---

Record, attribution and exact subject

PASS. A fresh reviewer replayed the eighteen guarded textual operations that closed the six correction groups requested by the full-chain review, confirmed that no unreviewed mathematics changed, and that the PDF is unchanged. Completed 2026-09-06T09:17:02Z. Reviewer: a fresh review context distinct from the author of the reconstruction and from the compilation-supplied corrections; it did not build on the subject before reviewing it. No distinct grader is recorded, so no numerical claim tier is assigned.

The frozen candidate necessarily carried the full-chain review's conditional mathematical PASS and its manifest fields (_index.md lines 54-60 and integral_lower_bound.md lines 46-49, 189-191 and 231-233 as of 2026-09-15, and mathematical_composition_review=true, external_proof_review=false), because correction groups 4 and 5 of the full-chain review ordered that standing text; a separately spawned grader (Claude Fable 5.1) ruled this exposure immaterial by the content test on 2026-09-18, since the standing text was the object of the fidelity check and neither states nor implies whether the eighteen operations replay exactly, and the retained report's reasoning does not lean on it.

At filing on 2026-09-16 the bodies of _index.md and node_gap_lemma.md were byte-identical to this successor's approved bodies; node_gap_lemma.md is unchanged since 2026-09-15, and _index.md has since gained a generated navigation row and reworded its citation of the full-chain review; see the full-chain review's record for the other pages. The pages the report names are identified as they stood on 2026-09-15, before this record's filing on 2026-09-16; the exact reviewed copies were review-packet candidates and are not retained.

This record was filed on 2026-09-16 from a retained report, the review text and its machine-readable companion. The report text is retained below in full. The filing changed only the wrapper, participant identifiers, private paths and operating-history material; it records no new verdict, and the first-person readings and judgments below belong to the historical reviewer, not to the filing author.

Retained report

Verdict: PASS. The successor closes all six requested groups with exactly 18 guarded textual operations and one nonmutating metadata successor. Every operation replays forward to the frozen candidate and inversely to the reviewed prior version.

All 56 publication artifact rows match their declared identities. The five Markdown candidates match, and the complete source PDF remains unchanged. The failed first build is preserved as 23 historical payloads plus its own manifest.

R1–R3 fix the two TeX separators and define $N_n$ exactly as requested. R4 expands all eleven wiki targets to canonical names, leaving no short target. R5 maps the four actual prior version passages to the completed mathematical/composition review state. R6 preserves the historical pending report while superseding it with mathematical_composition_review=true and external_proof_review=false.

No unreviewed mathematics changed. The selected qualitative chain retains complete independent mathematical review with $c_3=1/256$, conditional on Bernstein’s local bound, Markov’s inequality, and Erdős–Turán Lemma IV. The printed $1/40$, sharp $2/\pi$, external-proof, formal, acceptance, status-change, and E1153-sharp credits remain zero.

The publication manifest and the exact operation record are working-storage receipts. Full candidate identities and per-group verdicts are in the review's machine-readable companion, and replay evidence in its inspection record. Review completed 2026-09-06T09:17:02.383944Z.