Source and review scope

Reviewed edition

Repository: OpenAI/math.

Manuscript date: 2026-09-24; review date: 2026-10-14; 7 PDF pages.

Reviewed PDF SHA-256: 713430a73f1530f5d89cd38050c45a6bc2ccc458878a191917bb37b451b2f26a.

Expanded reviewed TeX SHA-256: 22909d746ababe3e7547271619ddf54da33f386a954f5b7cfab13c251f32ebb8.

Upstream main TeX SHA-256: 08dcd32a1a8266b990a407e814b44f672452cdb315d2a8c07301ee9f2e429086.

Source preparation

Recursive literal TeX include expansion; brace-valued BibTeX metadata rendered as bibitems where needed. Original bibliography source retained. Bibliography numbering in a rendered BibTeX expansion is not the PDF numbering. No manuscript code or TeX executed.

Expanded includes: main.tex, sections/01-statement.tex, sections/02-cycles.tex, figures/path-to-cycle.tex, sections/03-characters.tex, sections/04-quotient.tex.

The expanded TeX has no single upstream-file equivalent. The reading-page checkout comparison uses the reviewed PDF; the expanded TeX has its own independent frozen hash.

Dependency map

The reading map indexes the supplied claims, sections and bibliography. Literal references are candidate relations, with exact source anchors; they are not independent checks of referenced publications. The complete cited bibliography is retained.

Panel scope

Four models each received the same frozen manuscript in two independent prompt conditions: baseline-v2 and source-first-v2, at high effort and a 32768-token output cap. This is eight requested assessments, not eight different models. The cap includes billed reasoning. No generation retries or automatic escalation were used.

Reviewers had no external-reference retrieval tool and did not receive each other's conclusions. Failed/capped requests contribute no mathematical verdict. The panel page lists every outcome and estimated cost, including failures.

A completed assessment records a model's examination of the supplied text. Human substantiation, coverage and mathematical quality grades remain pending. Independent source and algebra checks have limited scope and do not certify the whole proof.

External obligation

The exact positive-genus resolution statement, including the stated hypotheses on the model and the resulting cover/model morphism, remains unverified against the cited Mochizuki–Tsujimura publication. The panel's favorable internal assessments are relative to that imported result. Standard GAGA/SGA1 inputs were also not independently audited.