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OpenAI 构造反例否证 Kaplansky 直接有限性猜想

OpenAI 在特征为 2 的群代数中构造出非直接有限的反例，直接否证 Kaplansky 直接有限性猜想。arXiv 论文 2611.08268 对该构造给出人类可读的阐述。作者进一步推广：对每个素数 p，都存在双曲群 G_p，使得 F_p[G_p] 非直接有限。这一结果将原构造扩展到任意素特征。

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OpenAI 用模型做出了数学上的反例构造，这篇论文还把这个结果推广到所有素数，数学向读者别错过。

6 sources57° AI heatLast updated 2026/11/5 16:40:14

Evidence

6 sources

Primary sourcearXiv: OpenAI

2026/11/5 16:40:14View source

Related source 1Stanford AI Lab

2026/11/4 21:05:05View source

Related source 2IT之家

2026/11/4 22:51:59View source

Related source 3rohanpaul_ai

2026/11/5 01:06:09View source

Related source 4kimmonismus

2026/11/5 09:14:00View source

Related source 5DAIR.AI

2026/11/5 13:41:04View source

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