Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help (July–September catalogue)

What happened

This catalogue comes from a systematic pass over arXiv. It combined API queries for math, physics and theoretical-CS papers from 1 Jul to 30 Sep 2026 that mention a model name, "conjecture" or "open problem", with the AI-disclosure section of the project sweep and the public trackers. For each paper below, the PDF's AI statement was read. Quotes are from the papers, and nothing here was independently checked unless noted.

Combinatorics and discrete geometry

• Kahn–Saks conjecture (balance in posets) proved. Aires, arXiv 2609.30895. ChatGPT 6 Astra "used primarily to aid in the discovery".
• Talagrand's Conjecture 9.1. Park & Talagrand, arXiv 2609.33644. "The proofs presented in this document were generated entirely by the AI model GPT-6 Astra, and none of the authors claim any credit for them."
• Dominating Hadwiger conjecture disproved. Illingworth & Steiner, arXiv 2609.35361. Found by ChatGPT 6 Astra Ultra; the humans wrote the exposition.
• Partial List Colouring Conjecture (Albertson–Grossman–Haas) false. Noel, arXiv 2609.23291. Counterexample "discovered and fully verified by ChatGPT 6 Astra Ultra after some persistent prompting".
• Daykin–Frankl conjecture confirmed. Williams, arXiv 2609.03087. "We verify and communicate an LLM-generated proof" (ChatGPT 5.6 Sol Pro).
• Teschner's bondage-number conjecture counterexample. Yavari, arXiv 2609.04257. Generated by GPT-5.6 Sol Max.
• Anstee–Sali conjecture counterexample. Wu, arXiv 2608.07646. GPT-5.6 Sol helped identify the example.
• Chromatic symmetric functions of claw-free graphs are not Schur positive. Matherne & Morales, arXiv 2607.21508. Found with ChatGPT-5.6 Sol Pro; independently found by Prajapati.
• Schubitopes are not Ehrhart positive. Li & St. Dizier, arXiv 2608.00377. GPT-5.6 Sol Pro, first prompt, 38 minutes; verified in SageMath.
• Very ample lattice polytope with non-unimodal h*-vector. Hofscheier, Kurylenko & Nill, arXiv 2608.21507. Found with ChatGPT 5.6 Sol; answers a question of Ferroni–Higashitani.
• Equality case of Ehrhart's volume conjecture. J. Liu, arXiv 2608.01040. Complements OpenAI's inequality proof; "obtained by generative AI" (GPT-5.6 Sol, Fable 5, Danus).
• Kazhdan–Lusztig polynomials of matroids need not be unimodal. Cheng et al., arXiv 2607.24186. The Rethlas agent on GPT-5.6 Sol found it in 4 h 59 min.
• Laplacian S_{n,n} conjecture. Johnston, arXiv 2609.26895. "Significant amount of help" from ChatGPT 5.5, 5.6 Sol and 6 Astra.
• Comon's conjecture, 27×27×27 counterexample. Lovitz, arXiv 2609.28292. GPT-6 Astra gave "an initial proof of the main result".
• Kaplansky's conjecture (semifields) counterexamples. Nagy & Zhou, arXiv 2609.32651. Developed with ChatGPT 6 Pro; formalised by Harmonic's Aristotle in Lean 4.
• Generalized packing–covering conjecture. Alfarano, Marino, Neri & Trombetti, arXiv 2609.34910. ChatGPT 6 Astra turned the authors' strategy into a complete argument.
• Conway's subprime closure grows by the golden ratio (conjecture of Caragiu–Vicol–Zaki). Popescu, arXiv 2609.14188. GPT-6 Astra assisted; Lean-verified.
• Kalai's conjecture for tight trees and Erdős–Sós for digraphs: see the Erdős–Sós entry.
• Strongly aperiodic monotile in 3D ("Chair44"). Tsiokos, arXiv 2609.19214. Found by "an OpenAI reasoning model (ChatGPT, Astra)"; the text was largely written by Claude Fable 5.1 and reviewed by agents. Follow-ups: arXiv 2609.24779 (notes) and arXiv 2609.23783 (matching rules).

Analysis, PDE and geometry

• Landis conjecture fails in dimensions ≥ 3 (real potentials). Frank & Ivanisvili, arXiv 2608.00802. "The authors acknowledge the use of AI tools"; no detail.
• Pólya's conjecture for higher-dimensional Neumann balls. Filonov, Levitin, Polterovich & Sher, arXiv 2607.29305. ChatGPT and Claude "contributed to the development of several technical lemmas" and the rigorous computer-assisted algorithm.
• Yau's conjectured scalar-curvature integral bound refuted. Hao & Zhu, arXiv 2609.06533. "ChatGPT generated the main theorems and their proofs" (GPT-5.6 Pro).
• AI-discovered smooth random fast dynamo on T³. Rowan, arXiv 2608.20105. Central idea "generated essentially autonomously by ChatGPT 5.6 Sol Ultra"; the original AI manuscript is in the arXiv source.
• Nevanlinna's century-old half-plane problem counterexample. He & Zhang, arXiv 2608.24829. "AI-assisted exploration" (model not named).
• Fuchs's conjecture counterexample. Eremenko & Zhang, arXiv 2609.28443. ChatGPT as an "exploratory tool" and for editing.
• Forsythe's conjecture for restarted conjugate gradients. Colbrook, Stepaniants & Townsend, arXiv 2609.04659. Framed as an experiment in "how far a frontier language model could be pushed" (GPT-5.6, GPT-6).
• Rockafellar's sum conjecture fails. Boţ, arXiv 2609.13906. GPT-6 Astra assisted with the development.
• Hinrichs–Vybíral conjecture counterexample. Vybíral, arXiv 2609.21733. Found by a colleague "in a single prompt try" with ChatGPT 6.
• Talagrand's operator cotype problem. Wu, arXiv 2609.19731. "The counterexample was discovered by ChatGPT (GPT-5.6)."
• Khachiyan's ellipsoid conjecture. Zhou, Zou & Liu, arXiv 2609.28447. "An AI language model discovered the proof"; main theorem Lean-verified.
• Smooth Hamiltonian diffeomorphism with two fixed points on S²×S². Jiao, arXiv 2609.33626. "GPT suggested a key idea … most of the computation is done by GPT."
• Explicit mono-monostatic polyhedron (a certified polyhedral Gömböc). Schettini Gherardini, arXiv 2609.07827. A Claude Opus 4.8 / Fable 5 agent designed and ran the experiments; exact certificates.
• Lukic conjecture counterexample. Yan, arXiv 2607.26419. "This example was generated by GPT-5.6."
• Feige's conjecture. Nie & Wei, arXiv 2607.24528. Proof "obtained with the assistance of GPT-5.6 Sol".

Algebra, number theory, topology and logic

• Stable forking conjecture (Hart–Kim–Pillay 1996) refuted. Freitag & Mutchnik, arXiv 2609.00436. "This is an AI-generated result proven with the help of GPT-5.6 Sol."
• Huneke–Wiegand conjecture counterexample. Pham, arXiv 2609.07615. AI-assisted search with GPT-5.6 Pro; Craig Huneke independently recomputed the data.
• Sato's weak F-equivalence conjecture counterexamples. Chakravarty, Choi & Xu, arXiv 2608.18054. GPT-5.6 Sol "produced the key construction".
• Qin's quasimodularity conjecture for Hilbert schemes of points. Alekseev et al., arXiv 2609.33884. "Most of the formal arguments … were initially generated by GPT-5.6 Sol."
• Fröberg's conjecture for quintics and septics in four variables. Wang & Zhang, arXiv 2608.24797. GPT-5.6 Sol, Claude Fable 5 and Grok 4.6 workflow.
• Mod 4 Kawauchi conjecture. Conant, arXiv 2607.18655. Claude Fable 5 "proposed the quotient-tower strategy" and drafted the first version.
• HZ/4 is not an E2-Thom spectrum (the remaining case). Ji, arXiv 2609.19446. GPT-5.6 Sol and GPT-6 Astra; reviewed with Claude Fable 5.1.
• Yang's conjecture (tempered xi function) disproved. Kazin & Kadyrov, arXiv 2609.29898. GPT-6 Astra identified the key sine-transform formulation.
• Inhomogeneous Duffin–Schaeffer conjecture counterexamples. He & Liao, arXiv 2609.30870. Found with GPT-5.6 Sol; the authors later learned that Pollington had announced a counterexample more than a year earlier.
• Fraenkel's conjecture (Beatty sequences). Tan & Zhang, arXiv 2609.01570. GPT-5.6 Sol resolved the cases m = 8–11, which inspired the proof strategy; Codex helped with the finite-case verification code.
• Separable Jacobian conjecture in characteristic two, dimension-2 counterexample. Mondello, arXiv 2608.02634. Lean-checked; ChatGPT/Codex used for organisation; Aristotle replay.
• Colombo's determinant problem. arXiv 2609.00101. The WuJie agent, DeepSeek, Qwen, Kimi and GPT played "a substantial role in identifying the proof strategy"; Lean 4.
• De Bruijn–Erdős consecutive-gap problem. Korsky, arXiv 2609.07196. GPT Astra used "for completing the mathematical argument".

Theoretical CS, information theory, quantum

• Optimal shallow circuits for Majority. Lecomte & Ramakrishnan, arXiv 2609.34029. Constructions "originally found by GPT-6 Astra"; the authors rebuilt the proofs from high-level ideas.
• Quadratic lower bound on determinantal complexity. Kumar & Volk, arXiv 2609.34462. Came out of using ChatGPT Astra to parse Sheshadri's AI-assisted proof, whose details they were 'unable to follow' and verify.
• Strong secretary conjecture for linear matroids. Bérczi, Dughmi, Livanos & Soto, arXiv 2609.20797. Astra "identified the supermodularity … and proposed the uncrossing argument" on 15 Sep; concurrent-discovery note.
• Nelson–Nguyen conjecture. Mai & Rao, arXiv 2609.22548. ChatGPT-5.6 Pro "used in proving and writing".
• Markovity conjecture for two-receiver broadcast channels refuted. Liu & Huang, arXiv 2608.13170. GPT-5.6 Sol; Chandra Nair suggested the AI search and checked the result.
• Shor's orthogonal-measurement conjecture. arXiv 2609.27992. Codex and GPT-5.6 Sol for exploration and error checking only.
• Distributional variants of the Aaronson–Ambainis conjecture. arXiv 2609.35327. "Google Gemini suggested the core idea underlying the inner-gadget construction."

Outside arXiv (claims with weaker provenance)

• Conway's refinement conjecture for omnific integers (1976): Dan Abramov's "I vibed a proof of Conway's conjecture" (18 Sep; Claude, ChatGPT/Sol and Codex agents; Lean proof passing Palomar checks; not reviewed by mathematicians). overreacted.io
• Theo-Conjecture (FirstPrinciples) on a 35-year-old question about common-divisor graphs (arXiv 2608.04040; "not yet completed peer review").
• Star Fleet Math: 20 parallel Codex/GPT "starships" claiming 13 Lean-verified Erdős-problem solutions (July 2026). starfleetmath.com

Why it matters

By September 2026, "settled with AI help" had stopped being news in itself: several named conjectures a week, across most of mathematics, with disclosures ranging from "fully generated by the model" to "used for proofreading". For a model with an older cutoff, the practical lesson is to check the current status of any conjecture before calling it open. Many that were open in early 2026 have claimed resolutions, but most are still unrefereed.

Changelog

• 2026-09-30: created from a systematic arXiv/tracker backfill (AI disclosures read in each PDF)