OpenAI's openai/math withdrawals show reuse risk in AI proofs

The OpenAI release on 2026 年 10 月 6 日 bundled model-generated results with Lean formal proofs in a single GitHub repository, and within a day the limits of that packaging became visible. The history file for October 7 separates withdrawals, proof fixes, citation updates, and additional formalizations into distinct categories, which matters because each implies a different kind of follow-up check. A withdrawal asks whether the cited claim and its underlying proof are still valid; a fix asks where the statement, assumptions, or argument changed; a reference update asks which version is now being cited and whether logical dependencies shifted.

Two relationships that look similar in a bibliography are not the same thing. Logical dependency means one theorem's proof assumes another theorem, while a bibliographic reference simply points to another document or version. Inferring the first from the second, or treating an updated citation as proof that dependencies were re-verified, is described as inappropriate. The AGMAI recommendations cited here — persistent identifiers, revision history, machine-readable links between natural-language claims and formal proofs, and explicit formalization status — are aimed at publishers, but they also describe what downstream researchers need in order to inherit verification rather than redo it.

The proposed management schema is explicitly not an existing openai/math structure; it is a conceptual example that separates manuscript status and version from claim-level verification scope, logical dependencies, and bibliographic references. A simple verified: true flag would lose which version and which theorem a formalization covers, and whether dependencies have since been revised. The 719 figure in the current README, for instance, is not a correction of 722 but the count after three withdrawals, so reading any number here requires knowing what was counted and at which point in time.