{"schema":"postcutoff/event@1","as_of":"2026-10-27T13:45:00+01:00","url":"https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-claim/","md":"https://postcutoff.com/e/2026-10-26-openai-eth-false-subexponential-sat-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-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":[{"n":1,"title":"Anthropic: A 2^o(n) Time Algorithm for 3-SAT (independent refutation)","url":"https://github.com/anthropics/formal-math/tree/16a5ce41304fcdaea4e0be7c132e1c361dc26da5/eth","type":"paper","group":"primary","domain":"github.com"},{"n":2,"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":3,"title":"OpenAI (paper, PDF): The Exponential Time Hypothesis is False (17 Oct, revised 25 Oct 2026)","url":"https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf","type":"paper","group":"primary","domain":"github.com"},{"n":4,"title":"openai/math history.md (26 Oct 2026 changelog)","url":"https://github.com/openai/math/blob/main/history.md","type":"official","group":"primary","domain":"github.com"},{"n":5,"title":"Lean scope note for family 378","url":"https://github.com/openai/math/blob/main/lean/docs/378.md","type":"code","group":"primary","domain":"github.com"},{"n":6,"title":"Ryan O'Donnell: Some exposition of 'The Exponential Time Hypothesis Is False' (12 pp., LLM-assisted)","url":"https://www.cs.cmu.edu/~odonnell/some_eth_false_exposition.pdf","type":"paper","group":"primary","domain":"cs.cmu.edu"},{"n":7,"title":"Stefan Szeider (Zenodo 23688832): OpenAI's claimed refutation of ETH: exhaustive search below 2^131071","url":"https://zenodo.org/records/23688832","type":"paper","group":"primary","domain":"zenodo.org"},{"n":8,"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":9,"title":"PANews: OpenAI announces three new AI science discoveries, says it has disproved the ETH","url":"https://panews.io/articles/01a17a35-769f-778a-a1fc-704ce7e3b9e2","type":"press","group":"press","domain":"panews.io"},{"n":10,"title":"Techmeme headline (26 Oct 2026)","url":"https://www.techmeme.com/261026/p48","type":"press","group":"press","domain":"techmeme.com"},{"n":11,"title":"Greg Brockman on X announcing the three discoveries (~1.2M views)","url":"https://x.com/gdb/status/2114837059462627533","type":"discussion","group":"reactions","domain":"x.com"},{"n":12,"title":"Hacker News: The Exponential Time Hypothesis Is False [pdf]","url":"https://news.ycombinator.com/item?id=50251661","type":"discussion","group":"reactions","domain":"news.ycombinator.com"},{"n":13,"title":"Tao's blog (AGMAI guest post, 25 Oct): Disadvantages of designating mathematicians for AI output releases","url":"https://terrytao.wordpress.com/2026/10/25/disadvantages-of-designating-mathematicians-for-ai-output-releases/","type":"discussion","group":"reactions","domain":"terrytao.wordpress.com"},{"n":14,"title":"Ryan Williams on X: thread explaining the claim (27 Oct, ~37k views)","url":"https://x.com/rrwilliams/status/2114891835403633038","type":"discussion","group":"reactions","domain":"x.com"},{"n":15,"title":"Ryan Williams on X: open, independent examination of the claim (Oct 26, ~2.26M views)","url":"https://x.com/rrwilliams/status/2114833319431209352","type":"discussion","group":"reactions","domain":"x.com"},{"n":16,"title":"Ryan O'Donnell on X: results assuming ETH do not 'fall, per se'","url":"https://x.com/BooleanAnalysis/status/2114860617924243776","type":"discussion","group":"reactions","domain":"x.com"},{"n":17,"title":"Scott Aaronson, Shtetl-Optimized: Podcasts about the Topic: Part II (26 Oct, with comments on ETH)","url":"https://scottaaronson.blog/?p=10239","type":"discussion","group":"reactions","domain":"scottaaronson.blog"},{"n":18,"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":19,"title":"oai-math-revised: AGENT_NOTES for the ETH paper (collected reactions)","url":"https://github.com/mathcommunity/oai-math-revised/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/AGENT_NOTES.md","type":"discussion","group":"reactions","domain":"github.com"}],"official":7,"filed":"2026-10-26","updated":"2026-10-27","orgs":["OpenAI"],"title":"OpenAI claims the Exponential Time Hypothesis is false: a deterministic subexponential-time, polynomial-space algorithm that counts k-SAT solutions (Lean-formalized; working group of Impagliazzo, Paturi and Williams to examine it)","summary":"On 26 Oct 2026 OpenAI added \"The Exponential Time Hypothesis is False\" (67 pages, credited to \"OpenAI\", dated 17 Oct, revised 25 Oct) to its github.com/openai/math repository and announced it in a blog post with two other results (Kakeya and local smoothing; a 4D quantum field theory claim). The paper gives a deterministic algorithm that counts the satisfying assignments of any k-CNF with n variables and m clauses in time (n+m)^O_k(1)·2^(n/(log n)^(1/2+o(1))) and polynomial space. This would refute ETH, which Impagliazzo and Paturi proposed in 1999–2001. OpenAI lists a Lean formalization of a slightly weaker time bound. An independent working group led by Impagliazzo, Paturi and Ryan Williams will examine and explain the proof. It is a claim, not an accepted result.","key_facts":["Independent second claim (27 Oct): Anthropic published 'A 2^o(n) Time Algorithm for 3-SAT' by 'Claude (Anthropic)', with a Lean 4 proof (github.com/anthropics/formal-math, eth/). Its core algorithm 'was found on October 16 by an internal Claude research model with 14M output tokens and no human input'. It uses tensor-network contraction and rank bounds instead of OpenAI's linear summaries and sparse polynomial systems, and reaches the same 2^O(n log log n/√log n) shape. Press accounts of OpenAI's post say OpenAI's model also found its disproof on 16 Oct and checked it in Lean on 17 Oct. See 2026-10-27-anthropic-claude-eth-refutation-3sat-subexponential","Working group statement (as quoted by TNW): 'Our involvement should not be taken as certification of the claim' and 'If the claim is correct, it will change an important part of theoretical computer science'. The three say they signed no NDAs, are unpaid, and asked OpenAI to release all raw data; Williams and OpenAI say OpenAI agreed","Repository changelog (history.md, 'October 26, 2026', verbatim): 'The Exponential Time Hypothesis is False. The paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The case of 3-SAT refutes the Exponential Time Hypothesis. An independent working group of computer scientists led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine and explain the proof. At the group’s request, we are making the materials public immediately so others can examine them as well.'","Main theorem (paper, Theorem 1.1): for each fixed k ≥ 2, #F is computed deterministically in (n+m)^O_k(1)·2^(O_k(n·log log n/√log n)) bit operations and (n+m)^O_k(1) bits of space; for m ≤ Dn the bound improves to 2^(O_k,D(n/√log n))","Paper's own statement of consequences: 'Theorem 1.1 refutes ETH, SETH, Gap-ETH, and NSETH', and it 'also refutes the bounded-error randomized versions of ETH'. Catalogue entry (family 378) adds 'superlinear circuit lower bounds for a language in E^NP on infinitely many input lengths'","Lean scope note (lean/docs/378.md): Lean proves that a deterministic machine counts satisfying assignments of a canonically encoded k-CNF in time (L+1)^O_k(1)·2^(O_k(n(log log n)²/√log n)), visiting at most (L+1)^O_k(1) tape cells; the sharper bound of the 25 Oct manuscript is on paper only. Comparator statement: ComparatorChallenges/SubexponentialSAT.lean","Techniques named in the table of contents: 'shared linear summaries', 'low-degree replacement forms', counting common zeros of sparse polynomial equations, and a reduction of #k-SAT to that counting problem","Background: ETH (Impagliazzo–Paturi 1999/2001) says 3-SAT needs 2^Ω(n) time. It underlies a large share of fine-grained and parameterized lower bounds. Earlier self-published claims that ETH is false (e.g. a 2021 arXiv preprint on #k-SAT) were not accepted","OpenAI blog (26 Oct, RSS description): 'OpenAI shares model results on the Kakeya conjecture, Exponential Time Hypothesis, and quantum chromodynamics—and how researchers can verify and build on them.' The post itself returned HTTP 403 to our fetch; its contents here come from the repository and press relays (PANews, Techmeme headline)","Reactions (26–27 Oct): the HN threads on the PDF and on OpenAI's post reached 664 points / 250 comments and 969 / 512. Ryan Williams (working group) on X, 27 Oct, ~37k views: 'If true, their claim implies a variety of other NP problems now all have faster algorithms as well … this should make every computer scientist put at least a little more weight on the possibility of P = NP', and 'one of the first things I wanted OpenAI to check is that no existing cryptosystems are compromised by the result. Apparently they are safe...'","Reach on X (fxtwitter, Oct 27): Ryan Williams's announcement thread that he, Impagliazzo and Paturi will organise an open examination (no NDAs, no pay; OpenAI agreed to release raw data and sponsor a conference) ~2.26M views on its first post, the most-viewed post about the claims; OpenAI's Dan Roberts's announcement ~1.53M; Greg Brockman 'p still probably doesn't equal np' ~410k; Eric S. Raymond 'my odds on [P≠NP] have shortened dramatically' ~382k; OpenAI board chair Bret Taylor 'I was and am shocked the exponential time hypothesis is false' ~113k, treating the unverified claim as settled; Sébastien Bubeck 'maybe the biggest surprise I have seen during my 20 years following theoretical computer science' ~75k","Ryan O'Donnell (CMU) on X: 'No results assuming ETH fall, per se. All these results are of the form \"there is a very efficient algorithm reducing 3SAT to problem X\"' (the reductions stay valid; their lower-bound conclusions lose their premise). He posted a 12-page LLM-assisted exposition specialised to counting independent sets in 3-regular graphs, with the disclaimer 'no idea if it's correct' (~27k views)","Scott Aaronson (Shtetl-Optimized, 26 Oct) relayed the claim and in comments raised his 'personal probability of P=NP from 3% to 5%'; he says Impagliazzo and Paturi 'were a bit greedy' and retreats to a 'Weak ETH' (3SAT needs exp(n^(1−o(1))) time), which would move him to '20-30%' if it fell. Commenters note the bound does not beat the number field sieve for factoring and that the manuscript's exponent has log log n where the Lean bound has its square","Stefan Szeider (TU Wien), Zenodo note, 27 Oct, from the paper's own parameters: the main-text algorithm is 'an exhaustive search on every input with fewer than 2^(10^10) variables', and the Appendix D version, which attains the main theorem's bound, on every input with fewer than 2^131071 variables and clauses. He read the 220-line Lean statement: 'It is a correct statement of the intended result, for a weaker but still subexponential bound.' Disclosure: 'I used Claude Code to assist me in drafting this note and in writing the script'","Earlier (26 Oct) only a 3-point HN submission; a 25 Oct guest post on Terence Tao's blog by the AGMAI group argued against 'designating mathematicians for AI output releases' without naming this release. Lance Fortnow's and Bill Gasarch's Computational Complexity blog had no post on it by 27 Oct"],"key_numbers":[],"tags":["computer-science","complexity-theory","sat","exponential-time-hypothesis","openai","openai-math-release","lean","unverified","claim"],"science":{"field":"computer-science","subfield":"computational complexity (exact exponential algorithms, SAT)","problem":"Exponential Time Hypothesis (Impagliazzo–Paturi 1999/2001), Strong ETH, Gap-ETH, NSETH","result":"Claimed deterministic (n+m)^O_k(1)·2^(n/(log n)^(1/2+o(1)))-time, polynomial-space algorithm for #k-SAT, every fixed k ≥ 2, which would refute ETH and its variants","open_since":"1999","ai_system":["OpenAI internal model (openai/math release)"],"human_role":"Credited to 'OpenAI' with no named human authors; OpenAI says it is model output. Human examination is assigned to an outside working group (Impagliazzo, Paturi, Williams)","verification":{"key":"lean","label":"Lean-verified","text":"Unrefereed manuscript; Lean formalization of a weaker bound per OpenAI's scope note (not checked by us); working group to examine"},"status":"pending","shock":"ETH is among the most widely used assumptions in complexity theory; most experts expected it to be true, and refuting it would invalidate the conditional lower bounds of hundreds of papers."},"body_md":"## What happened\n\nOn Monday 26 Oct 2026 OpenAI updated its public maths repository and published a blog post about three model results and how\nresearchers can check them. The computer-science result is a 67-page paper titled bluntly \"The Exponential Time Hypothesis is\nFalse\". Its abstract: \"We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF\nformula … Our algorithm refutes the Exponential Time Hypothesis (ETH), which postulates that deciding 3-SAT on n variables\nrequires 2^Ω(n) time in the worst case.\"\n\nThe running time is subexponential but only just: 2 to the power n/(log n)^(1/2+o(1)). That is far from practical, but ETH only\nsays that no 2^o(n) algorithm exists, so any such bound refutes it. Because the algorithm counts solutions exactly and\ndeterministically, the paper says it also refutes the Strong ETH, Gap-ETH and the nondeterministic NSETH.\n\nUnlike the 6 Oct release, OpenAI did not just post the files. Its changelog says an outside working group led by Russell\nImpagliazzo and Ramamohan Paturi (who formulated ETH) and Ryan Williams (MIT) \"will examine and explain the proof\", and that the\nmaterials went public at once \"at the group's request\". OpenAI's Lean scope note says the formal proof covers a slightly weaker\ntime bound, (log log n)² instead of log log n in the exponent.\n\nThe blog post itself could not be read here (HTTP 403). Its RSS summary and the press relays name the other two results: the\nlocal smoothing conjecture in every dimension, with the Kakeya conjecture as a corollary (separate entry), and a rigorous\nexistence proof for four-dimensional quantum field theories including QCD and pure Yang–Mills, to be reviewed by a group led by\nDavid Gross. The QFT materials are withheld at the reviewers' request (separate entry, 2026-10-26-openai-yang-mills-qcd-existence-claim).\n\n## Why it matters\n\nETH is a working assumption across complexity theory. Hundreds of lower bounds in parameterized and fine-grained complexity are\nstated \"assuming ETH\". If the proof holds, those results lose their footing. Lean covers the main theorem, so the open questions\nare whether the Lean statement says what the paper claims and whether the encoding and machine model match the usual meaning of\nETH. Those are the questions the working group will answer. Until it reports, treat this as an extraordinary claim from a\ncompany, made without peer review.","disputed":[{"label":"Verification","text":"Unrefereed manuscript; Lean formalization of a weaker bound per OpenAI's scope note (not checked by us); working group to examine","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-yang-mills-qcd-existence-claim","url":"https://postcutoff.com/e/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":8,"official":1,"filed":"2026-10-27","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":"2026-10-24-oai-math-revised-community-hub","url":"https://postcutoff.com/e/2026-10-24-oai-math-revised-community-hub/","date":"2026-10-24","date_precision":"day","short_title":"oai-math-revised: mathematicians launch a community hub to revise OpenAI's AI-written math manuscripts (guest post on Tao's blog)","deck":null,"takeaway":"This is the first organized attempt by research mathematicians to digest and credit the OpenAI catalogue.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":6,"official":5,"filed":"2026-10-25","updated":"2026-10-27","orgs":["OpenAI","mathcommunity"]},{"id":"2026-10-08-dualization-eth-lower-bound-gpt-6-astra","url":"https://postcutoff.com/e/2026-10-08-dualization-eth-lower-bound-gpt-6-astra/","date":"2026-10-08","date_precision":"day","short_title":"GPT-6 Astra finds a 3SAT reduction showing monotone Dualization (minimal hypergraph transversals) has no polynomial algorithm under ETH","deck":null,"takeaway":"Whether monotone Boolean dualization, equivalently enumerating all minimal transversals of a hypergraph, can be done in output-polynomial time has been open since the 1990s. A short preprint says no, assuming the Exponential Time Hypothesis, and its authors say the proof 'was originally discovered by GPT-6 Astra'.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-10-09","updated":"2026-10-13","orgs":["Hokkaido University","Okayama University","Hosei University","OpenAI"]},{"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"]},{"id":"2026-10-06-unique-games-conjecture-openai","url":"https://postcutoff.com/e/2026-10-06-unique-games-conjecture-openai/","date":"2026-10-06","date_precision":"day","short_title":"OpenAI model claims a proof of Khot's Unique Games Conjecture, with Lean formalization","deck":null,"takeaway":"If OpenAI's claimed proof holds, it settles the Unique Games Conjecture, a central open problem in hardness of approximation since 2002. It comes with a Lean formalization, but experts have not yet checked it.","category":"science","category_label":"Science & math","importance":5,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":11,"official":5,"filed":"2026-10-07","updated":"2026-10-09","orgs":["OpenAI"]},{"id":"2026-09-29-agmai-recommendations-ai-math-results","url":"https://postcutoff.com/e/2026-09-29-agmai-recommendations-ai-math-results/","date":"2026-09-29","date_precision":"day","short_title":"Mathematicians' AGMAI publishes norms for AI labs releasing AI-generated results","deck":"Simons Institute TCS group issues 12 actions","takeaway":"These are the first detailed, community-backed norms for how AI-generated mathematics should be disclosed, verified and absorbed.","category":"research","category_label":"Research","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":5,"official":2,"filed":"2026-09-30","updated":"2026-10-26","orgs":["AGMAI","Simons Institute"]}],"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":"bret-taylor","name":"Bret Taylor","url":"https://postcutoff.com/person/bret-taylor/"},{"id":"scott-aaronson","name":"Scott Aaronson","url":"https://postcutoff.com/person/scott-aaronson/"},{"id":"sebastien-bubeck","name":"Sébastien Bubeck","url":"https://postcutoff.com/person/sebastien-bubeck/"}],"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-rrwilliams-eth-independent-examination","title":"Ryan Williams: Impagliazzo, Paturi and I will organise an open, independent examination of OpenAI's claimed ETH refutation","url":"https://postcutoff.com/p/2026-10-26-rrwilliams-eth-independent-examination/"},{"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-btaylor-shocked-eth-false","title":"OpenAI board chair Bret Taylor: 'shocked the exponential time hypothesis is false'","url":"https://postcutoff.com/p/2026-10-26-btaylor-shocked-eth-false/"},{"id":"2026-10-26-esrtweet-eth-p-np-odds","title":"Eric S. Raymond: after the ETH disproof claim, 'my odds on [P≠NP] have shortened dramatically'","url":"https://postcutoff.com/p/2026-10-26-esrtweet-eth-p-np-odds/"},{"id":"2026-10-26-gdb-p-still-not-np","title":"Greg Brockman: 'p still probably doesn't equal np'","url":"https://postcutoff.com/p/2026-10-26-gdb-p-still-not-np/"}],"videos":[],"models":[],"changes":[{"date":"2026-10-27","type":"edit","text":"X reach of the main reactions (Williams thread 2.26M, Roberts, Brockman, Raymond, Taylor, Bubeck; fxtwitter) (news agent)"},{"date":"2026-10-27","type":"edit","text":"Expert reactions (Williams, O'Donnell and his exposition, Aaronson), Szeider's Zenodo threshold note and Lean-statement check, HN reach"},{"date":"2026-10-27","type":"edit","text":"Added Anthropic's independent ETH refutation, the working group's statement, Brockman's post and the 16 Oct discovery date; linked the Yang–Mills/QCD entry"},{"date":"2026-10-26","type":"filed","text":"Created from the repository, the Lean scope note, the PDF and press relays; blog post not readable (403)"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-26","run":null,"sources_read":"The repository, the Lean scope note, the PDF and press relays; blog post not readable (403)","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-eth-false"}