{"rewrite":{"id":"r_dffd518a1946b03026f3f9e9","clusterId":"c_17a97145e6c9fbc4c4dd0c39","slug":"openai-reports-results-in-harmonic-analysis-complexity-theory-and-quantum-field-theory","model":"deepseek-v4-1-flash","headline":"OpenAI Reports Results In Harmonic Analysis, Complexity Theory, And Quantum Field Theory","summary":"OpenAI announced on October 26, 2026 that its models produced results in harmonic analysis, computational complexity theory, and quantum field theory. The mathematics result concerns the local smoothing conjecture tied to the Kakeya set problem. The computer science group published a natural-language proof and a Lean formalization in OpenAI's GitHub repository, while the physics group will write its own paper.","whyItMatters":"OpenAI is treating the outputs as raw research data and handing verification to unpaid outside groups, which puts the burden of proof on independent researchers rather than on the lab that generated the results.","webCardHtml":"\u003cp\u003eOpenAI says it does not yet know which of its three publication routes works best, and it plans to ask the public for feedback on what to keep and what to change. The mathematics output is being released so researchers can work through it freely. The computer science group published a natural-language proof and a Lean formalization directly in OpenAI\u0026#39;s GitHub repository. The physics group declined to publish the AI-generated deliverables and will compile a paper of its own instead.\u003c/p\u003e\u003cp\u003eParticipants in the outside groups are unpaid and join voluntarily. OpenAI says it will not claim academic credit for discoveries made by its in-house models, and that coordinating a group does not make its members the originators of the result.\u003c/p\u003e","blueskyPost":"OpenAI announced results in harmonic analysis, complexity theory and quantum field theory on Oct 26. The CS group published a natural-language proof and Lean formalization on GitHub; the physics group will write its own paper instead of releasing the AI output.","twitterPost":"OpenAI announced results in harmonic analysis, complexity theory and quantum field theory. The CS group published a proof and Lean formalization on GitHub. The physics group skipped the AI deliverables and will write its own paper.","threadsPost":null,"newsletterBlurb":"OpenAI announced on October 26, 2026 that its models produced results in harmonic analysis, computational complexity theory, and quantum field theory. The computer science group published a natural-language proof and a Lean formalization in OpenAI's GitHub repository, while the physics group chose to write its own paper rather than release the AI-generated materials. OpenAI says it does not yet know which publication method works best and will solicit public feedback.","attributionJson":"[{\"source\":\"GIGAZINE\",\"url\":\"https://gigazine.net/news/20261027-openai-three-new-discoveries/\",\"title\":\"OpenAI Announces Three New Discoveries in Harmonic Analysis, Computational Complexity Theory, and Quantum Field Theory in Mathematics, Computer Science, and Physics; Exponential Time Hypothesis Is False\"}]","lintFlagsJson":null,"lintHits":0,"costUsd":0,"inputTokens":5126,"outputTokens":700,"status":"published","repairAttempts":0,"nextRepairAt":null,"factsAttemptedAt":1793089842,"createdAt":"2026-10-27T08:25:06.000Z","publishedAt":"2026-10-27T08:29:27.000Z","updatedAt":"2026-10-27T08:29:27.000Z"},"cluster":{"id":"c_17a97145e6c9fbc4c4dd0c39","canonicalTitle":"OpenAIが数学・コンピュータサイエンス・物理学における調和解析・計算複雑性理論・量子場理論に関する3つの新たな発見を発表、指数時間仮説は誤りである","representativeArticleId":"a_844795dda8e2391ba94cee0c","sourceCount":1,"writtenSourceCount":1,"writeAttempts":0,"isSolo":true,"entitiesJson":"{\"anime_titles\":[],\"manga_titles\":[],\"work_titles\":[],\"studios\":[],\"people\":[],\"type\":\"news\",\"domain\":\"other\",\"is_roundup\":false}","contentType":"news","status":"published","firstSeenAt":"2026-10-27T07:42:00.000Z","lastSeenAt":"2026-10-27T07:42:00.000Z","updatedAt":"2026-10-27T08:29:27.000Z"},"attribution":[{"source":"GIGAZINE","url":"https://gigazine.net/news/20261027-openai-three-new-discoveries/","title":"OpenAIが数学・コンピュータサイエンス・物理学における調和解析・計算複雑性理論・量子場理論に関する3つの新たな発見を発表、指数時間仮説は誤りである"}],"entities":{"anime_titles":[],"manga_titles":[],"work_titles":[],"studios":[],"people":[],"type":"news","domain":"other","is_roundup":false},"keyFacts":["OpenAI announced the results on October 26, 2026.","The mathematics result concerns the local smoothing conjecture proposed by Christopher Sogge in 1991.","The computer science group published a natural-language proof and a Lean formalization in OpenAI's GitHub repository.","The physics group decided not to publish the AI-generated deliverables and will compile a paper itself.","OpenAI says it will not seek academic credit for discoveries produced by its in-house models."],"pageLinks":{"healthSlugs":[],"storySlugs":[],"entities":[],"stories":[],"entitiesOk":true,"storiesOk":true}}