3-uniform hyperclique hypothesis refuted with ChatGPT Sol 6.1
Event confirmedAwaiting review
Importance: major (4 of 5)Status
- Claim
Event confirmedAwaiting review
- Our reporting
- High confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 5 November 2026
Your AI and this story
- GPT-6 Astra189 days after its cutoff
- Claude Opus 5.5128 days after its cutoff
- Gemini 4 Argon219 days after its cutoff
- Grok 4.7158 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 128 days before it.
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)’
What happened
On 5 Nov 2026 Timothy M. Chan, Reina Itakura, Zhiyuan Ma and Yuancheng Yu posted arXiv 2611.068131. 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)!”
AI 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.”
Why it matters
The 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).
What is disputed or not yet verified
| Verification | Unrefereed preprint; authors verified correctness |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
- arXiv 2611.06813: The 3-Uniform Hyperclique Hypothesis is Falsearxiv.org, paper
Changes
- Filed from the arXiv PDF