OpenAI Withdraws 3 Math Papers

For any withdrawn papers, their README files explain the gap and link to the retracted manuscript. For any updated papers, previously published editions remain accessible through the version notes in their README.

对于任何已撤回的论文，其 README 文件均解释了其中的缺漏并提供了指向已撤回手稿的链接。对于任何已更新的论文，之前发布的版本仍可通过其 README 中的版本说明进行访问。

In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers. As a result, we have withdrawn the following three manuscripts:

在《分裂阿贝尔八重流形上韦伊类的代数性》（Algebraicity of Weil classes on split abelian eightfolds）一文中，一个符号错误导致一个稳定迹抵消论证以及两篇相关论文所使用的构造失效。因此，我们撤回了以下三篇手稿：

The withdrawn papers now carry notices explaining the gap and linking to the archived manuscripts.

这些已撤回的论文现在附有说明，解释了其中的缺漏并提供了指向已归档手稿的链接。

We have revised 14 other manuscripts with proof repairs, corrected statements, clearer hypotheses and dependencies, and one correction to an obsolete citation. The changes include:

我们修订了另外 14 篇手稿，包括修复证明、更正陈述、使假设和依赖关系更清晰，以及对一处过时引用的更正。这些更改包括：

Also, as a consequence of these fixes we updated 13 additional manuscripts to cite the revised editions of companion papers. These changes update references and version dates.

此外，作为这些修复的结果，我们更新了另外 13 篇手稿，以引用相关论文的修订版本。这些更改更新了参考文献和版本日期。

Additional Formalizations

其他形式化内容

We have added an additional 6 formalizations and 5 other additions covering supporting results. This brings the total percentage of top-line results formalized to 300 / 719 = ~42%.

我们增加了 6 项额外形式化内容和 5 项涵盖支持性结果的其他补充。这使得已形式化的顶层结果总比例达到 300 / 719 ≈ 42%。