AI 模型和平台
OpenAI 称其模型在数学，CS，和物理方面产生了三个证明
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OpenAI 称在2026年10月26日的一则公告中称，其内部模型在数学，计算机科学，和物理学方面产生了三个研究成果，其中包括对"判断时间假说"的解析，这是计算复杂性理论中的长期猜想。
公司认为，人工智能生成的手稿相当于原始研究数据，必须转化为科学理解，它正在为此尝试一种新的释放方法。 OpenAI请外聘专家出任牧羊人，组织小组来了解新结果，而牧羊人称则建议了三种不同的放出策略：直接释放数学AI输出，研究人员可以自由地组织自己的解释性工作；在公布AI输出的同时，为计算机科学结果组成外部合作者小组，供任何人检查和借鉴；在发布材料的同时，为物理结果组成这样的小组。 称公司尚不知道这三种办法中哪一种最有用，请各方就哪些办法可行和哪些办法可以改进提出反馈意见。
根据公告，合作将遵循四项原则：透明度，没有不披露协议，参与者可以自由讨论工作、分享工作进展并发表结论；没有学术信用，意思是OpenAI不寻求内部模型的发现，邀请研究人员管理合作并不意味着研究者做出了最初的发现；承认，根据这种认识，每个团体都能获得对了解、撰写和其他材料的信用，并且有助于确保研究者的适当信用、技术和想法；独立，在自愿和无报酬的情况下，成员自己得出结论，成员或OpenAI都不代表他人发言。 OpenAI 称它将把与结果相关的材料和文物移交给协作。 该公司承认，这些办法涉及权衡——选择最初的牧羊人必然会先决定谁参与，并造成信息的不对称——称欢迎关于如何扩大参与的反馈。
局部平滑和Kakeya猜想
1991年，索格提出了"局部平滑猜想"，该猜想涉及波浪变得有重点时的表现，并认为最极端的聚焦只能是短暂的，因此在典型时间的聚焦远远弱于最坏情况下。 公告将猜想现象描述为根本现象，在整个数学分析中具有广泛的影响；猜想暗示了卡凯亚猜想和斯泰因的限制猜想。 古斯，王同和张在2019年证明了两个空间维度的猜想，而王同扎尔在2025年将三维卡基亚猜想确定。
OpenAI 称它的模型为每个维度的局部平滑猜想提供了证明，依靠了一种新颖的辅助部分微分方程，在这样做时，也解决了卡凯亚猜想和斯泰因在各个维度上的限制猜想。 公司于2026年10月18日获得AI出品，次日在利恩正式出品，后与一位专家联系，商讨围绕结果形成合作。 根据该专家的建议，OpenAI在其公开的GitHub寄存器中公布了由其模型制作的AI自然语言书写和精益证，这与它在2026年10月6日的数学发布时所使用的策略相同。
模拟时间
计算机科学的结果涉及"指向时间假说"(Expothesis)，这是关于确定布尔公式能否满足与P对NP问题密切相关的复杂性的猜测。 公告称该假说被广泛相信，称在上百篇论文中被用来获得硬度结果，条件是它跨越了包括图论，计算生物学，数据库，和计算几何等多个领域。 OpenAI 称它的系统证明了这个假说是虚假的，结果随后在Lean被验证。 AI于2026年10月16日生产出自然语言防伪，结果于2026年10月17日在利恩正式确定。
根据OpenAI公共数学库内存放的、最新承诺日期为2026年10月26日的文件，Lean的证明确定，对于至少2个固定K，确定性机器完全算上在次责任时间和多诺米空间内对n变量的犬形编码克-CNF公式的满意分配，对附带的2026年10月25日手稿中给出的m项条款的事例有更明确的时间界限。
作品将由UC圣迭戈的罗素·英帕格利亚佐和拉马莫汉·帕图里(英语：Russell Impagliazzo and Ramamohan Paturi)所领导的小组进行验证和牧羊，他们最初与弗朗西斯·赞恩(英语：Francis Zane)共同提出这个假说，而麻省理工的瑞安·威廉斯(英语：Ryan Williams)则被OpenAI所注意到的强烈版本所反驳并连接了算法和下限。 OpenAI 称同意小组的要求，即公布结果背后的所有原始数据，以便利社区进行独立核查，OpenAI承诺资助一次关于工作对实地的影响的会议。 该小组还邀请社区帮助组织对索赔的公开审查并讨论其称 AI在核查、获取、信贷和研究的未来方面产生的更广泛的问题。 OpenAI 称反驳者重新提出了关于这些任务可以实现多快的问题，而将理论进展转化为实际改进将需要大量的进一步研究。
QCD 和标准模型存在证明
OpenAI 称物理结果提供了某种相互作用的量子场理论的数学上严格的存在证明，这些理论包含量子染色体动力学(QCD)和粒子物理标准模型的统一完成等四个维度的量子场理论，并且工作建立在巴拉班在建设性量子场理论中的方法上。 作为次问题，它包括证明存在纯洁的杨 - 米尔斯理论，是克莱数学研究所"量子"杨-米尔斯理论千年奖问题的一部分。 存在证明适用于最简单的大统一理论，其中包含标准模型的测量场和发热量，即公告称，因为标准模型本身不能被任意推导到短距离。 《标准模型》描述了基本亚原子粒子在四种基本力量中的三个作用下，除重力外的所有作用；QCD描述了夸克和克吕翁等粒子如何通过强力相互作用；纯阳- 米尔斯理论描述了克鲁恩斯自相交流，力载体，而不是夸克等物质。
OpenAI 称它的型号于2026年9月9日产生了杨-米尔斯存在的自然语言证明，后于2026年9月18日为QCD提供了证明。 鉴于工作时间长而复杂，公司推迟发行，直到精益正规化完成，完成对杨-的正规化。 米尔斯于2026年10月16日存在——一个里程碑，由称公司领导发展了合作。
大卫·格罗斯将领导一个包括迈克尔·道格拉斯，亚瑟·贾夫，伊戈尔·克勒巴诺夫，和尼基塔·涅克拉索夫在内的团体。 Gross 1973年关于杨的不对称自由的工作- 米尔斯理论帮助建立了QCD作为强相互作用的理论，并让他获得了2004年诺贝尔物理学奖的一分。 贾夫与维滕一起制定了"量子杨-米尔斯理论千年奖"(Quantum Yang-Mills Theory Million Prize)问题并共同创办了克莱数学研究所。 道格拉斯在2004年报告了该问题的现状，并全面介绍了2026年初的进展情况。 Klebanov是应用量表的先行者之一 — — 限制的双重性，这是QCD的关键财产，现在领导西蒙斯合作公司(Simons Complex on Confinement)和QCD Strings。 涅克拉索夫为杨–米尔斯理论的通论发展出精确的方法，并获得2023年丹妮·海涅曼数学物理学奖。 物理组决定暂停释放AI出产的文物，而自行将结果写出，并要求与其成员的所有关于这项努力的通信都直接发给YANGMILLS4D@gmail.com。
支持科学家
OpenAI 称合作补充了它以前对西蒙斯基金会的500万美元捐款，该基金会管理和奖励该基金会支持讲习班、会议和特别方案，帮助研究人员了解和借鉴大赦国际的成果。 称公司致力于确保资助研究人员独立检查，解释，并基于三个结果，它希望与AI合作的人类能够提供对计算复杂性的新的理解，并阐明高效计算固有的能力和局限性。 OpenAI也叫作称，它继续邀请各方反馈披露结果和与科学家接触的最佳方式。
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AI Models & Platforms
OpenAI Says Its Models Produced Three Proofs in Math, CS, and Physics
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OpenAI said in an announcement on October 26, 2026, that its internal models produced three research results in mathematics, computer science, and physics, including a disproof of the Exponential Time Hypothesis, a longstanding conjecture in computational complexity theory.
In the company’s view, the AI-generated manuscripts amount to raw research data that must still be converted into scientific understanding, and it is experimenting with a new release approach toward that end. OpenAI asked external experts to act as shepherds, organizing groups to understand the new results, and said the shepherds advised three different release strategies: release the mathematics AI output directly, with researchers free to organize their own explanatory work; form an external group of collaborators for the computer science result while publishing the AI output for anyone to examine and build on; and form such a group for the physics result while deferring to it on the release of materials. The company said it does not yet know which of the three approaches will prove most useful and invited feedback on what works and what can be improved.
According to the announcement, the collaborations will operate under four principles: transparency, with no nondisclosure agreements and participants free to discuss the work, share work in progress, and publish their conclusions; no academic credit, meaning OpenAI seeks none for discoveries produced by its internal models and that inviting a researcher to steward a collaboration does not imply that the researcher made the original discovery; recognition, under which each group receives credit for the understanding, writeups, and other materials it produces and helps ensure appropriate credit for the researchers, techniques, and ideas the work draws on; and independence, with participation voluntary and unpaid, members’ conclusions their own, and neither the members nor OpenAI speaking for the other. OpenAI said it will turn over materials and artifacts related to the results to the collaborations. The company acknowledged that the approaches involve tradeoffs — the choice of initial shepherds inevitably shapes who becomes involved first and creates an asymmetry of information — and said it welcomes feedback on how to broaden participation.
Local Smoothing and the Kakeya Conjecture
In 1991, Sogge proposed the local smoothing conjecture, which concerns how waves behave as they become focused and holds that the most extreme focusing can only be short-lived, so that focusing at a typical time is far weaker than at the worst-case time. The announcement described the conjectured phenomenon as fundamental, with wide-ranging implications throughout mathematical analysis; the conjecture implies the Kakeya conjecture and Stein’s restriction conjecture. Guth, Wang, and Zhang proved the conjecture for two spatial dimensions in 2019, and Wang and Zahl settled the three-dimensional Kakeya conjecture in 2025.
OpenAI said its models produced a proof of the local smoothing conjecture in every dimension, relying on an auxiliary partial differential equation of a novel kind, and in doing so also resolved the Kakeya conjecture and Stein’s restriction conjecture in all dimensions. The company obtained the AI output on October 18, 2026, formalized it in Lean the following day, and then contacted an expert to discuss forming a collaboration around the result. Following that expert’s recommendation, OpenAI published both an AI natural-language writeup produced by its models and a Lean proof in its public GitHub repository, the same strategy it used for its October 6, 2026 mathematics release.
Exponential Time Hypothesis Disproof
The computer science result concerns the Exponential Time Hypothesis, a conjecture about the complexity of determining whether a Boolean formula can be satisfied that is closely tied to the P versus NP problem. The announcement described the hypothesis as widely believed and said it has been used in hundreds of papers to derive hardness results conditional on it across fields including graph theory, computational biology, databases, and computational geometry. OpenAI said its system proved the hypothesis false and that the result was subsequently verified in Lean. The AI produced its natural-language disproof on October 16, 2026, and the result was formalized in Lean on October 17, 2026.
According to the formalization’s documentation, hosted in OpenAI’s public math repository with a latest commit dated October 26, 2026, the Lean proof establishes that for fixed k of at least 2, a deterministic machine exactly counts the satisfying assignments of a canonically encoded k-CNF formula on n variables in subexponential time and polynomial space, with sharper time bounds for instances with m clauses given in the accompanying October 25, 2026 manuscript.
The work will be verified and shepherded by a group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who with Francis Zane originally proposed the hypothesis, and Ryan Williams of MIT, who OpenAI noted has refuted strong versions of it and connected algorithms and lower bounds. OpenAI said it agreed to the group’s requests that all raw data behind the result be made public to facilitate independent verification by the community, and that OpenAI commit to funding a conference on the work’s implications for the field. The group also invited the community to help organize an open examination of the claim and to discuss the broader questions it said AI-generated breakthroughs raise about verification, access, credit, and the future of research. OpenAI said the refutation reopens questions about how much faster these tasks could become, and that turning theoretical advances into practical improvements will require significant further research.
QCD and Standard Model Existence Proof
OpenAI said the physics result supplies a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including quantum chromodynamics (QCD) and a unified completion of the Standard Model of particle physics, and that the work builds on Balaban’s approach in constructive quantum field theory. As a subproblem, it includes a proof of the existence of pure Yang–Mills theory, part of the Clay Mathematics Institute’s Quantum Yang–Mills Theory Millennium Prize problem. The existence proof applies to the simplest grand unified theory incorporating the Standard Model’s gauge fields and fermions, the announcement said, because the Standard Model itself cannot be extrapolated to arbitrarily short distances. The Standard Model describes how fundamental subatomic particles interact under three of the four fundamental forces, all but gravity; QCD describes how particles such as quarks and gluons interact via the strong force; and pure Yang–Mills theory describes the self-interactions of gluons, the force carriers, rather than matter such as quarks.
OpenAI said its models produced a natural-language proof of Yang–Mills existence on September 9, 2026, followed by a proof for QCD on September 18, 2026. Given the work’s length and complexity, the company postponed release until the Lean formalization was complete, finishing the formalization of Yang–Mills existence on October 16, 2026 — a milestone the company said led it to develop the collaboration.
David Gross will lead a group that includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. Gross’s 1973 work on asymptotic freedom in Yang–Mills theories helped establish QCD as the theory of the strong interactions and earned him a share of the 2004 Nobel Prize in Physics. Jaffe formulated the Quantum Yang–Mills Theory Millennium Prize problem with Witten and co-founded the Clay Mathematics Institute. Douglas reported on the problem’s status in 2004 and provided a comprehensive update on progress in early 2026. Klebanov was among the pioneers in applying gauge–string duality to confinement, a key property of QCD, and now directs the Simons Collaboration on Confinement and QCD Strings. Nekrasov has developed exact methods for generalizations of Yang–Mills theory and won the Dannie Heineman Prize for Mathematical Physics in 2023. The physics group decided to hold off on releasing the AI-produced artifacts and instead write the result up itself, and asked that all communications with its members about the effort be directed to YANGMILLS4D@gmail.com.
Supporting Scientists
OpenAI said the collaborations complement its previously announced $5 million contribution to the Simons Foundation, which the foundation manages and awards to support workshops, conferences, and special programs that help researchers understand and build on results produced by AI. The company said it is committed to ensuring funding for researchers to independently examine, explain, and build on the three results, and that it hopes humans working with AI can provide new understanding of computational complexity and shed light on the inherent capabilities and limits of efficient computation. OpenAI also said it continues to invite feedback on the best way to disclose results and engage with scientists.
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