AI-assisted results, 8 Nov: Hexagon of 7 Nov and arXiv

Your AI and this story

Key facts

• Own entries: 2×2 matrix mortality claimed undecidable (AI-assisted, Lean) (arXiv 2611.06562), Quasiplanar graph conjecture proved by ChatGPT-6 (Pach, Tardos, Zeng) (2611.07314), D-equivalence for generalized Kummer hyperkählers (ChatGPT-6 assisted) (2611.04118), Anthropic’s Claude physics papers: Hawking–Page and modular bootstrap (Hexagon 2611.00175, 2611.00174)
• Qiyue Tang (Tsinghua), GPT-6-Pro sessions of 2–10 hours reviewed by Codex, ‘some’ human understanding, Rethlas-OSV review ‘planned’: the multiplication part of Lusztig’s positivity conjecture for symmetric Cartan data (2611.00190, a 5 h 46 min session; would be a major result, no expert check); the Lu–Wenzel conjecture (2611.00179); disproof of Xi’s conjecture on representation dimension of idempotent corners (2611.00137, ‘passed the Rethlas-OSV review’); Conjecture 5.5 of Armstrong-Williams–Hirst–Jackson–Lee (2611.00181); counterexamples to Reading–Stella source–sink recursions (2611.00186); NP/RE-completeness of mutation equivalence (2611.00180); singleton dominance regions (2611.00185)
• Gasull’s problem on globally periodic rational difference equations answered yes at every order (was known for k ∈ {1,2,3,4,5,7,9,11}); John Rudge (Cambridge Earth Sciences) with Claude Opus 5.5 and Fable 5.1, Lean-formalized: ‘almost entirely AI-generated … Human input was mostly limited to encouragement (“keep going” etc)’; ‘I understand the statement … but not the details’ (2611.00183)
• Foregger’s conjecture (per A ≥ 2^{1−n} for nearly decomposable doubly stochastic matrices) claimed by Yair Lavi with GPT Sol, GPT Astra and Claude Fable; mixed text, all parts human-checked (2611.00169)
• L’vov–Kaplansky conjecture, partial cases: standard polynomials in every degree, Y. T. Miah with GPT-6 Pro, which ‘contributed substantially to developing the odd- and even-degree mathematical arguments’ (2611.00184); multilinear polynomials of degrees 4–6, Shengyong Pan (Beijing Jiaotong), declared human-written (2611.00173)
• Other Hexagon 7 Nov: Černý-type reset threshold cubic coefficient 8242/49923 (Shitov’s was 8257/49923), ‘primarily AI-generated’ by Codex, no human understanding (2611.00172, Sungbin Hong, U Tokyo); Subset Sum exponent 0.48758, Jennifer Voitle with Claude Opus 5.5, conditional on OpenAI’s and Kapila’s written proofs (2611.00178); four exponentials conjecture at CM and Beta periods and a Lean formalization of Waldschmidt’s subgroup theorem, Shawn Krisman, ‘done by Claude Opus 5.5’, no human check (2611.00171, 2611.00170); ‘orphan theorem’ for perpendicular billiard orbits in rational right triangles, Joshua Boorstein with Claude (2611.00191); two Grothendieck Montpellier-notes results in Lean, Michel Hua with Claude Opus 5/5.5 (2611.00189, 2611.00188); four-cycle supersaturation at q²+q vertices, Codex-revised (2611.00176); positive holomorphic sectional curvature of flag manifolds, alternative proof with ChatGPT, all human-checked (2611.00168)
• arXiv, AI credited with content: a second proof that dimension 6 has no four MUBs, by topology of complex Hadamard matrices; ‘ChatGPT 6 Astra and Claude Opus 5.5 assisted significantly in developing the proof’ (Wuttig, Tindall; 2611.06917; follows OpenAI’s family-266 claim); a fourth AI-assisted proof of the Courtade–Kumar conjecture, ‘obtained with interactive collaboration with GPT-6 Astra and DeepSeekV4.1-Flash’ (Kramer, Saglam; 2611.05430; see Courtade–Kumar ‘most informative Boolean function’ conjecture (2013) proved three times in two days, all with AI: Ky & Tran (ChatGPT), Google + CUHK (Gemini, Lean-verified end-to-end), Mahdavifar & Beirami); Behnezhad and Azarmehr break the 2-approximation barrier for sublinear metric TSP (sublinear.info problem 71), ChatGPT-6 Astra ‘played a substantial role in developing parts of the final algorithm’ (2611.04283); Kaplansky’s four group-ring conjectures fail for torsion-free hyperbolic groups in every positive characteristic, extending OpenAI’s constructions (Mghirbi, Douglas; 2611.04599); Fujita’s advanced generalised Mukai conjecture, single author, after reading OpenAI’s generalised Mukai proof with ChatGPT 6 (Duo Li; 2611.05452); Tarun Grover extends OpenAI’s Haldane gap proof to higher dimensions with ChatGPT Astra and Codex (2611.07400)
• arXiv, AI found key steps: ‘Theorem 1.2 was resolved using GPT-6 Astra with Xean in 13 hours’ (all minimum cuts of symmetric submodular functions, 2611.08253); quickest transshipment result ‘obtained by using GPT-6 Astra’ (2611.07369); robust streaming clustering developed with GPT Astra (2611.07678); Runge–Kutta order barrier and SSP bound, ‘AI-assisted proofs’ (Gottlieb et al., IBM; 2611.07981); 29-point counterexample to the happy edge conjecture found with ChatGPT-Sol 6.1 (2611.05300); Douglas’ conjecture for m-Kronecker quivers with Astra and Fable in Lean (2611.04862); VOA library in Lean with Claude and Codex (2611.06616); Monodromy computation model, AI ‘contributed substantially to the conception’ (2611.04377); Claude Code pipeline refuting 162,964 and proving 117,390 spectral-graph conjectures, 79,505 Lean-verified (2611.03879); Bergeron’s two diagonal-harmonics conjectures with ChatGPT (2611.00629); hypercube noise stability of order 7/8 with GPT-6 Astra (2611.00868); log-concavity criterion with Claude, Codex and GPT-6 Pro (2611.01561); Katok periodic-point counterexamples, GPT-6 for construction details (2611.01980); weighted convolution counterexample, ChatGPT strategies for Theorem 1.2 (2611.03334); parity decision trees with GPT Astra (2611.03452); non-pseudo-arithmetic hyperbolic 4-manifolds with Codex (2611.05795)