Focused statement-fidelity review

../

---

Accepted scope. The independent report has verdict refutation-failed for the frozen source statements, definitions, sparse series formulas, disclosed proof-outline comparison, and exact specialization to Problem 250. It found no transcription, hypothesis, quantifier, sign, index-range, locator or application defect. This is focused statement-fidelity acceptance. It awards no native tier and does not certify the complete source proof, any unread external theorem or its applicability, a formalization, or a result about the totient binary series.

Exact subject and retained evidence

The examined text is the campaign working repository as it stood on 2026-09-17, at its Duverney filing. That repository, including its final integration state, is separate from this one and no part of this repository's history. The examined pages were the campaign's earlier extraction pages of this note, then filed at erdos/library/irrationality/duverney_1995_irrationalite_q_analogue_zeta2/ (the report's D/: _index.md, main_theorem.md, lemma.md), and the Problem 250 page of that revision, all frozen here as the subjects/*.txt copies; the report and the manifest name the paths as of that date. The source's current pages are _index.md, theoreme.md and lemme.md of this card, complete reconstructions reviewed separately, and the current Problem 250 page is wiki/problems/irrationality/E0250/_index.md; the current text is not the reviewed text.

The rebased Duverney filing of 2026-09-17 in this repository adds the record as filed, the reviewer's report.txt, the subject.json manifest and the four subjects/*.txt copies unmodified, at erdos/library/irrationality/duverney_1995_irrationalite_q_analogue_zeta2/verify/fidelity/ (below, F/). The subject manifest here identifies all five inputs by path at the campaign repository's state of 2026-09-17 and byte count, labels that date and those paths as the campaign repository's, names the frozen copy of each reviewed text in its frozen_copy field, and names the PDF by path and byte count as the comparator identity (Git LFS records its digest). The four Markdown subjects survive as plain-text assets, each byte-identical to its copy in that filing except that the PDF's SHA-256 value in subjects/_index.txt was replaced by a removal marker on 2026-10-02:

• Source digest: the reviewed D/_index.md, frozen as subjects/_index.txt here and as F/subjects/_index.txt in that filing.
• Unnumbered theorem: the reviewed D/main_theorem.md, frozen as subjects/main_theorem.txt here and as F/subjects/main_theorem.txt in that filing.
• Unnumbered lemma and sparse-series outline: the reviewed D/lemma.md, frozen as subjects/lemma.txt here and as F/subjects/lemma.txt in that filing.
• E0250 assessment: the reviewed wiki/problems/irrationality/E0250/_index.md as of that date, frozen as subjects/E0250.txt here and as F/subjects/E0250.txt in that filing.

The primary comparator was the author's three-page scan, 2,438,038 bytes, fetched from https://danielduverney.fr/documents/theorie-des-nombres/qAnalogueZeta(2).pdf on 2026-09-17 (UTC). The report gives the printed/file-page correspondence and an ordinary Poppler rendering recipe. Its section 1 table, its section 9 recipe and the manifest name the PDF at the frozen state's path; a copy of that size fetched from the same address, placed at that path, recovers the examined subject together with these four assets, without private branches or working directories.

The report and the manifest here are migrated copies of the filing of 2026-09-17, edited in place under AGENTS.md convention 9 (Git identity, not byte hashes) (a record identifies what it examined by git identity, the commit and the repository-relative paths, and nothing else; the repository does not byte-hash its own files unless they are gold; filed records may be edited in place, keeping their subject revision, paths, scope, dates and verdict, and removing names of people, seats, sessions and tool harnesses) and docs/verification.md, section "Exact subjects and durable evidence". Removed from subject.json: the sha256 and git_blob fields of the four Markdown subjects, the git_blob of the PDF entry, the sha256 of the four frozen assets, and the sha256 and git_blob of the archived pointer; added: the frozen_copy fields and the provenance label. Removed from report.txt: the SHA-256 column of the section 1 subject table, whose PDF entry now stands in the sentence below the table; the pointer's git blob id; and the section 1 sentences matching blob and content identities against the manifest, now identity by path at the frozen revision. Section 9's byte-count-and-SHA-256 check now names the retained subjects/*.txt copies and the PDF's size and, since 2026-10-02, its Git LFS pointer in place of its SHA-256. Section 2 is reduced to its independence facts: the reviewer's attribution and exposure, the actual mathematical reading, the guidance read and not read, and the exclusions; its pin of the operating set to a commit that is not an object in this repository and its description of the review station, launch packet and node configuration are removed. Seven spellings (catalog, analogs) are American. Nothing else in the report or the manifest changed then; both kept the subject revision, paths, scope, dates and verdict as filed, and on 2026-10-02 the revision was restated as the date 2026-09-17 and the PDF's SHA-256 values removed. This index and subjects/_index.md were rewritten for the new location under the same rule, dropping their own hash lines and the seat identifiers. The snapshots preserve the older statement that review was outstanding; the present acceptance does not rewrite that historical subject.

Acceptance and independence

Reviewer: a fresh-context reviewer (model: Codex) who had not authored or collaborated on the extraction; its mathematical reads were restricted to the five pinned inputs, including all three independently rendered primary page images, and it records the allowed and actual operating reads separately, reporting no exposure to author advocacy, other verdicts, moving research or external search. Acceptance: the campaign's integrator (model: Codex), after reading the complete report and the frozen subject and checking the exact subject bytes against the frozen copies. The focused report and independence contract are accepted under the library statement-fidelity remit. This acceptance is not tier-bearing whole-claim grading: the integrator also participates in the surrounding research and its author checks.

The report supplies its own restatements, a clause-by-clause source comparison, all ten checklist dispositions, three substantive attack groups, explicit premise interfaces and reading limits. Its strongest sparse-range attack checks the actual nonzero position exactly $k$ places before the selected pentagonal index, late coefficient cancellation when parameters vary, and the fixed-parameter qualification on the eventual bound. The frozen extraction retains each needed restriction. Other re-derivations justify absolute rearrangement of the divisor sums, the scalar factor and $q=2$ application, the linear-independence reformulation, and the logarithmic derivative. The divisibility conclusion is checked conditional on the source's displayed (12).

There is no computation-dependent theorem claim or keeper mathematical program in this review. Hash comparisons establish identity; the exposed source comparison and symbolic derivations supply the scoped evidence.

Remaining boundaries

Duverney (1993), theorem 2, including its hypotheses and applicability to the step producing (12), remains unread and uncertified here. The other external books and papers retain their recorded reading limits. Complete source-proof compilation and its separate independent review remain open. The source result remains a published external theorem used at its stated scope; this focused verdict supplies no local independent proof of it.

Historical acquisition and author-reading acts, current catalog and formalization links, the inherited Nesterenko reference, and current literature were not authenticated by this pass. The frozen subject's pages are the campaign's extraction pages; this card's current pages are the separately reviewed complete reconstructions of the same Lemme and Théorème, so the current text is not the reviewed text. The statements and proof outline the report compared are unchanged in the frozen copies; the report does not purport to examine later mathematical revisions.

Extracts reproducing the paper's text are not held, since no license on record permits redistribution.