{"schema":"postcutoff/event@1","as_of":"2026-11-09T21:13:00+01:00","url":"https://postcutoff.com/e/2026-11-05-3-uniform-hyperclique-hypothesis-false-chatgpt-sol/","md":"https://postcutoff.com/e/2026-11-05-3-uniform-hyperclique-hypothesis-false-chatgpt-sol/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":"2026-11-05-3-uniform-hyperclique-hypothesis-false-chatgpt-sol","date":"2026-11-05","date_precision":"day","short_title":"3-uniform hyperclique hypothesis refuted with ChatGPT Sol 6.1","deck":null,"takeaway":null,"category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"pending","labels":["Event confirmed","Awaiting review"]},"sources":[{"n":1,"title":"arXiv 2611.06813: The 3-Uniform Hyperclique Hypothesis is False","url":"https://arxiv.org/abs/2611.06813","type":"paper","group":"primary","domain":"arxiv.org"}],"official":1,"filed":"2026-11-05","updated":"2026-11-05","orgs":["OpenAI","University of Illinois Urbana-Champaign"],"title":"Chan, Itakura, Ma and Yu refute the 3-Uniform Hyperclique Hypothesis; both proofs obtained with ChatGPT Sol 6.1","summary":"An arXiv preprint by Timothy M. Chan and three co-authors gives an O(n^3.957)-time algorithm for finding 4-hypercliques in 3-uniform hypergraphs, refuting the Lincoln–Vassilevska Williams–Williams (2018) hypothesis that underlies many conditional lower bounds, and giving a faster exponential-time algorithm for Max-3-SAT. The authors say both of their proofs were obtained using ChatGPT Sol 6.1 and then rewritten by them. Unrefereed preprint.","key_facts":["arXiv 2611.06813, announced 5 Nov 2026; authors Timothy M. Chan, Reina Itakura, Zhiyuan Ma, Yuancheng Yu","Main theorem: 3-uniform 4-hyperclique in O(n^3.957) deterministic time (Theorem 2.8), via reduction to rectangular matrix multiplication; implies O(n^(k−ε⌊k/4⌋)) for k-hyperclique, k ≥ 4","Implies an O(2^((1−ε/4+o(1))n)) algorithm for Max-3-SAT, improving Alman–Chan–Williams (2016), and disproves what some called the Max-3-SAT Hypothesis","Hypothesis 1.1 was introduced by Lincoln, Vassilevska Williams and Williams (SODA 2018) and used for lower bounds on induced 4-cycle detection, Klee's measure problem, hypercycles and database problems","AI disclosure: 'Both proofs in this paper are obtained using ChatGPT Sol 6.1, prompted by different suggestions. This manuscript is human-written: we (the authors) rewrote the proofs … (the initial solutions were not easy to understand)'"],"key_numbers":[],"tags":["math","computer-science","fine-grained-complexity","chatgpt","gpt-6-1-sol","arxiv"],"science":{"field":"computer-science","subfield":"fine-grained complexity","problem":"3-Uniform Hyperclique Hypothesis (Lincoln–Vassilevska Williams–Williams 2018)","result":"Truly subquartic (O(n^3.957)) algorithm for detecting or counting 4-hypercliques in 3-uniform hypergraphs; the hypothesis is false","open_since":"2018","ai_system":["ChatGPT Sol 6.1"],"human_role":"AI-assisted: authors prompted the model with different suggestions; both proofs came from the model, the authors verified and rewrote them","verification":{"key":"preprint","label":"Preprint only","text":"Unrefereed preprint; authors verified correctness"},"status":"pending","shock":"A widely used hardness assumption in fine-grained complexity falls to a short reduction to standard rectangular matrix multiplication."},"body_md":"## What happened\n\nOn 5 Nov 2026 Timothy M. Chan, Reina Itakura, Zhiyuan Ma and Yuancheng Yu posted [arXiv 2611.06813](https://arxiv.org/abs/2611.06813). They give two different, short algorithms that solve 4-hyperclique in 3-uniform hypergraphs in truly subquartic time. The first, with exponent 3.957, reduces the problem to counting colour-alternating 4-cycles and uses anti-commuting matrix families. The second is shorter and works directly with formulas. Neither needs a new algorithm for the generalized 3-wise matrix product. The paper says: \"We have actually found two different proofs of the result (both using AI)!\"\n\nAI disclosure (verbatim): \"Both proofs in this paper are obtained using ChatGPT Sol 6.1, prompted by different suggestions. This manuscript is human-written … The authors verified the correctness and originality of all content, including references.\"\n\n## Why it matters\n\nThe h-uniform hyperclique hypothesis was a standard assumption for conditional lower bounds. The paper lists applications to induced 4-cycles, Klee's measure problem, LCAs in DAGs, CSPs and geometric problems, and most of them use the h = 3 case. Those lower bounds now need other assumptions. No public reactions had been found as of 5 Nov (HN search: none).","disputed":[{"label":"Verification","text":"Unrefereed preprint; authors verified correctness","sources":[]}],"related":[{"id":"2026-11-04-huffman-unequal-letter-costs-np-complete-codex","url":"https://postcutoff.com/e/2026-11-04-huffman-unequal-letter-costs-np-complete-codex/","date":"2026-11-04","date_precision":"day","short_title":"Huffman coding with unequal letter costs is NP-complete (Codex)","deck":null,"takeaway":"A classical problem in information theory, listed as open in surveys of prefix coding for decades, appears settled with the key reduction attributed to a coding agent.","category":"science","category_label":"Science & math","importance":4,"confidence":"medium","status":{"key":"pending","labels":["Awaiting review"]},"sources":1,"official":1,"filed":"2026-11-04","updated":"2026-11-04","orgs":["OpenAI","Indian Institute of Science"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-11-05","type":"filed","text":"Created from the arXiv PDF"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-11-05","run":null,"sources_read":"The arXiv PDF","updated":"2026-11-05","human_review":null,"version":{"date":"2026-11-05"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":189,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":128,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":219,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":158,"in_training_data":false}],"short_url":"https://postcutoff.com/s/3-uniform-hyperclique-hypothesis"}