Temporal adjoints and injectivity lengths in stationary quantum processes
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We distinguish local pointwise adjoints from genuine temporal reversal in stationary quantum processes. Explicit finite ergodic qubit cocycles disprove a pointwise injectivity-length identity and, even for bistochastic local channels, can change onset distributions. The correctly reversed process preserves fixed-block distributions and, under local and dual faithfulness, first and eventual onset laws. These findings concern an auxiliary identity and do not refute the source paper’s main parent-Hamiltonian or gap theorems.
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Cite this paper
Lluis Eriksson (2026). Temporal adjoints and injectivity lengths in stationary quantum processes. AIRR.SCIENCE, ARR-2026-5BWNCWFTY79W79RF, v1. https://airr.science/notes/ARR-2026-5BWNCWFTY79W79RF/versions/v1/ Technical note; ARR-2026-5BWNCWFTY79W79RF 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 Not peer reviewed by AIRR.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.
Technical-note scope
- Kind
- Result
- Maturity
- Complete In Scope
Contribution boundary
Explicit periodic counterexamples to a pointwise local-adjoint injectivity-length identity; correctly shifted inverse-base reversal and scoped onset-law repair.
Limitations
Specialist correction of arXiv2607.01446v1 LemmaA.1; no refutation or repair of main parent/gap theorems; established persistence ingredient attributed to sourceA.3; priority search limited. M1-M5 minor issues retained and addressed by accompanying clarifications.
AI assistance statement
Author-directed OpenAI Codex assistance in mathematics, writing and exact computation. One full exact-PDF AI assessment REVIEW1225: overall4/10, supplementary technical5/10 and importance3/10; accept with minor revisions as model recommendation. No material mathematical objection found; M1-M5 retained in full. Requested GPT-6 Astra xhigh in separately initiated context; effective identity, effort, isolation and independence unattested. Shared filesystem and prior component-audit summary disclosed; no verified independent human peer review, native acceptance gate completion or editorial acceptance. Accompanying response supplies immutable scripts, sourceA.3 attribution and terminology clarifications without changing assessed PDF; minor wording/citation issues remain visible. Single limited-provenance model report does not establish founder-authored admission eligibility. No main parent/gap theorem refutation, Lean proof or certified priority claimed.
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; Benchmark match incomplete; Adverse reports or unresolved objections require editorial disposition
Review input clarification
One full exact-PDF REVIEW1225: overall4/10, supplementary technical5/10, importance3/10; accept with minor revisions as model recommendation, no material mathematical objection found. All original M1-M5 comments retained. M1 immutable supplement references; M2 persistence attribution to sourceA.3 and limited novelty; M3 downstream source scope; M4 faithfulness/unital/reverse-channel terminology; M5 provenance and prior audit cues. Accompanying response clarifies these without changing assessed PDF; wording/citation issues remain visible in that PDF. Requested GPT-6 Astra xhigh; effective identity, effort, isolation and independence unattested. Shared filesystem and prior component-audit summary disclosed. Operator projection is a serialization of this one judgment, not another model vote or native gate pass. Normal author caseSUB-3A7257486A0E5BDF, clean exactPDF, native CC BY4permission09:53:05UTC and founder declaration09:53:30UTC29October2026. Working paper only: no admission, independent human peer review, main-theorem refutation or certified priority.
Operator record · · Source files and affected reports
- REVIEW1225.txt · SHA-256
2ef94aa1ce33afc42ac06c80620c3105abe277435f31d9219cdfc4a1f07661bf - verdict1225.json · SHA-256
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74544f6b75f03b3a0f0849fd17f369c6d72fd02b044795f94ff86b49c0099e91 - RESPONSE1230.json · SHA-256
ef3dd4b5628cb0f33cd92da39cba8e014d5c06b713924b1af9184342fc66ac3d - MODEL-CONTEXT1230.json · SHA-256
48d1e7c6344cb363ddbd15e09397ac487bf43065c80c9f670d173484583b8ca4 - projection-provenance.json · SHA-256
46576e488209748c3aa765fa55f1999510e8633baa4823d8c1a61ec8c62fd659
OpenAI (requested; runtime unverified) · GPT-6 Astra xhigh (requested; runtime unverified) · unknown · review context: unknown4.00
Recommendation: Minor Revision · Material objections: 0
Operator serialization of the single original REVIEW1225 exact-PDF assessment, not a new model vote. Overall4, supplementary technical5, importance3. Accept with minor revisions as model recommendation; no material mathematical objection found. M1-M5 preserved with author clarifications. Author-directed OpenAI Codex assistance in mathematics, writing and exact computation. One full exact-PDF AI assessment REVIEW1225: overall4/10, supplementary technical5/10 and importance3/10; accept with minor revisions as model recommendation. No material mathematical objection found; M1-M5 retained in full. Requested GPT-6 Astra xhigh in separately initiated context; effective identity, effort, isolation and independence unattested. Shared filesystem and prior component-audit summary disclosed; no verified independent human peer review, native acceptance gate completion or editorial acceptance. Accompanying response supplies immutable scripts, sourceA.3 attribution and terminology clarifications without changing assessed PDF; minor wording/citation issues remain visible. Single limited-provenance model report does not establish founder-authored admission eligibility. No main parent/gap theorem refutation, Lean proof or certified priority claimed.
- Correctness confidence
- All central claims checked by hand algebra, exact controls and source comparison; no material error found. Not proof certification.
- Rigor
- Adequate all-length arguments; attribution, wording and public evidence version pinning need minor improvements.
- Novelty
- Credible local novelty in explicit periodic examples and onset-law distinction. Persistence and adjoint product reversal are established. Exhaustive novelty not checked.
- Significance
- Worthwhile specialist correction, with no demonstrated broader gap or classification theorem.
- Reproducibility
- Frozen inputs and exact checks reproduce, and proofs are self-contained; immutable public supplement references are incomplete in the PDF.
Strengths
- Explicit bistochastic counterexamples and onset-law distinction checked by exact algebra.
- Correct inverse-base shifted-adjoint repair with faithful persistence hypotheses.
Weaknesses
- The three supplements are available and reproducible in the frozen packet, but the PDF does not bind all of them to immutable public file versions. This is not evidence that the public files are absent.
- Full-span persistence is already in source Lemma A.3; the positive theorem combines this with elementary inverse-base adjunction. The one-source bibliography provides limited novelty context.
- The source uses A.1 in later appendix proofs, but the manuscript does not trace the affected dependencies or name A.9 explicitly. No counterexample to the main theorems is established.
- Faithfulness is not explicitly defined; all channels used below is overbroad relative to the later reset; genuinely reversed can be confused with a normalized physical reversal; the one-step shift is an endpoint convention.
- The prior favorable component-audit summary is contextual exposure, not proof. Runtime identity, effort, isolation, underlying-model participation and independence remain unattested.
Potential errors
None reported.
Strong novelty candidates
- Concrete periodic counterexamples and temporal-law clarification; limited literature comparison, priority unverified.
Unresolved material objections
None reported.
arr:assessment:8d742bb4-5dcc-4798-b825-a77091c95fd0 · prompt ARR-ASSESS-1.0 · response SHA-256 3ac715e351e25bcedf738897698ae31442304f428ef2e94cbf1d64e6f182fe09 · canonical PDF SHA-256 cd158f0570ed8d05be7c4b77cde8bb19cc2b8c4d615a89fb71a85714c4fb666f
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Author-authorized Working paper; not admitted to accepted collection. Native founder declaration and author-editor role disclosed; no independent human decision or gate pass claimed.