距离上次一口气公开数百篇论文还不到一个月，OpenAI在10月26日又公布了数学、计算机科学与物理学领域的三项“重大”成果，并首次尝试让外部专家以“牧羊人”（shepherd）的身份主导成果的理解与发布流程。
与此前做法最大的不同在于发布策略的分化：针对计算机科学与物理学的成果，OpenAI邀请外部专家牵头组织团队来解读结果；而针对数学问题，专家则建议直接把AI输出公之于众，让研究者自行组织解释工作。OpenAI在官方博客中把三篇手稿定位为一种“原始研究数据”，并坦言“目前还不知道这三种方式哪一种最有用”。
三项成果中，数学结果针对调和分析。Sogge在1991年提出“局部光滑猜想”，讨论波在聚焦时的行为——最极端的聚焦必然是短暂的，随机时刻的聚焦强度远低于最坏情况。由于这一猜想极为基础，它同时蕴含Kakeya猜想与Stein限制猜想。2019年Guth、Wang与Zhang证明了二维情形，2025年Wang与Zahl证明了三维修Kakeya猜想；而OpenAI的模型给出了任意维度的局部光滑猜想证明，从而在所有维度上解决了Kakeya猜想与Stein限制猜想。新证明基于一个全新的辅助偏微分方程，模型输出获得于2026年10月18日，次日完成Lean形式化。
计算机科学方面，成果指向“指数时间假设”（ETH）被证伪。ETH是关于布尔公式可满足性计算复杂度的长期猜想，与P vs. NP问题密切相关，过去被大量论文用来推导图论、计算生物学、数据库、计算几何等领域的条件性困难结果。OpenAI称其系统证明ETH不成立，并在Lean中完成验证：论文给出了一个确定性算法，可在次指数时间内精确统计固定宽度CNF公式的可满足赋值数目，且只占用多项式空间，其中3-SAT情形即构成对ETH的反驳。这项工作由Russell Impagliazzo、Ramamohan Paturi与Ryan Williams领衔的独立工作组负责检验与解释，Impagliazzo和Paturi正是ETH最初的提出者（与Francis Zane合作）。应工作组要求，相关材料立即公开；OpenAI还承诺出资支持一场会议，讨论该成果对整个领域的意义。自然语言层面的反证于10月16日产生，10月17日完成形式化。
物理成果则给出了四维中包含规范场与费米子的某些相互作用量子场论的严格存在性证明，涵盖量子色动力学（QCD）以及标准模型的一个统一完备化版本。该工作建立在Balaban在构造性量子场论中的方法之上，作为子问题还包含纯Yang–Mills理论的存在性证明——后者属于克莱数学研究所“量子Yang–Mills理论”千禧年大奖难题的一部分。标准模型无法外推到任意短距离，而该存在性证明针对的是包含标准模型规范场与费米子的最简单大统一理论。这项工作由2004年诺贝尔物理学奖得主戴维·格罗斯领衔，成员包括迈克尔·道格拉斯、阿瑟·贾菲、伊戈尔·克莱巴诺夫与尼基塔·涅克拉索夫；贾菲曾与威滕共同提出Yang–Mills千禧年问题并参与创办克莱数学研究所，道格拉斯已跟踪该问题二十年。工作组要求所有相关联络统一发送至[email protected]。模型的自然语言证明于9月9日给出Yang–Mills存在性、9月18日给出QCD，因篇幅与复杂度极高，发布推迟至10月16日Lean形式化完成后才启动；该组决定暂不公开AI生成的产物，而是自行撰写论文。
OpenAI为这些外部合作设定了四条原则：透明，不要求参与者签署保密协议，可自由讨论、分享中间产物并发表结论；不索取学术荣誉，内部模型产生的发现不寻求学术功劳，邀请研究者参与也不意味着他们做出了原始发现；承认贡献，工作组因所建立的理解、撰写的文稿及其他材料获得认可，并负责恰当引用所借鉴的研究者、技术与思想；独立，参与自愿且无报酬，成员不代表OpenAI发言，OpenAI也不代表他们。
不过这一模式本身也有争议。OpenAI承认，选择最初的“牧羊人”必然会决定谁先参与、并造成信息不对称，因此欢迎外界就如何扩大参与面提出意见。更直接的批评来自OpenAI自己组建的AGMAI数学顾问小组：就在前一天（10月25日），该小组明确表示“建议AI公司不要采用”指定特定人群优先获取输出的做法，理由是准入不平等、借用他人声誉以及遴选存在偏见。
在支持科研方面，OpenAI提到此前宣布向西蒙斯基金会投入的500万美元，该笔资金由基金会管理与发放，用于支持研讨会、会议和专项计划，帮助研究者理解并基于AI产生的结果继续工作。
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Less than a month after the last few hundred papers were made public, Open AI released three more “significant” results in the fields of mathematics, computer science and physics on October 26, and for the first time attempted to get outside experts to lead the understanding of the results as “herders” and the publish process.
The greatest difference from previous practice is the fragmentation of the publish strategy: Open AI invites outside experts to lead teams to interpret the results for the results of computer science and physics; and for mathematical issues, experts suggest that AI be made public directly and that researchers organize their own interpretation. Open AI has identified three manuscripts in the official blog as “original research data” and has stated that “it is not known which of these three methods is most useful”.
Of the three outcomes, the mathematical results were targeted at reconciliation and analysis. Sogge put forward a "local smooth guess" in 1991, discussing the behaviour of the wave at focus... – The most extreme focus is necessarily short-lived, and at random moments it is much less intense than the worst. As this assumption is extremely grounded, it also carries with it the assumption of Kakeya and Stein ' s restrictions. In 2019, Guth, Wang and Zhang proved a two-dimensional situation, while in 2025 Wang and Zahl proved a three-maintenance Kakeya guess; and Open AI ' s model provided partial smooth proof of an arbitrary dimension, thus addressing the Kakeya guess and Stein ' s limit in all dimensions. The new certificate was based on a completely new AMS equation, and the model output was obtained on 18 October 2026, with Lean formalizing the following day.
With regard to computer science, results point to the perjury of the index time scenario (ETH). ETH is a long-term conjecture of the solvency of the Boolean formula and is closely related to the Pvs. NP issue, which was used in the past to extrapolate difficult conditions in the fields of graphics, computational biology, databases and geometry. Open AI stated that its system proved that ETH was not valid and was validated in Lean: the paper gave a definitive algorithm that accurately measured the number of deliverables of the fixed width CRF formula over the time frame of the sub-indicator and only used multiple space, of which 3-SAT scenarios constituted a rebuttal of ETH. The work was tested and explained by an independent working group headed by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, the original authors of ETH (in cooperation with Francis Zane). At the request of the Working Group, the material was immediately made public; Open AI also pledged to finance a meeting to discuss the implications of the outcome for the whole area. Counter-arguments at the natural language level were produced on 16 October and formalized on 17 October.
The physical results give a strict proof of the existence of a four-dimensional quantitative field theory containing certain interactions between the normative field and the Phemium, covering quantum colour dynamics (QCD) and a unified and complete version of the standard model. This work is based on the approach of Balaban in the tectonic quantum field theory, and as a sub-problem includes proof of the existence of the pure Yang-Mills theory - The latter is part of the millennium award challenge of the Clay Mathematics Institute's Quantum Yang-Mills Theory. The standard model cannot be extrapolated to any short distance, and the existential proof is directed to the simplest general theory that contains the standard model field and the Phemium. This work was led by the 2004 Nobel Prize laureate for Physics, David Gross, and was composed of Michael Douglas, Arthur Jaffi, Igor Klebanov and Nikita Nekrasov, who, together with Witten, raised the Yang-Mils millennium and participated in the creation of the Clay Mathematics Institute, which Douglas has been following for 20 years. The Working Group requested that all relevant contacts be sent uniformly to [email provided]. The natural language proof of the model was given on September 9, the existence of Yang-Mills, on September 18, the QCD, which was delayed until October 16, when Lean was formalized; the group decided not to disclose the products produced by AI but to write its own papers.
Open AI sets out four principles for such external cooperation: transparency, without requiring participants to sign confidentiality agreements, freedom to discuss, share intermediate products and issue conclusions; no academic honour, no academic merit in findings from internal models, and the involvement of researchers does not mean that they have made original discoveries; recognition of contributions, the recognition of the working group by the understandings it has developed, the writing of texts and other materials, and the proper reference to researchers, technologies and ideas it has drawn upon; independence, voluntary and unpaid participation, and the non-representation of Open AI by its members.
However, the model itself is controversial. Open AI acknowledges that the selection of the original “herder” will inevitably determine who will participate first and create information asymmetries, and would therefore welcome outside views on how to broaden participation. More directly, criticism comes from the AGMAI Mathematics Advisory Group, formed by Open AI itself: just the day before (25 October), the group made it clear that it “recommends not to adopt” the practice of assigning priority access to specific groups of people, on the grounds of unequal access, borrowing the reputation of others and bias in selection.
In support of scientific research, Open AI refers to the $5 million previously announced to the Simons Foundation, which is managed and disbursed by the Foundation to support seminars, conferences and special programmes to help researchers understand and continue their work based on the results of AI.
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