AI-assisted results, 9 Nov: arXiv and Hexagon

Your AI and this story

Key facts

• Own entries: Matroid secretary conjecture resolved, with GPT Astra (arXiv 2611.08869, 2609.14555), Reflexive polytopes conjecture disproved, GPT-6.1 Sol (2611.08819)
• Böhm–Lafuente conjecture (every negative-Einstein manifold with cocompact symmetries splits as H × K), with a new proof of the Alekseevskii conjecture; Marcos Martinez Wagner, single author: ‘ChatGPT 5.6 and ChatGPT 6.1 have made the following two main contributions’ (Theorem 9.7 and an Iwasawa-type decomposition, Theorem B.1) (2611.09257)
• AI found main results: ‘OpenAI’s ChatGPT 5.6 Sol and 6 Astra generated the proofs of the main results’ (sharp universality thresholds for random profinite groups, Jung & Lee, 2611.09477); ‘The proof of Theorem 1.1 was originally obtained by Claude Code (Opus 4.6)’ (separating measures by hyperplanes, Correa, Solan et al., 2611.09166); ‘The proof of Theorem 1.2 was discovered with AI assistance (ChatGPT Astra)’ (deterministic factorization of constant-depth circuits from PIT, Kumar, Saptharishi, Saraf et al., 2611.09035); GPT-5.x/6 Pro, Gemini 3.1 Pro and GPT-6 Astra used to construct clauses for exponential Moser–Tardos/WalkSAT separations (2611.09335); quantum query complexity of Hamming weight beyond n/2, AI used for approach and proof development under the Simons AI+TCS methodology template (2611.09809); Sinkhorn convergence, ChatGPT ‘assisted with counterexample construction’ (2611.08963)
• AI credited with parts: GPT-5.5/5.6 Sol ‘generated ideas for Lemma 2.25, Propositions 2.26, 2.32–2.34’ and all Section 5 examples (ordered vector spaces, 2611.08735); Theorems 3.12 and 5.10 ‘found by modifying outputs’ of ChatGPT-5.6 Sol (2611.09011); Claude Opus 5.5 filled gaps incl. Theorem 4.1 (IC-planar weak-strict degeneracy ≤ 6, 2611.09125); GPT-6 Astra helped develop the proof (convex polytopes with dihedral angles ≤ π/2+δ, 2611.09021); Theorems 4.1 and 6.4 with GPT Astra 6 Pro (cube tilings, 2611.09844); Claude explored constructions for a uniformly quasiregular map with Cantor-of-spheres Julia set (2611.08773); Stacks agentic workflow on Claude Opus 5.5 and GPT-5.6 Sol (Conley index, 2611.08591); smaller roles: 2611.08574, 2611.09392, 2611.09064, 2611.09675, 2611.09887, 2611.08796, 2611.08653. The rest of the 175 mention AI only for editing, literature, code or checking
• Conjecture papers without AI disclosure: ‘The BCC lattice is the optimal 3D lattice quantizer for all p ≥ 1’ (2611.09523); no other famous problem
• Repo: google-deepmind/formal-conjectures commit of 8 Nov proves the Erdős #338 variant ‘Kelly’s conjecture’ false in Lean (a basis of order 2 with no restricted order 3, explicit base-3 construction); ‘AI-usage disclosure: Claude (Anthropic) was used as assistant’
• Hexagon 2611.00204 (8 Nov), Rahul Ajit and S. Lee: AI-found counterexamples in positive characteristic (globally +-regular rational surface with nef, non-big, non-semiample anticanonical divisor; F-finite splinter not weakly F-regular); ‘Primarily AI-generated’; ‘their mathematical details were quite incomprehensible to the humans’, who ‘think the math in this draft is correct’ and are verifying it
• Hexagon backlog (20 lines): Benjamin Severn, Weil classes on Weil-type abelian sixfolds for Q(i), discriminant −3, are algebraic (a Hodge conjecture case), ‘Primarily AI-generated’, partly human-checked (2610.00477); Khai Hoan Nguyen Dang with ChatGPT, Mahlburg–Ono and Cullinan–Hajir conjectures on Jacobi/Legendre polynomials (2610.00468); Troy Winarski, Lean-recorded 15/16 zero-free half-plane for angular Hecke L-functions over Q(√−3), extending OpenAI Math Family 003, ‘Primarily AI-generated’, partly checked (2610.00458; strong claim, no expert check); Andy Jiang, nonexistence of lim Cohen–Macaulay sequences, ‘produced end-to-end by GPT’ (2610.00465); Deep Bhattacharjee with Claude Code: Wigderson’s nilpotent-free conjecture fails for 3×3 over F_3 (2610.00480), densest two-translate lattice packings in R^5 (2610.00479), Kimberling’s Fibonacci–Lucas conjecture (2610.00478), bridge index of 13-crossing knots (2610.00475), Shankar’s Catalan conjecture (2610.00474), Simpson’s abelian-squares conjecture with Lean (2610.00473), Welch function not third-order sum-free (2610.00472), Wang–Tian τ_k-maximal conjecture (2610.00459), supersymmetric Yang–Mills obstructions (2610.00471); John Tripodo, double Hall degree and projective-plane determinant bounds, no human check (2610.00462, 2610.00457); heat-evolved random polynomials, no human check (2610.00483); Ramsey for pairs in Pincus’s model N48 (2610.00464); Manjil Saikia with Claude Fable 5.1 skeleton (2610.00469); human-written: 2610.00470, 2610.00463