AI-assisted results, 10 Nov: arXiv and Hexagon

Your AI and this story

Key facts

• Own entries: X_ns+(121): two AI-generated proofs in two days (2611.00231, 2611.00255, 2611.00234), Benjamini–Schramm p_c < p_u: OpenAI bond proof in Lean, Claude site form (2611.00251); Smale constant deposits 2611.00258 and 2611.00187 added to GPT-6 Astra autonomously disproves Smale’s mean value conjecture in Lean; Euler Part II (arXiv 2611.10211) to 2D Euler non-uniqueness without force claimed three times, all with AI; Dixmier Lean commit to Claude Fable 5 finds a counterexample to the Jacobian conjecture in dimension 3
• Pavel Etingof (MIT), Hexagon 2611.00226: a one-parameter family of 1024-dimensional complex Hopf algebras with fixed coalgebra and varying algebra structure, answering ‘negatively the finiteness question of Etingof and Gelaki’; ‘This text has been produced by ChatGPT at a request by Pavel Etingof. It was repeatedly checked by AI agents’; human understanding ‘some’
• Manor Mendel, Hexagon 2611.00209: metric cotype q inequality with scaling m = O(n^(1/2+1/q)) for Banach spaces of Rademacher cotype q; ‘The proofs in this paper were obtained by GPT~6 Astra … verifying the correctness of the proofs’ by the author; human understanding ‘all’
• James Milne, Hexagon 2611.00244 (human-written): ‘a report on two preprints of OpenAI, “Milne’s rationality conjecture for abelian varieties” and “The rational Hodge conjecture for CM abelian varieties”, placing them in context’
• Nicholas Nash, 2611.00196: deterministic adversary forcing (1−o(1)) n log₂ n comparisons on any sorting algorithm (previous 37/64); ‘Except for the abstract, the text is AI-generated using GPT 6 Astra’
• Yue Ma, 2611.00248: R(12,12) ≥ 1661 by extending the Mathon–Shearer colouring; Claude Opus 5.5 in Claude Code ‘designed and ran the searches’ (SAT with CaDiCaL), Lean 4 listed
• Claude-agent deposits with little or no human checking: holographic entropy inequalities lacking unscaled contraction proofs (2611.00252, ‘checked only by other instances of the same models’); Boshernitzan 1992 complete-periodicity conjecture for rational right triangles, two papers (2611.00250, 2611.00213); ten DSRG parameter sets excluded (2611.00230, Lean listed); interpolation lemma of OpenAI’s Landau–Siegel paper formalized (2611.00200)
• Other Hexagon 9–10 Nov: Cereceda’s 2007 conjecture for bipartite 2-degenerate graphs (Dave Goel, 2611.00260, ‘overwhelmingly by AI models’); Cazenave’s eigenvalue conjecture μ₂² ≥ 4λ₂+1 (2611.00232, Codex); Yair Lavi with GPT and Claude Fable: cubic-lattice dimer constant ℓ₃ ≥ 0.44477 (2611.00227), counterexamples to a Drury-conjecture inequality (2611.00198) and three more (2611.00197, 2611.00201, 2611.00225); Palcoux et al. fusion categories (2611.00233); Banica (2611.00221, ‘Written by Chat GPT, with help from Teo Banica’); Enomoto pretorsion theories (‘Sol proved almost all materials’, 2611.00207); Kominers, Fibonacci polynomials (2611.00212); Yampolsky, non-computable derivatives (2611.00243); Qiyue Tang, ten deposits on L’vov–Kaplansky, Lusztig, Laurent positivity and Markov numbers (2611.00195, 00205, 00206, 00210, 00216, 00218, 00219, 00238, 00239, 00194, 00192)