发表机构
Polish–Japanese Academy of Information Technology; Chair of Theoretical Physics of Naturally Intelligent Systems (NIS)（波兰-日本信息技术学院; 自然智能系统理论物理研究所（NIS））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文审计OpenAI相关工作中AI生成的数学证明，发现其量子并行重复中贪心条件引理的证明存在极性错误，给出反例并提供局部修正证明，揭示AI论证可能隐藏互补事件的关键反转。
AI 中文摘要
OpenAI的《数学与理论计算机科学十大进展》第6章声称，针对所有有限两人单轮纠缠游戏，存在指数级并行重复定理。该章在证明早期使用了一个量化贪心条件引理，该引理旨在选择一个小坐标集D，使得在以赢得D中所有坐标为条件后，随机选取的剩余坐标被赢得的平均概率至少为(1-δ)。该引理的表述是正确的，但印刷版证明存在极性错误：其延续测试是基于平均成功概率编写的，而下一步需要的是具有大条件失败概率的坐标，该推论不成立，甚至简单示例都可能导致印刷版程序无有效下一步操作。本注给出了一个明确的反例，确定了预期的延续条件，并提供了完整的修正证明。该修正具有局部性：它保留了引理的表述及该章后续使用的参数。不过，不应将其视为主并行重复定理的独立验证。更广泛地说，该示例表明，数学上看似合理的AI生成论证可能隐藏互补事件间微小但决定性的反转。
英文摘要
We assess 18 chapter-specific reviews of the ten mathematical results announced by OpenAI on 1 August 2026, alongside review standards, Lean formalizations, subsequent research, and mathematical references. The article audits this review record without claiming a complete reconstruction of all ten proofs. No confirmed substantive mathematical error in a principal result remains in the examined assessments, although review depth varies and some dependencies remain partly checked. Chapter 8 presents the strongest reservation: a specialist review requests major revision of compressed analytic arguments. In Chapter 6, an apparent polarity error was withdrawn after an overbar lost during PDF extraction was recovered from the typeset source. Subsequent research independently reuses the Chapter 3 proof mechanism and confirms that Connes's rigidity conjecture is false, without independently reproducing Chapter 4's stronger infinite-family result. Among the cited follow-ups, Chapter 7 receives the strongest direct theorem-level corroboration through a stronger hardness theorem. Related equality results in Chapter 8 do not verify the analytic inequality proof. Some follow-ups disclose material AI assistance. We argue that confidence should combine formal checking, human reconstruction, independent mathematical use, and a public record supporting correction of both proofs and reviews.
Comments8 pages, 5 references. V2: 11 pages, 8 references. V3. 13 pages, 27 references. Revised and updated version
