AI-assisted results, 7 Nov: Hexagon of 6 Nov and arXiv

Your AI and this story

Key facts

• Own entries: Axiom: the Weil conjectures proved in Lean (AxiomMath/Weil), Axiom: the Stacks Project formalized in Lean (AxiomMath/Stacks), Navier–Stokes: unforced Leray–Hopf non-uniqueness, AI-written (Hexagon 2611.00143)
• Rigidity: James Cruickshank (Galway) with a co-author, Whiteley’s conjecture that every nontrivial vertex split of a generically globally rigid graph preserves generic global rigidity in R^d for all d; ‘All the proofs of the main results presented in this paper were created by ChatGPT 6.1 Sol’, all parts human-checked (Hexagon 2611.00140)
• Geometry and analysis: Yi Wang and Wenchang Yang, every closed Riemannian n-manifold embeds isometrically in R^{n(n+1)/2+28} (was surplus max{n+5, 2n}); ‘the detailed technical arguments have not yet been fully verified or understood by humans’ (2611.00153). Scott Armstrong and Vlad Vicol, anomalous regularization of passive scalars up to the Obukhov–Corrsin exponent: their 2022 outline ‘was fed to LLMs (Claude Opus 5.5 and GPT 6 Astra)’ who produced ‘a complete but very long (612 page) natural language (slop) proof’, then autoformalized and simplified (2611.00165). Dave Goel, Sheil-Small’s 1974 covering problem (Hayman–Lingham 4.24) answered yes, ‘done overwhelmingly by AI models’ (2611.00154)
• Combinatorics: Matthew Kwan and Huy Tuan Pham, the constant Steiner kernel is not optimal at large girth, found ‘Using ChatGPT 6 Pro’, primarily AI-written, all human-checked (2611.00166); Alexander Kramer disproves the Cambie–Jooken–Wagner edge-contraction conjecture on mean subtree order (2611.00151); Max Glass, R_2(n) for binary rich words is not O(n^{C√n}), disproving a conjectured bound, GPT-6 Astra, Lean end to end, no human checking (2611.00167); Teo Banica, regular complex Hadamard matrices of order 7, 8, ‘Written by Chat GPT’ (2611.00079)
• Qiyue Tang (Tsinghua) with GPT-6-Pro sessions of 2–24 hours, audited by Codex, ‘some’ human understanding: equivalence of the four-variable Hessian and planar Jacobian conjectures (2611.00156); deterministic polynomial-time factorization over finite fields using ‘a Dedekind zeta zero-free theorem’ (2611.00135; would settle a long-open derandomization question; it relies on that cited input and has no expert check); undecidability of quiver mutation equivalence (2611.00158), decidability of mutation-acyclicity (2611.00163), Schmeisser’s conjecture in large degree (2611.00162), no minimum adapted CAD in dimension ≥ 4 (2611.00131)
• Hessian conjecture HC_4: David Niedbala Giraudin with Claude, degree ≤ 5 potentials (2611.00161, 2611.00134), ‘None of this contribution has been checked and understood by any human’
• Complexity after the ETH refutations: Xiaoyu Li (UNSW) with Claude Opus 5.5 in Claude Code, exact exponent of fast attention after SETH (2611.00132) and the price of Bayes-optimal in-context learning, where ‘Claude chose the question, proved the results and wrote the text’ (2611.00133); Vaibhav Tulsyan with Claude, barriers for the OpenAI and Anthropic counting engines, 45 Lean theorems (2611.00149)
• Number theory and Lean: twinheterodox with Codex Astra-6-Max, irrational even Dirichlet beta values (at least one of β(m+1)…β(67m−1); counts for s ≥ 160) (2611.00160, 2611.00139); Steve Hubbard, Lean proofs of Dudek’s RH prime gap and Saouter’s criterion toward odd Goldbach to 10^20, ‘No human expert has reviewed the mathematics’ (2611.00157, 2611.00159); Antonio Mennillo, prime sums and Riemann zeros in Lean (2611.00130); Yi-kun Li, Gauss law for eras of Bianchi IX, Lean (2611.00150); Lean formalizations of SPR synthesis (2611.00146) and COBOL-to-Rust/Java translations (2611.00152)