AI-assisted results, 14 Nov

Your AI and this story

Key facts

• Hexagon, number theory (13 Nov): square-difference-free sets have size ≤ C·N^0.9999873, an explicit exponent for the power saving in OpenAI’s Furstenberg–Sárközy preprint, ‘written by Claude Opus 5.5, GPT Astra 6, and Muse Wonder-Full 1.0, under my prompting and supervision’, some parts human-checked (Eric Naslund, 2611.002931); every even N ≥ 4 is p + η with η a product of at most 18 primes, against 395 (Johnston–Starichkova), primarily AI-generated, ‘None of this contribution has been checked and understood by any human’ (Wren Aquila, 2611.004152); de Bruijn–Newman Λ ≤ 0.174 (previously 0.2, from Polymath 15’s criterion with Platt–Trudgian’s RH check to 3·10¹²) via optimised mollifiers and an Arb interval certificate, human-checked, Claude ‘used throughout as a research and writing aid’ (Pedro Caceres, 2611.003493); irrationality of χ₂(1/q), Ti₂(1/q) and χ₂(2/q) in stated ranges, abstract says formalised in Lean, no human check (Shawn Krisman, Claude Opus 5.5, 2611.004327); zero-free half-plane Re s > 0.87334… for unitary Hecke L-functions, improving the quasi-Riemann constants, Codex GPT-6.1 Sol and Claude Opus 5.5 (Baiying Liu, 2611.00421)
• Hexagon, more number theory: conditional power-saving asymptotics for all four of Landau’s prime problems from the Ratios Conjecture, mixed authorship, fully human-checked (Haozhe Gou, Victor Wang, Max Wenqiang Xu, 2611.004234); an irregular extension of an Euler triple forces c < 4·10⁴⁸ (He–Togbé: 10⁹⁸), ‘prepared with the help of Aleph, an AI research assistant for mathematics’, key ideas from the authors (Siniša Slijepčević, Andrej Dujella, 2611.004315); Σ1/(a_n²a_{n+1}) irrational when log a_n/(√3)ⁿ is unbounded, lowering the base from 2 in Barreto–Kang–Kim–Kovač–Zhang, ‘two cooperating Codex research sessions’ with GPT-6-Astra max (twinheterodox, 2611.00428); Markov uniqueness verified for the first 10¹² Markov values, ChatGPT and Claude (Elleard Heffern, 2611.00410)
• Hexagon, combinatorics and algebra: an 11×11 sign matrix with permanent 2,029,568 not attainable with all-+1 sub-diagonal, answering a question of Ingram and Razborov negatively, primarily AI-generated, human-checked (Weiming Zhang, 2611.004246); sharp exponential constant for permanents of 6-regular circulants and a conjectured permanent inequality for PSD matrices proved for n ≤ 5, Codex/GPT and Claude Fable (Yair Lavi, 2611.00430, 2611.00429); a law of large numbers for infinitesimal characters, ‘Claude Opus 5.5 supplied the original proofs of all results’ (Andrew Salmon, 2611.00422); higher invariants c_k of complex Hadamard matrices, ‘Written by Claude Opus, with help from Teo Banica’ (2611.00418); class-two Lie algebras, sections ‘generated and revised between author, Opus 5.5 and Astra 6’ (Ammar Husain, 2611.00412); global twistor sources for analytic Einstein spacetimes, GPT-6 Pro, gpt-6.1-sol and Opus 5.5 (Lior Isthmus, 2611.00425); Zhenyu Sun, two Codex-assisted papers (2611.00419, 2611.00416); human-written: 2611.00262, 2611.00413. Qiyue Tang’s six deposits: see Six unchecked GPT-6-Pro proofs of named conjectures (Qiyue Tang)
• arXiv: arXiv announced no new listing after Fri 13 Nov (checked arxiv.org/list/math/new: ‘Showing new listings for Friday, 13 November 2026’). Uncatalogued 10–13 Nov papers with substantive AI roles: Appendix A of the law of fractional logarithm for the β corner process, ‘All the ideas belong to the authors, except for those in Appendix A which were given by ChatGPT 6 Astra’ (Bao, Xu, 2611.150969); polynomial swap coboundary expansion for KMS complexes (LTCs, PCPs), ‘We used Open AI’s Astra 6 to simplify arguments and optimize constants in the proof of Lemma 3.7 as our original proof had a bound of r ⩾ 10^2700’ (Dikstein, Oppenheim, Valentiner-Branth, 2611.162958); a covering-number conjecture generalising Vizing’s, ‘The lower bound on the volume Wn in §A.2 was found with the help of GPT-5.2-pro’ (K. and M. Cieliebak, 2611.15599); exact (ARV, Spearman’s ρ) region, AI used ‘for the construction of the extremal families and of the Kantorovich potentials’ (Anzilli, Durante, 2611.14645); quadratic convexification with two switching variables, ChatGPT GPT-5.6 Sol ‘throughout … including the formulation of results, proof development’ (Zhang, Ouyang, Yang, 2611.15745); Wigner-vs-Wishart tensor CLT gaps with Codex GPT-6 Astra ‘to help develop and check proofs’ (De, Kunisky, 2611.15803); K-stable Fano varieties with obstructed deformations, AI for ‘some hints for the appendix’ and Remark 1.5 (Petracci, Villa, 2611.15330); products of projective spaces and quadrics, ‘Remark 4.14 and the idea of using it to prove Lemma 4.15 was suggested by AI models’ (Ghosh, Kovács, 2611.16529); TraceFEM for surface Stokes–Cahn–Hilliard, Opus 5.5 and ChatGPT 6 Astra extended the estimates to L^p (Olshanskii, Shakipov, 2611.15982); examples built with ChatGPT (Li, Tian, 2611.15643); proofs partly developed with ChatGPT (Edigarian, Nikolov, 2611.15261; Kim, Kwon, Shim, 2611.15174); an LLM ‘found the explicit form of Equation (4.4)’ (Bassi, 2611.14747). The rest of the 387 listed papers disclose editing, literature search or proof-checking only, or were catalogued on 12–13 Nov
• Backlog of 6–11 Nov arXiv papers with AI statements never catalogued before (titles naming conjectures or problems were re-read; four got own entries: k-Clique hypothesis refuted, Herzog–Schönheim for solvable groups, Bloom’s conjecture in all dimensions, graphic TSP 89/64). Others: Smale’s 7th problem, a linear-time construction on S² whose log-energy exceeds the Brauchart–Hardin–Saff expansion by only Θ(N^(2/3)) under a locality assumption, ‘This work was produced using Gemini 4 Argon, which carried out most of the day-to-day technical, computational, and expository work’ (Kabra, Dehaen, Karlova, Hamilton, Carreira, Ovsjanikov, Barron; Google DeepMind, UCL, UCT Prague, MIT; 2611.15783); van der Put–Singer conjecture on the inverse problem in difference Galois theory, ‘The original results in this paper were entirely generated by ChatGPT 6 and the MechMath Agent Team (MMAT)’ of AMSS, CAS, author-checked (Ruyong Feng, 2611.11397); the Theta conjecture of Interdonato–Iraci and the valley Delta conjecture, ‘developed with the help of ChatGPT 6 Astra’ (Bai, Gu, Lin, Qiu, Zhang, 2611.12451); Jaeger’s circular-flow conjecture for planar graphs, χ_c < 2ℓ/(ℓ−2) for signed planar graphs of negative girth ℓ, ‘benefited from the assistance of ChatGPT’ (Reza Naserasr, 2611.08862); Merino–Welsh for sparse and dense graphs, ‘The proofs are due to ChatGPT 6 Astra’ (Benedek Váli, 2611.15008); Oliver’s p-group conjecture for class ≤ (p+5)/2, GPT-6 for proof strategies (Duan, An, 2611.15156); Brualdi–Quinn strong edge-colouring fractionally and asymptotically, Claude Opus 5.5 (Luo, Yu, Zhou, 2611.10883); Terao’s conjecture for 17 lines (Monteiro, Sá Earp, Silva, 2611.14689); cable-knot counterexamples to the all-knot volume conjecture, Codex (Haibin Hang, 2611.09063); q-permanent monotonicity conjecture disproved, ‘GPT-6 (ProReasoning) in ChatGPT was used to find the initial counterexamples’ (da Fonseca, Goyal, 2611.14694); no regular icosahedron has a rational point on every face, answering Bogdanov’s MathOverflow question, argument and Lean ‘produced by AI systems (OpenAI Codex and Anthropic Claude)’ (Mikhail Levit, 2611.11577); monotonicity of Erdős sums f_k for k ≥ 6 with Claude Opus 5 (Padhi, 2611.11418); bin packing additive Ω(log* OPT) hardness, results ‘developed’ with ChatGPT (Doron-Arad, 2611.09447); Tuza’s conjecture under density conditions, Codex (Tsujimura, 2611.11128); Comon’s conjecture for real Hankel tensors, ChatGPT 6 Astra ‘throughout’ (Jianze Li, 2611.13823); Rolle words of degree six, mostly ChatGPT-generated (2611.15505). Follow-ups to OpenAI’s release: Alexander Lytchak streamlines OpenAI’s sharp Euclidean filling inequalities in CAT(0) spaces (2611.13159); Cârstea and Oksanen give a Lean 4 proof of a case of OpenAI’s anisotropic Calderón uniqueness theorem, which OpenAI released without Lean (2611.10537); David Gamarnik’s ‘human-friendly exposition’ of the random k-SAT resolution (2611.10139)
• Checked, no AI statement in the PDF (conjecture list, 73 papers, all from 6–13 Nov): Gromov’s conjecture that quasi-isometric torsion-free nilpotent groups have isomorphic Mal’cev completions (Kajal Das, 2611.1200910); Pólya–Szegő buckling conjecture in dimensions 2–47 (Dai, Sun, Zhang, 2611.15243); Fourier dimension of complex GMC on the circle (Guo, 2611.15733); anisotropic De Giorgi in ℝ⁴ (2611.13745); Woo–Yong conjecture (2611.09237); Gorsky–Oblomkov–Rasmussen over ℚ (2611.10885); a counterexample to the pure semisimplicity conjecture (2611.09749); Kourovka 21.7 (2611.13792); three De Deyn–Van den Bergh NCCR conjectures disproved (2611.12679); exponential EGZ lower bounds (2611.15210); an ‘elementary proof’ of binary Goldbach in math.GM (2611.09007, unvetted)
• Aaronson–Ambainis follow-ups on arXiv (Turturean 2611.09773; Stanford exposition 2611.11626; independent short proof 2611.12795, whose authors used ChatGPT 5.6 and 6): added to PSI claims Lean-checked proof of the Aaronson–Ambainis conjecture
• Result repos (formal-conjectures, 13–14 Nov): Palomar link for a Lean proof of the classical bound R(5,5) ≥ 43 (commit); Lean refutation of Written on the Wall II conjecture 291 via a 12-vertex graph from a family found by a GitHub user, ‘Lean formalization by Wentao Li, with AI assistance’ (commit); new statements of weighing and Butson–Hadamard conjectures (commit); a refactor (commit); Erdős 190, 297 and 739 as in the 13 Nov listing. openai/math, anthropics/formal-math and oai-math-revised: no new commits. Watched-repo list: google-deepmind/code-verification (AlphaProof Code, added to its entry) and deepseek-ai/chat-demo (tooling)