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Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

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Record, attribution and exact subject

Approved for publication integration. A fresh reviewer replayed the eleven editorial substitutions against the already approved mathematical successor and confirmed that all display-math blocks and proof regions, including the corrected plus sign in the two-sided telescoping display, are byte-identical to it. This was an editorial review; it did not reopen the proof, and the approval record of the one-byte successor it relies on is not retained here, so the mathematical standing rests on the local-chain review together with the presence of the correction on the current page. 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 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, and the corrected plus sign is on the committed equation (32) page as it stood on that date.

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

FINAL verdict: approved for publication integration.

This was a bounded editorial review against the already approved mathematical successor. I did not reopen the Bernstein proof. The frozen publication manifest and its candidate manifest are working-storage receipts.

All 11 declared editorial substitutions match the whitelist exactly at their guarded byte offsets. Replaying them on the frozen canonical baselines yields the nine candidate Markdown files byte-for-byte; applying the inverse list in reverse composition restores every baseline exactly. Each canonical baseline body equals its approved-successor body before those editorial changes.

The substitutions accurately replace pending-review prose with review-complete prose dated 6 September 2026. They consistently limit that review to the selected local proof chain and separately attributed elementary companion. In particular:

  • the gap companion remains distinct from Bernstein's published argument and is still expressly not described as a published erratum;
  • the uniform-separation qualification for the half-logarithm result and the unresolved bare-interiority implication remain intact;
  • the unresolved selected-point claim in the large-local-maximum branch remains outside credit;
  • the global, external-interface, circle, and shrinking-interval branches stay outside the reviewed proof scope; and
  • no problem-status, publication-acceptance, formal-verification, or composer mathematics credit is introduced.

All display-math blocks and all seven explicit proof regions are byte-identical to the approved successor. The corrected plus sign in the two-sided telescoping display is preserved. The PDF is unchanged. The exact credit boundary is one approved selected-local-chain credit and zero for the full 26-page proof, uncompiled global branches, bare-interiority claim, selected-point large-M claim, problem status, formal verification, acceptance, and publication-composer new mathematics.

The forward editorial record, its inverse and the proof-preservation record are working-storage receipts. No findings remain.