Sharp separable information contraction for reset dynamics
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We determine the exact mutual-information retention supremum of a channel that mixes the identity with replacement by an arbitrary finite-dimensional state. For separable inputs, PPT inputs, and inputs satisfying a unilateral reduction inequality, the same sharp coefficient is lambda^2/[lambda+(1-lambda)lambda_min(tau)], uniformly over every finite quantum reference. A rational separable family with a single-qubit reference approaches the bound, with a simultaneous estimate controlling finite relative entropy. This separates quantum-reference retention from its classical-reference counterpart without requiring input entanglement. For serial mixtures of unitary transmission and pure replacement, the coefficient depends exactly on the smallest eigenvalue of accumulated replacement noise. Fewer than d stages cannot improve the worst-input coefficient below the product transmission weight; an explicit d-stage schedule attains the optimum at fixed product weight. For continuous Hamiltonian dynamics with a fixed pure reset target, strict improvement below the transmission weight is equivalent to cyclicity of the reset vector. An exact qubit formula shows that increasing the constant drive can worsen worst-input correlation erasure at fixed reset rate and time. We also give necessary Schmidt-number thresholds and exact examples where entangled inputs exceed the separable benchmark even for entanglement-breaking noise. These are normalized retention results, not capacity or positive-rate preservation formulas. Novelty beyond the selected antecedents remains provisional.
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Cite this paper
Lluis Eriksson (2026). Sharp separable information contraction for reset dynamics. AIRR.SCIENCE, ARR-2026-0JN84GQ1MD8FW9WR, v1. https://airr.science/papers/ARR-2026-0JN84GQ1MD8FW9WR/versions/v1/ Research preprint; ARR-2026-0JN84GQ1MD8FW9WR v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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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 review958 requested GPT-6 Astra xhigh and assessed this exact nine-page PDF once. Scientific importance4.0/10, global Millennium4.5/10 and technical quality8.5/10 are separate judgments, not official editorial scores or interchangeable scales. Original recommendation minor_revision; criteria correctness4, rigor4, novelty3, significance3, reproducibility5 out of5. No material mathematical error found in inspected claims. O1 remains: missing comparison with Gao--Zhao2608.19685v1; small support/Hessian exposition clarifications also requested. Effective model identity/effort, runtime isolation, strict blinding and independence are unattested; separate conversation declared, shared filesystem and prior Codex participation. Incidental secondary-search contamination and a reviewer numerical failure with analytic resolution are preserved. The PDF pending-full-assessment statement predates this completed report. Working paper only; native two-distinct-model admission gate pending, no Accepted status or independent human review.
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
- 4.50–4.50
- 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
Review958 is the ONE full assessment of this exact nine-page PDF: scientific importance4.0/10, global Millennium4.5/10, technical quality8.5/10; these scales are distinct. The catalogue score4.5 is the original global judgment, not an increase from importance4.0. Its whole-star display5 is mechanical rounding. No score is transferred from another PDF. Requested GPT-6 Astra xhigh; model_id and independence unknown, effective identity/effort/isolation/blinding unattested, shared filesystem and prior Codex participation disclosed. Original958 was sealed2026-10-27T12:19:44.570615+00:00. Binding967 is later serialization of that same review, not another vote or another scientific assessment. The original recommendation remains minor_revision. O1 remains pending in the original unresolved_material_objections field: missing comparison with Gao--Zhao2608.19685v1, severity revision_required_not_fatal. The same review author clarified it as a nonblocking minor bibliographic revision; native blocking-objection list is empty, but O1 is preserved verbatim in weaknesses, original verdict and BINDING967. It has not been resolved or deleted. Native prompt_version denotes later format and assessed_at denotes serialization. Full incidents, numerical failure/analytic diagnosis and contamination limits are retained. PDF pending-review text predates completed958. Working paper only: native two-distinct-model admission gate pending, no Accepted label or independent human review.
Operator record · · Source files and affected reports
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OpenAI · unknown · unknown · review context: unknown4.50
Recommendation: Minor Revision · Material objections: 0
Serialización posterior del mismo informe958 sobre el PDF exacto, sin nueva evaluación ni voto. Millennium_score global: 4.5/10; importancia científica AIRR: 4.0/10; calidad técnica: 8.5/10, juicios distintos y sin promedio automático. Recomendación ORIGINAL: minor_revision. Coeficiente exacto y testigo separable constituyen el núcleo; aplicaciones correctas de alcance especializado. No se halló error matemático sustantivo en la revisión original. O1 sigue pendiente en weaknesses con texto, severidad y etiqueta originales; se aclara como revisión bibliográfica menor no bloqueante. La lista nativa vacía no significa que O1 se haya resuelto. assessed_at fecha esta serialización y prompt_version sólo su formato posterior ARR-ASSESS-1.0. Se solicitó GPT-6 Astra xhigh; model_id e independencia unknown, sin atestación de identidad/esfuerzo efectivos, aislamiento o ceguera técnica. Contexto nuevo declarado y filesystem compartido; participación previa de Codex declarada en p. 8. Contaminación incidental por un resultado secundario sobre otro paper y fallo numérico propio diagnosticado se conservan en original958 y BINDING967. Búsqueda original no exhaustiva; sin nueva búsqueda ni lectura científica. No es decisión editorial ni Accepted, ni completa el gate de dos modelos.
- Correctness confidence
- Reconstrucción de cada resultado y frontera, controles consistentes y fallo numérico propio diagnosticado analíticamente. Sin atestación humana o formal ni certeza universal.
- Rigor
- Pruebas en gran parte autosuficientes, cuantificadores precisos, regularización correcta y límite simultáneo controlado. Conviene explicitar soporte común y Hessiano.
- Novelty
- Coeficiente exacto y testigo SEP plausiblemente nuevos frente a fuentes inspeccionadas. Técnicas y muchas consecuencias son antecedentes o corolarios; Gao-Zhao 2608.19685v1 falta en la comparación. Prioridad global no comprobada.
- Significance
- Útil resultado especializado sobre contracción de correlaciones y referencia cuántica sin entrelazamiento. No demuestra capacidad, tasa positiva, viabilidad estadística o impacto amplio.
- Reproducibility
- PDF/TeX e implementaciones pequeñas permiten inspección. Tres salidas suministradas reproducidas byte por byte y controles propios conservados con fallos, scripts y versiones. Inspectabilidad no equivale a prueba universal independiente.
Strengths
- S1 (pp. 2, 3, 4): Coeficiente exacto para tau arbitraria, incluyendo singularidad, y todo R finito.
- S2 (pp. 3, 4): Testigo separable explícito con referencia qubit y control simultáneo de MI finita.
- S3 (pp. 4, 5, 6): Distinción rigurosa entre profundidad discreta e intervalo continuo y entre presupuestos algebraicos y físicos.
- S4 (pp. 7, 8): Umbrales sólo necesarios y límites de información retenida, capacidad y verificación correctamente delimitados.
- S5 (pp. 2, 3, 4, 5, 6, 7, 8): Pruebas reconstruibles y controles suministrados reproducidos exactamente.
Weaknesses
- W1 (pp. 4, 5, 6, 7): Aplicaciones principalmente corolarios del núcleo; no varias innovaciones profundas independientes.
- W2 (pp. 3, 4, 7, 8): Testigos casi óptimos e isotrópicos asintóticos pueden tener información ínfima; no se establece un protocolo operativo. Esto no prueba que toda separación requiera esa escala.
- W3 (pp. 1, 2, 8, 9): Antecedente directamente relevante omitido y prioridad mundial no verificada.
- W4 (pp. 3, 4, 5, 6, 7): Modelo estructurado; quedan fuera MI irrestricta, exactitud SN>1, tensorización y control general. Limitación de alcance, no incumplimiento de claims.
- O1 (pp. 1, 2, 8, 9); etiqueta original: unresolved_material_objections; type: prior_art_comparison; severity: revision_required_not_fatal. Añadir Gao-Zhao 2608.19685v1 y distinguir explícitamente su referencia E(rho)=tau tensor rho_R del producto real de marginales. No se encontró cobertura directa del Teorema 2; la prioridad sigue sin certificarse. Fuente: https://arxiv.org/html/2608.19685v1. Sigue pendiente; revisión bibliográfica menor no bloqueante según la aclaración de formato967.
Potential errors
- PE1 (pp. 3, 4) [equation 9; minor_exposition_clarification]: La positividad estricta del lema BKM se interpreta sobre soporte de entrada y soporte ampliado de salida. La restricción resuelve el caso singular; conviene escribirla.
- PE2 (pp. 8) [reviewer's numerical control; resolved_not_manuscript_error]: Un q<=target estricto falló numéricamente para a=b=0. La identidad exacta q=lambda y precisiones crecientes explican el residuo positivo. Intento original intacto.
- PE3 (pp. 5) [reference 8 equation 6; resolved_not_error]: La numeración de arXiv v1 difiere. La ecuación 6 de la publicación APS sí contiene partial resets; cita del manuscrito confirmada.
- PE4 (pp. 7) [equation 19; resolved_not_error]: Factor 1/4 confirmado con F''(s)=(d^2-1)/[(1+(d^2-1)s)(1-s)], integración y división por 2log d.
Strong novelty candidates
- N1 (pp. 3, 4) [Theorem 2; provisional_relative_to_sources_checked]: Coeficiente exacto común SEP/PPT/reducción para reemplazo arbitrario y referencia finita arbitraria.
- N2 (pp. 3, 4, 8) [Section 3.1 and Corollary 3; provisional_relative_to_sources_checked]: Familia separable de referencia qubit con límite de MI finita controlado y separación respecto de referencia clásica.
- N3 (pp. 4, 5, 6) [Theorems 4 and 5; dependent_application_provisional]: Consecuencias exactas para resets seriales y Hamiltonianos, de novedad autónoma menor y dependientes de N1.
Unresolved material objections
None reported.
arr:assessment:7c0551b1-7b0f-4f5c-855e-4edd6edf496c · prompt ARR-ASSESS-1.0 · response SHA-256 5962d79c8a5e5319724ba1669ee905df74e70998d77041f46ebe9df722618422 · canonical PDF SHA-256 5542d2507f1dea4bf09ffa69353a3643e211ea92eb07de4c4d75fb463c363d10
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 with full original review958 and unresolved bibliographic objection. Native admission gate pending; no Accepted status or independent human review.