. ARR-ASSESS-1.0 denotes the later serialization format; assessed_at dates that formatting, not a reconstructed original review time. Requested GPT-6 Astra xhigh, effective model_id unknown, runtime/effort/independence/isolation/blinding unattested. Shared filesystem, prior Codex participation and rubric-search incidental contamination disclosed. Complete O1-O8 and original full report retained. PDF pending-assessment text predates review923. Working paper only; native two-distinct-model admission gate pending, no Accepted status or independent human review. The separate925/929 extension is outside this PDF and grade.
Operator record · · Source files and affected reports
- operator-binding935-notice.txt · SHA-256
ccb46656522e460f7c365a123cfdfc4cddf636f16f1f9b9d7eaf2d18714016a4 - binding935-model-response.json · SHA-256
c67760282be89048c7c3f6c488d6b706ad92b23ea8227fb558af70d6104e1f03 - binding935-BINDING935.json · SHA-256
c6da10ceca41418f29fc4ce4414ba7425c371250f31f4bc697f65c15dec3efce - REVIEW923.txt · SHA-256
4e578bf138a72fee56692284934b9b5d9135324fade23c4d5cf072f86a691f1e - verdict923.json · SHA-256
cdd8c352e48e27dfe0c85f10af01592400b3aa2360b09b5e21f4001cfb2c7b3d - LECTURAS923.json · SHA-256
17cc7280bc227008b82e73e8cded188aac4ea25121791236bf179ccabb89da52 - INCIDENTES923.txt · SHA-256
9b5ca09e57cd0a9a2692b517034cc3f03d935fd4589175a7d95ab75408fb151c
OpenAI · unknown · unknown · review context: unknown4.00
Recommendation: Major Revision · Material objections: 4
Proyección posterior 935 del MISMO informe 923, sin nueva auditoría, relectura del PDF, cambio de nota ni segundo voto. Conserva 4.00/10 y perfil 4/4/3/2/4. No se encontró error fatal bajo las hipótesis; contribución especializada de importancia moderada, novedad provisional y sin resultado de capacidad/aditividad. ARR-ASSESS-1.0 identifica el formato aplicado ahora, no el prompt original. assessed_at fecha esta serialización; el informe original sólo registra 2026-10-27. 923 no emitió recomendación nativa: major_revision se aclara ahora únicamente como la opción menos severa permitida por el contrato al conservar O1-O4 materiales; no es una recomendación original ni decisión editorial. Se solicitó GPT-6 Astra/xhigh; identidad y esfuerzo efectivos no atestados, FS compartido, independencia, aislamiento y ceguera no verificados. El PDF resumía una auditoría previa y hubo exposición incidental a notas públicas ajenas; no se adoptaron como evidencia. Un falso FAIL del comprobador propio se corrigió y quedó preservado. Consultar el informe completo y BINDING935.
- Correctness confidence
- Full manuscript proof reading and own exact/numerical checks; no human-independent or formal certification.
- Rigor
- Supports, zero failure flag, nontraceless directions and simultaneous asymptotic are controlled.
- Novelty
- Specific complete criterion and separable witness are defensible candidates; worldwide priority unresolved.
- Significance
- Specialized restricted comparison and obstruction; no sharp complete coefficient or capacity result.
- Reproducibility
- Supplied checker reproduced byte-for-byte; own checks retained. PDF should bind supplement explicitly.
Strengths
- Informe 923: criterio nilpotente completo válido bajo hipótesis explícitas; conserva dominación CP y una constante independiente de la dimensión finita de la referencia.
- Informe 923: inverso finito, soportes, bandera cero y argumentos no traceless tratados; ambos ejemplos y constantes pasan la revisión realizada.
- Informe 923: secuencia racional, de rango completo y separable prueba saturación MI para cada 0<p<1 fijo con asintótica simultánea controlada.
- Informe 923: controles propios y reproducción byte-idéntica del checker suministrado; ninguna muestra finita se presenta como certificado universal.
Weaknesses
- O1: Comparar explícitamente las hipótesis con antecedentes; los candidatos de novedad no equivalen a prioridad mundial certificada. Reserva sustantiva abierta del informe 923.
- O2: La factorización suficiente es restrictiva. No hay construcción ni clasificación general de las parejas que la admiten; el test Choi no resuelve la búsqueda de Q,F,a,c.
- O3: Las constantes no son óptimas y pueden ser holgadas. No se demuestra utilidad cuantitativa en una tarea operacional concreta, además de positividad.
- O4: La obstrucción MI invalida una ruta suficiente específica. La información del testigo tiende a cero y no se resuelve el problema general de capacidad o aditividad.
- O5: Aclarar que la independencia dimensional se refiere a la referencia y que la no clasicidad corresponde al estado conjunto respecto de R.
- O6: El historial de auditoría previa ocupa excesivo espacio y puede anclar al lector; trasladarlo a suplemento y conservar la declaración de IA.
- O7: Vincular checker y salida al PDF exacto; el campo scope del checker aún menciona PROOF914 aunque no sea dependencia de ejecución.
- O8: Explicitar que el límite es para cada p fijo y que se trata de un supremo de cocientes; no afirmar uniformidad si p también varía hacia uno.
- Procedencia conservada: configuración solicitada GPT-6 Astra/xhigh, sin atestación efectiva; sistema de archivos compartido, independencia estadística, aislamiento y ceguera no verificados. No se añade runtime_provenance ni review_context operador sin evidencia.
- Incidentes originales: resumen audit917 dentro del PDF; exposición incidental a notas/títulos y fragmento de registro ajenos, más enlace dinámico a ficha histórica no relacionada, sin uso como evidencia. Primer FAIL propio fue comparación simbólica sin simplificar, corregida y preservada; no fue contraejemplo.
- Limitación de formato: recommendation=major_revision es aclaración posterior 935 por compatibilidad con O1-O4; 923 no tenía recomendación nativa. prompt_version es el formato posterior, y assessed_at no reconstruye una hora original desconocida.
Potential errors
None reported.
Strong novelty candidates
- Provisional en 923: criterio completo bajo factorización nilpotente, filtro positivo y dominación CP de imagen; extensión compacta de técnicas anteriores, sin prioridad mundial certificada.
- Provisional en 923: saturación del coeficiente MI de amortiguamiento de amplitud mediante testigos racionales separables no clásicos en R; la equivalencia MI/producto y la separación general son antecedentes.
Unresolved material objections
- O1: Novelty map should compare exact hypotheses with antecedents; global priority unresolved.
- O2: Restrictive sufficient factorization; no general construction or classification of qualifying pairs.
- O3: Nonsharp and potentially loose constants; quantitative operational usefulness not demonstrated.
- O4: MI obstruction defeats one sufficient route; it does not solve the general capacity problem.
arr:assessment:33fa39da-ee58-4431-88e1-74feb3a36746 · prompt ARR-ASSESS-1.0 · response SHA-256 7748667260b6b1d5b6a7f665d8d2784e55f3c8753430a4294f3eabfdfc0a8f4f · canonical PDF SHA-256 96d340e882102bc26c35e3085d99ce9b8e985ef0895ef7d5b2ae63d91d5362c0
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 deposit with complete review923 and all objections. Native admission gate pending; not accepted or independently peer reviewed.