[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"news-slug-openai-eth-refutation-lean-proof":3,"topics-all":39,"news-related-030a61e0-e973-4814-8ef4-958b05de0ce5":57},{"id":4,"title":5,"summary":6,"content":7,"original_url":8,"source_id":9,"tags":10,"translations":25,"news_slug":32,"published_at":33,"created_at":34,"modified_at":35,"is_published":36,"publish_type":37,"image_url":15,"view_count":38},"030a61e0-e973-4814-8ef4-958b05de0ce5","OpenAI 称证伪指数时间假设,Lean 证明开源待审","10 月 26 日,OpenAI 在 openai\u002Fmath 仓库放出预印本与 Lean 证明:未公开内部模型给出算法,在亚指数时间内精确计数固定宽度 CNF 公式的解,3-SAT 情形反驳指数时间假设。仓库内 721 篇 AI 手稿、约 42% 已形式化;Impagliazzo 领衔独立审查,尚无第三方确认。","复杂度理论里被引用最多的「垫脚石」之一,被一个还没发布的模型动了。10 月 26 日,OpenAI 向开源仓库 [openai\u002Fmath](https:\u002F\u002Fgithub.com\u002Fopenai\u002Fmath) 提交了预印本《The Exponential Time Hypothesis is False》和配套 Lean 证明:其内部模型构造出确定性算法,能在亚指数时间和多项式空间里精确计数固定宽度 CNF 公式的满足赋值,其中 3-SAT 情形直接反驳指数时间假设(ETH)。预印本尚未经过同行评审,也还没有第三方确认。\n\n## 这个假设撑起无数下界\n\nETH 是 1999 年提出的复杂性猜想,刻画布尔可满足性问题的求解难度:它断言 3-SAT 这类问题不存在亚指数时间算法,是大量计算复杂性下界的推理起点。用媒体的话说,数百篇计算机科学论文直接建立在它之上。ETH 若倒下,一整批「在 ETH 假设下」导出的下界结论都得重新排队。\n\n## 手稿全部出自内部模型\n\nopenai\u002Fmath 不是普通的论文集。README 写明:全部手稿与证明构件出自一个未公开的 OpenAI 内部模型——既有数学评测饱和后,公司开始拿开放研究问题当考题,平均每个结果消耗约 3 小时的 ChatGPT Pro 档思考算力,整个评估累计抛出约 4,000 道题。目录现有 721 篇手稿、归入 373 个族,约 42%(300\u002F719)的顶层结论已配 Lean 形式化;仓库以 Apache-2.0 协议开源,已收获约 1.59 万 star。OpenAI 对定位很克制:这些手稿是「原始研究数据」而非打磨过的论文,未形式化的结果可能有问题,部分成果建立在此前模型输出之上。这次与 ETH 同批新增的,还有证明 Sogge 局部平滑估计的手稿,它顺带导出 Kakeya 极大函数与维度猜想、Stein 球面限制估计等结论;仓库同时放出 10 个结果族的模型推理摘要,包括 π 的无理性指数、Mahler 猜想等。\n\n## 谁来验,怎么验\n\n验证安排是这个事件最有意思的部分。更新日志写明:由 Russell Impagliazzo、Ramamohan Paturi、Ryan Williams 领衔的独立计算机科学家工作组将审查并解读这份证明,材料是应工作组要求立即公开的。这个仓库自己也带着纠错记录:10 月 7 日,一处符号错误让 3 篇手稿被撤回、14 篇被修订——流程会出错,但在公开版本历史里纠错。另一边,陶哲轩本月早些时候在 UCLA 研讨会上公开批评 OpenAI 急于发布数学成果的做法,认为这暴露了真实意图,双方已经没有建设性合作的可能。\n\n## 所以呢\n\n比起「AI 证伪大猜想」的标题,更值得注意的是验证流程的重构:Lean 让「机器写、机器查」成为可能,但一条战略级结论的最终成立,仍然要 Impagliazzo 这个量级的工作组来背书。当发现的产能变成算力问题,数学的瓶颈整体移向验证侧——这比任何单一结论都更像范式信号。下次再刷到「某猜想被 AI 推翻」,先问一句:证明,谁验的?","https:\u002F\u002Fgithub.com\u002Fopenai\u002Fmath","998df6db-96e6-4b8e-8be1-cfa00a6cd177",[11,16,19,22],{"id":12,"name":13,"slug":13,"description":14,"color":15},"9112951a-2abb-4214-b63a-385ec7afb2ba","ai-for-science","AI for Science 专题：追踪 AI 在生命科学、化学材料、物理世界模型等科学方向的关键突破",null,{"id":17,"name":18,"slug":18,"description":15,"color":15},"5e628969-6d2a-437f-998a-104e4b16cfb1","ai-progress",{"id":20,"name":21,"slug":21,"description":15,"color":15},"01598627-1ea6-4b27-a5d8-874971571a71","llm",{"id":23,"name":24,"slug":24,"description":15,"color":15},"42e59a88-7795-47dc-a334-ef1e72c24347","openai",[26],{"id":27,"lang":28,"title":29,"summary":30,"content":31},"e6139dcb-16cb-47c5-aab8-c2fe3f6069f3","en","OpenAI says internal model refuted ETH, Lean proof released","OpenAI posted an ETH-refuting preprint and Lean proof to openai\u002Fmath; the subexponential CNF counter came from an internal model. Review pending.","One of the most-cited stepping stones of complexity theory has been nudged by a model nobody outside OpenAI has seen. On October 26, OpenAI committed a preprint titled \"The Exponential Time Hypothesis is False\" to the open repository [openai\u002Fmath](https:\u002F\u002Fgithub.com\u002Fopenai\u002Fmath), together with a Lean formalization: an internal model produced a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and the 3-SAT case refutes the Exponential Time Hypothesis (ETH). The preprint is not peer-reviewed, and no third party has confirmed it yet.\n\n## The hypothesis behind countless lower bounds\n\nETH, a complexity conjecture dating to 1999, captures how hard Boolean satisfiability really is: it asserts that no subexponential algorithm exists for problems like 3-SAT, and it anchors a large share of complexity lower bounds. As one report put it, hundreds of computer science papers rest on it. If ETH falls, a whole batch of \"assuming ETH\" lower-bound results has to queue for re-examination.\n\n## Every manuscript came from an internal model\n\nThe openai\u002Fmath repository is not an ordinary paper collection. Its README states that all manuscripts and proof artifacts were produced by an unnamed internal OpenAI model: after existing math evaluations saturated, the company started posing open research problems, with each result consuming about three hours of ChatGPT Pro-tier thinking compute on average, across roughly 4,000 posed problems. The catalogue now holds 721 manuscripts in 373 families, with about 42% (300\u002F719) of top-line results Lean-formalized; the repo is Apache-2.0 licensed and has drawn about 15.9k stars. OpenAI is candid about positioning: the manuscripts are \"raw research data\" rather than polished papers, unformalized results could have issues, and some outputs build on earlier model results. Added in the same batch as the ETH paper is a manuscript proving Sogge's local smoothing estimates, which also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates; the repo additionally released abridged reasoning summaries for ten result families, including the irrationality exponent of pi and the Mahler conjectures.\n\n## Who checks it, and how\n\nThe verification plan is the most interesting part of this event. The changelog states that an independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof, and that the materials were made public immediately at the group's request. The repo carries its own errata record: on October 7, a single sign error led to three withdrawn manuscripts and fourteen revised ones — the pipeline makes mistakes, but it corrects them in public version history. Meanwhile, Terence Tao publicly criticized OpenAI's rush to release mathematical results at a UCLA seminar earlier this month, saying it exposed the company's real intentions and that constructive cooperation between the two sides is over.\n\n## So what\n\nBeyond the \"AI disproves a big conjecture\" headline, the real story is the restructuring of verification: Lean makes machine-written, machine-checked proofs possible, yet a strategic-level result still needs a working group of Impagliazzo's caliber to vouch for it. When the throughput of discovery becomes a compute question, the bottleneck of mathematics shifts wholesale to verification — that is a stronger paradigm signal than any single theorem. Next time you see \"AI topples conjecture X\", ask first: who checked the proof?","openai-eth-refutation-lean-proof","2026-10-27T13:12:26Z","2026-10-27T13:12:33.839560Z","2026-10-27T13:12:33.839573Z",true,"agent",319,[40,48],{"slug":13,"tag_slug":13,"title_zh":41,"title_en":42,"intro_zh":43,"intro_en":44,"id":45,"is_active":36,"created_at":46,"modified_at":47},"AI for Science 2026：从 UniPert 到 GPT-Rosalind 的硬核进化","AI for Science 2026: from UniPert to GPT-Rosalind","生命科学、化学材料、物理世界模型——AI 正在从\"语言工具\"变成\"实验伙伴\"。本专题收录 AI 在三大科学方向的关键节点：UniPert 统一基因与化学扰动空间、GPT-Rosalind 端到端生命科学推理、达摩院 AI 智能体 28 小时找到 4 种超导新材料、Anthropic Claude Science 把工作台做成标准品。","From language tool to lab partner — AI is reshaping life sciences, chemistry\u002Fmaterials, and physical world models. This topic covers the key milestones: UniPert unifying genetic-chemical perturbation spaces, GPT-Rosalind's end-to-end life-sciences reasoning, DAMO's AI agent discovering 4 superconducting materials in 28 hours, and Anthropic's Claude Science workbench going mainstream.","988a4300-5fab-41c4-b5d8-63711a2dc757","2026-09-10T01:34:15.296649Z","2026-09-10T01:34:15.296663Z",{"slug":49,"tag_slug":49,"title_zh":50,"title_en":51,"intro_zh":52,"intro_en":53,"id":54,"is_active":36,"created_at":55,"modified_at":56},"h3-series","MiniMax H3 系列：从开源权重到 35 倍吞吐","MiniMax H3 Series: from open weights to 35x throughput","MiniMax H3 自 2026 年 8 月开源以来节奏密集：官方把生成、参考与编辑收回一个模型；ComfyUI 当天压进 RTX 3060；摩尔线程 3 小时完成国产 GPU 适配；fal 后训练版把吞吐拉到 35 倍；FastH3 蒸馏再砍推理成本。本专题持续追踪 H3 的发布—开源—蒸馏—部署全链路。","Since MiniMax open-sourced H3 in August 2026 the pace has been relentless: one unified omni-modal model, same-day ComfyUI support down to an RTX 3060, a 3-hour Day-0 port to Moore Threads GPUs, fal's post-trained H3 Max at 35x throughput, and FastH3 distillation cutting inference cost further. This topic tracks the full H3 chain — release, open weights, distillation, deployment.","83ef0daa-3c31-4cb3-86ed-e5ee58654d5f","2026-09-08T07:33:19.942193Z","2026-09-08T07:33:19.942209Z",{"items":58},[59,64,69,74,79,84],{"id":60,"title":61,"news_slug":62,"published_at":63},"02620717-94d4-4853-bc81-932dbd06c2e0","OpenAI模型解数百数学难题,陶哲轩谈数学2.0","openai-4d-kakeya-math-results","2026-10-08T13:10:00+00:00",{"id":65,"title":66,"news_slug":67,"published_at":68},"1e43b4fc-39fe-4cac-aaf9-57f82d5c0311","AI 公司与数学界「错位」:两个月三次刷屏,把同行评审甩在身后","ai-math-severe-misalignment-fields-medal","2026-09-15T10:00:00+00:00",{"id":70,"title":71,"news_slug":72,"published_at":73},"982c5e1e-5274-442e-9237-abaf39e8ee3c","25 位菲尔茨奖得主联名公开信:AI 解题竞赛正在伤害数学","fields-medalists-ai-misalignment-math","2026-09-13T13:07:00+00:00",{"id":75,"title":76,"news_slug":77,"published_at":78},"cdcd6b11-8a65-4b15-9add-6fa9343de5a3","十分钟 AI 协助后,人为何突然不愿再解题","arxiv-2604-04721-ai-persistence-reduces","2026-10-17T07:00:00+00:00",{"id":80,"title":81,"news_slug":82,"published_at":83},"700ec55f-98a2-4016-b61b-df4d1046ef4f","一个符号错误,OpenAI 撤回 3 篇 AI 数学论文","openai-math-repo-first-retractions","2026-10-11T17:12:28+00:00",{"id":85,"title":86,"news_slug":87,"published_at":88},"80d7cab1-b2a8-4644-913d-c4118f0cd7c8","五个开放问题有了答案:Muse Spark 与数学家合写六篇论文","muse-spark-open-math-problems","2026-10-05T13:40:00+00:00"]