{"schema":"postcutoff/event@1","as_of":"2026-10-27T13:45:00+01:00","url":"https://postcutoff.com/e/2026-10-26-openai-yang-mills-qcd-existence-claim/","md":"https://postcutoff.com/e/2026-10-26-openai-yang-mills-qcd-existence-claim/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-10-26-openai-yang-mills-qcd-existence-claim","date":"2026-10-26","date_precision":"day","short_title":"OpenAI claims 4D Yang–Mills and QCD existence","deck":null,"takeaway":"The physics third of OpenAI's 26 Oct announcement claims that certain interacting 4D quantum field theories exist mathematically, among them pure Yang–Mills and quantum chromodynamics. That is the existence half of the Yang–Mills Millennium problem, not the mass gap. A group led by David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, is reviewing it. At the group's request the AI-produced material is not public while they write their own account. Nothing can be checked yet.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":[{"n":1,"title":"OpenAI: Working with academic communities to build scientific understanding (26 Oct 2026)","url":"https://openai.com/index/building-scientific-understanding-with-academic-communities/","type":"official","group":"primary","domain":"openai.com"},{"n":2,"title":"TNW: OpenAI says its AI model has disproved the Exponential Time Hypothesis","url":"https://thenextweb.com/news/openai-exponential-time-hypothesis-false-kakeya-yang-mills","type":"press","group":"press","domain":"thenextweb.com"},{"n":3,"title":"Superpower Daily: OpenAI claims three scientific breakthroughs and gives experts different review roles","url":"https://superpowerdaily.com/posts/openai-claims-three-scientific-breakthroughs-and-gives-experts-different-review-roles","type":"press","group":"press","domain":"superpowerdaily.com"},{"n":4,"title":"Engadget: OpenAI announces new discoveries in mathematics, computer science and physics","url":"https://www.engadget.com/2297941/openai-new-discoveries-mathematics-computer-science-physics/","type":"press","group":"press","domain":"engadget.com"},{"n":5,"title":"Greg Brockman on X: 'Announcing three major scientific discoveries…' (~1.2M views)","url":"https://x.com/gdb/status/2114837059462627533","type":"discussion","group":"reactions","domain":"x.com"},{"n":6,"title":"AISafetyMemes on X: explainer of the three claims (~185k views)","url":"https://x.com/AISafetyMemes/status/2114865886477926790","type":"discussion","group":"reactions","domain":"x.com"},{"n":7,"title":"Hacker News: Three new discoveries in mathematics, computer science, and physics (969 points)","url":"https://news.ycombinator.com/item?id=50251344","type":"discussion","group":"reactions","domain":"news.ycombinator.com"},{"n":8,"title":"Andrew Curran on X: summary of the three discoveries (~715k views)","url":"https://x.com/AndrewCurran_/status/2114836071028785289","type":"discussion","group":"reactions","domain":"x.com"}],"official":1,"filed":"2026-10-27","updated":"2026-10-27","orgs":["OpenAI"],"title":"OpenAI claims a rigorous existence proof for four-dimensional quantum field theories including pure Yang–Mills and QCD; a panel led by David Gross is reviewing it and the AI output is withheld (not the Clay mass gap)","summary":"OpenAI's blog post of 26 Oct 2026 ('Working with academic communities to build scientific understanding'; announced by Greg Brockman to ~1.2M views) lists a physics result alongside ETH and Kakeya. According to press accounts, its models produced \"the mathematical existence of certain interacting quantum field theories in four dimensions\", including QCD and pure Yang–Mills. OpenAI says the Yang–Mills part is \"not a solution to the full problem\", since the Clay problem also requires a mass gap. The reviewing group (Gross, Douglas, Jaffe, Klebanov, Nekrasov) chose to withhold the AI artifacts and prepare its own write-up. The claim has no public paper, Lean code or expert verdict.","key_facts":["Claim (as reported by TNW and Superpower Daily from the OpenAI post): a rigorous proof that certain interacting quantum field theories exist in four dimensions, including quantum chromodynamics, and a proof that pure Yang–Mills theory exists. That is the existence part of the Clay Millennium problem, 'not a solution to the full problem'. Andrew Curran's summary (~715k views) lists it as 'Existence of quantum chromodynamics and completions of the Standard Model'","Reviewers: a group led by David Gross (2004 Nobel Prize in physics) with Michael Douglas, Arthur Jaffe (co-author of the Clay problem statement), Igor Klebanov and Nikita Nekrasov","Artifacts: the physics group 'chose to withhold the AI-produced artifacts' while it prepares its own write-up. Unlike the ETH and local-smoothing results, nothing is in github.com/openai/math, and the press reports no Lean formalization","OpenAI on its review arrangements (quoted by Superpower Daily): 'choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information.' A 25 Oct AGMAI guest post on Tao's blog had argued against designating mathematicians for AI releases","Mass gap: AISafetyMemes's widely shared explainer (~185k views) says the result 'proves pure Yang–Mills exists, which is part of' the Millennium problem, but 'the full Clay problem also requires the “mass gap,” so it’s not a clean “AI wins $1M” headline'","Context: Anthropic's Levent Alpöge and Ethan Sussman have run a public repository since 6 Oct in which Claude tries to finish Bałaban's program; on 16 Oct they reported an unreadable 4D SU(2) Yang–Mills existence 'slop'. OpenAI's 6 Oct release already held 4D operational-QFT papers (scale and conformal symmetry, 26 Sept) and sigma-model papers that NYU's Roland Bauerschmidt said were too hard to verify","OpenAI blog itself not readable here (HTTP 403); facts are from press relays and X posts","Engadget (Mariella Moon, 27 Oct) describes the physics result as a proof of 'interacting quantum field theories containing gauge fields and fermions in four dimensions', says the expert group 'has yet to publish anything about it', and gives YANGMILLS4D@gmail.com as the contact for questions","Date (unverified): a Hacker News commenter quotes the OpenAI post as saying 'Our models produced a natural language proof for Yang–Mills existence on September 9th, 2026'; we could not read the post to confirm","No public comment from Gross, Douglas, Jaffe, Klebanov or Nekrasov found by 27 Oct"],"key_numbers":[],"tags":["physics","mathematical-physics","quantum-field-theory","yang-mills","qcd","millennium-prize","openai","unverified","claim"],"science":{"field":"physics","subfield":"mathematical physics / constructive quantum field theory","problem":"Existence of four-dimensional interacting quantum field theories (pure Yang–Mills, QCD); existence half of the Yang–Mills Millennium problem","result":"Claimed rigorous existence proof; details, method and paper not public","open_since":"1954","ai_system":["OpenAI internal model"],"human_role":"Unknown; a physics panel led by David Gross reviews it and will write its own account","verification":{"key":"lean","label":"Lean-verified","text":"Unverified claim; AI artifacts withheld; no paper or Lean code public"},"status":"pending","shock":""},"body_md":"## What happened\n\nOpenAI's 26 Oct post presented three model results with three different review arrangements. The Kakeya and local-smoothing\nproof was released as raw output with Lean. The ETH refutation was handed to an open working group. The physics claim went to a\nnamed panel of five senior physicists, who asked OpenAI to keep the AI-produced material private while they write it up\nthemselves. So, unlike the other two claims, this one cannot be read or checked by anyone outside the panel.\n\nThe claim is that interacting four-dimensional quantum field theories, including pure Yang–Mills and QCD, exist as rigorous\nmathematical objects. Constructing such a theory in four dimensions has been an open problem in mathematical physics for\ndecades. It is half of the Clay Millennium problem. The other half, the mass gap, is not claimed.\n\n## Why it matters\n\nIf confirmed, it would be the first rigorous construction of a four-dimensional interacting gauge theory, the framework behind\nthe strong force. The review panel's stature (Gross, Jaffe) means its verdict will carry weight. Until it reports, there is\nnothing public to evaluate. Anthropic-side work on the same problem (Alpöge–Sussman) has been public but unreadable since 16 Oct.","disputed":[{"label":"Verification","text":"Unverified claim; AI artifacts withheld; no paper or Lean code public","sources":[]}],"related":[{"id":"2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential","url":"https://postcutoff.com/e/2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential/","date":"2026-10-27","date_precision":"day","short_title":"Anthropic's Claude also refutes ETH","deck":null,"takeaway":"Hours after OpenAI's ETH announcement, Anthropic posted 'A 2^o(n) Time Algorithm for 3-SAT', credited to Claude. It is a deterministic #k-SAT algorithm built on tensor-network contraction, with a different approach from OpenAI's paper, a near-identical bound and a Lean 4 proof that uses only the standard axioms. The paper says the core algorithm was found on 16 Oct with 14M output tokens and no human input. OpenAI reports its model found its disproof that same day. Neither proof has had expert review.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":5,"official":4,"filed":"2026-10-27","updated":"2026-10-27","orgs":["Anthropic"]},{"id":"2026-10-26-openai-eth-false-subexponential-sat-claim","url":"https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-claim/","date":"2026-10-26","date_precision":"day","short_title":"OpenAI claims ETH is false","deck":null,"takeaway":"Anthropic independently posted a different Lean-checked refutation the next day (separate entry). OpenAI's model output claims a deterministic algorithm that counts the satisfying assignments of any k-CNF in time 2^(n/(log n)^(1/2+o(1))). If correct, it refutes ETH, SETH, Gap-ETH and NSETH, the assumptions behind hundreds of fine-grained hardness results. OpenAI says the main theorem is formalized in Lean. A working group led by ETH's proposers, Russell Impagliazzo and Ramamohan Paturi, with Ryan Williams, will examine the proof. No expert has assessed it in public yet.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":19,"official":7,"filed":"2026-10-26","updated":"2026-10-27","orgs":["OpenAI"]},{"id":"2026-10-26-openai-local-smoothing-kakeya-all-dimensions-claim","url":"https://postcutoff.com/e/2026-10-26-openai-local-smoothing-kakeya-all-dimensions-claim/","date":"2026-10-26","date_precision":"day","short_title":"OpenAI claims local smoothing and Kakeya in all dimensions","deck":null,"takeaway":"A 59-page OpenAI manuscript dated 25 Oct claims Sogge's local smoothing conjecture for the wave equation in every dimension n ≥ 2. The stated corollaries include the Bochner–Riesz conjecture, Fourier restriction throughout the interior of the conjectured range, the Kakeya and Nikodym maximal conjectures, and full Hausdorff dimension for every Euclidean Kakeya set. That last one is the Kakeya set conjecture, proved in ℝ³ only in 2025 (Wang–Zahl). OpenAI lists Lean comparator statements for the main estimate and the corollaries. No expert has assessed it yet.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":8,"official":5,"filed":"2026-10-26","updated":"2026-10-27","orgs":["OpenAI"]},{"id":"2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman","url":"https://postcutoff.com/e/2026-10-16-yang-mills-claude-balaban-program-alpoge-sussman/","date":"2026-10-16","date_precision":"day","short_title":"Alpöge and Sussman say Claude has an (unreadable) existence argument for 4D Yang–Mills on ℝ⁴, by finishing Bałaban's 1980s program","deck":null,"takeaway":"A public repo of raw Claude output claims a construction of four-dimensional SU(2) Yang–Mills theory, the existence half of the Millennium problem but not the mass gap; its authors call it 'slop in progress' that nobody can yet read or check.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":6,"official":4,"filed":"2026-10-18","updated":"2026-10-18","orgs":["Anthropic","Northwestern University"]},{"id":"2026-10-06-openai-math-release-722-manuscripts","url":"https://postcutoff.com/e/2026-10-06-openai-math-release-722-manuscripts/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI releases 722 AI-written math manuscripts claiming hundreds of open problems","deck":"Including quasi-Riemann, Unique Games, Hodge for CM abelian varieties and free group factors","takeaway":"If even a fraction of these results hold up, this is the largest single jump in mathematical knowledge on record, produced by an AI system in about six weeks.","category":"science","category_label":"Science & math","importance":5,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":77,"official":13,"filed":"2026-10-07","updated":"2026-10-25","orgs":["OpenAI"]}],"people":[{"id":"greg-brockman","name":"Greg Brockman","url":"https://postcutoff.com/person/greg-brockman/"},{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"},{"id":"levent-alpoge","name":"Levent Alpöge","url":"https://postcutoff.com/person/levent-alpoge/"}],"posts":[{"id":"2026-10-26-gdb-three-scientific-discoveries","title":"Greg Brockman announces OpenAI's three discoveries (Kakeya/local smoothing, ETH false, 4D QFT)","url":"https://postcutoff.com/p/2026-10-26-gdb-three-scientific-discoveries/"},{"id":"2026-10-26-danintheory-three-discoveries","title":"Dan Roberts (OpenAI) announces the three discoveries in maths, CS and physics","url":"https://postcutoff.com/p/2026-10-26-danintheory-three-discoveries/"},{"id":"2026-10-26-aisafetymemes-biggest-day-math-tcs","title":"AISafetyMemes explains OpenAI's three claims, quoting Claude Opus 5.5 ('biggest single day in the history of math and theoretical computer science')","url":"https://postcutoff.com/p/2026-10-26-aisafetymemes-biggest-day-math-tcs/"},{"id":"2026-10-26-andrewcurran-openai-three-discoveries","title":"Andrew Curran summarises OpenAI's three discoveries, incl. 'completions of the Standard Model'","url":"https://postcutoff.com/p/2026-10-26-andrewcurran-openai-three-discoveries/"}],"videos":[],"models":[],"changes":[{"date":"2026-10-27","type":"edit","text":"Engadget details, contact address, HN-quoted 9 Sept date (unverified); no reviewer comment yet"},{"date":"2026-10-27","type":"filed","text":"Created from press relays and X posts (blog post 403; no artifacts public); promoted from the 26 Oct lead"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-27","run":null,"sources_read":"Press relays and X posts (blog post 403; no artifacts public); promoted from the 26 Oct lead","updated":"2026-10-27","human_review":null,"version":null},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":179,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":118,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":209,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":148,"in_training_data":false}],"short_url":"https://postcutoff.com/s/openai-4d-yang-mills"}