AI-assisted results in the 28 Oct 2026 sweep
Bialostocki–Lotspeich (1992), part of Gross–Prasad in geometric Langlands, Fuglede in 𝔽₂⁸, a TEMPO structure found by Claude, agent swarms on fractional Chern insulators, and a human digest of GPT-6 Astra’s Smale counterexample
Awaiting review
The takeaway
The 28 Oct sweep covered the arXiv announcement of 26–27 Oct submissions and late papers from 23–26 Oct. Five results have their own entries: Axiom’s Lean proof of the Classification of Finite Simple Groups, OpenAI’s spin-one Haldane gap proof (found through Hal Tasaki’s follow-up), OpenAI’s De Giorgi dimension-eight claim, Morgan–Mullen with Claude and Lean, and formula minimization with GPT-Sol-6.1. This page lists the rest. Claude, GPT-6 Astra and GPT-6 Pro supplied ideas, counterexamples or whole arguments in papers on zero-sum sequences, geometric Langlands, quantum dynamics, fire-blocking and spectral bounds.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Lean-verified
- Importance
- 2 of 5
- Last verified
- 28 October 2026
Your AI and this story
- GPT-6 Astra181 days after its cutoff
- Claude Opus 5.5120 days after its cutoff
- Gemini 4 Argon211 days after its cutoff
- Grok 4.7150 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 120 days before it.
Key facts
- Own entries: Axiom: Classification of Finite Simple Groups formalized in Lean, OpenAI proves the spin-one Haldane gap (periodic chains) (with Tasaki’s arXiv 2610.34330), OpenAI claims De Giorgi’s conjecture in dimension eight, Morgan–Mullen conjecture confirmed with Claude, Lean-checked (2610.36534), Formula minimization Σ₂ᵖ-complete (proof found by GPT-Sol-6.1) (2610.34516). Enriched: Smale mean value (2610.36158), Yang–Mills (Gross committee statement, AGMAI release request), quasi-Riemann (Radziwiłł talk; first downstream use in 2610.36588), crossing numbers (Pasechnik’s forest), Navier–Stokes (Armstrong via 36Kr)
- Bialostocki–Lotspeich conjecture (1992) on the number of n-term zero-sum subsequences, N₀ⁿ(S) ≥ C(⌊|S|/2⌋, n) + C(⌈|S|/2⌉, n) (Guoqing Wang, Xiangneng Zeng; 2610.37125): ‘In this paper, we prove this conjecture completely.’ AI statement: ‘The authors used a large language model during the preparation of this manuscript for assistance with mathematical exploration, checking arguments, organization and language editing.’
- Gross–Prasad in geometric Langlands (Kaiyi Chen, Zeyu Wang, advised by Zhiwei Yun; 2610.36377): part of the global conjecture for SO_n × SO_{n−1} in the unramified de Rham setting of Ben-Zvi–Sakellaridis–Venkatesh. ‘Wang then prompted GPT-6 Pro with this idea and asked whether stronger statements beyond Euler characteristics could be established. This led to Proposition 1.7.’ GPT-6 and Claude Opus 5.5 helped with literature (notably Proposition 3.7)
- Fuglede’s conjecture in 𝔽₂⁸ (Samuel J. Ferguson, Joshua Iosevich; 2610.36417): every spectral set and tile has a linear-subspace tiling complement, with a simpler proof of Kadowaki’s dimension-seven result. ‘The authors acknowledge collaboration with OpenAI’s ChatGPT in preparing this draft, developing and checking the computer programs, and simplifying the presentation of the proofs.’
- Physics: TEMPO networks independent of system size (Valentin Link; 2610.37012): internal bond dimension (2m+1)(m+1); ‘This result was discovered by Claude Opus 5.5 during guided development of TEMPO methods. AI-generated code, cross-checked against our established code base, is available.’ MOSAIC (Zhang, Xu, Li, Sarkar, Sun, Viswanathan; 2610.35934): a Claude Opus 5.5 swarm explores a GPT-6 Astra-proposed framework and finds many-body gaps ‘more than an order of magnitude larger than in the ideal case’, with the real-space quantum metric as the governing quantity
- Model-suggested key ideas: fire-blocking lower bound λ ≤ 1.62621… cannot block (Alberto Bressan, Luca Talamini; 2610.36919): ‘the specific idea of using a weighted double-bubble configuration as a comparison was suggested by GPT-6 Astra’; Erdős–Ginzburg–Ziv constant of C_nʳ beyond Harborth’s bound (Christian Elsholtz; 2610.35819): research ‘carried out in interaction with … Claude (Anthropic, model Opus 5.5)’; graceful labelings of trees, a TAOCP exercise 7.2.2.3-106 asymptotic with b = 2/π (Shisheng Li; 2610.34877): ‘done with extensive use of AI systems’, with thanks to Donald Knuth for comments; NP-hardness of the cone of quantum states over time (Matt Hoogsteder-Riera; 2610.34972): ‘LLM assistance has been used to derive the results’
- More: ascending chain condition for radical well-mixed difference ideals, ‘a long-standing open problem in difference algebra’ (Wei Li, Jie Wang; 2610.34389): GPT-6 Astra for ‘brainstorming, mathematical development, and manuscript drafting’; Galois-type property for weakly compact actions (Chifan, Flood; 2610.33320): ChatGPT Astra 6 helped construct the counterexample in Theorem C; a conjecture of vom Ende–Chruściński–Kimura–Muratore-Ginanneschi on conditionally 2-positive maps (Petri Tanninen; 2610.37187): ChatGPT for ‘exploring proof strategies, drafting and checking derivations’; KL₁ completeness conjecture refuted (Presa, D’Asaro, Badino; 2610.37107): counterexample found without AI, Gemini gave a preliminary completeness argument, Claude Opus 5.5 checked proofs and helped the Agda formalization; Tam’s star-shapedness conjecture (Luan, Tam; 2610.35612): ChatGPT for exposition and Section 5; sheaves on nodal singularities (2610.34676): Theorem 4.1 ‘partly assisted by … ChatGPT-5.6 Sol’
- Lean: linear-time FPT rectilinear planarity of series-parallel graphs (Giacomo Ortali; 2610.37018): ‘All proofs … are additionally verified in Lean 4 with Mathlib’; ChatGPT and Claude helped develop proofs and the Lean code. Parabolic rectifiable Reifenberg (2610.35809): Lean code written by LLMs under the author’s direction
Show 7 more
- Downstream use of OpenAI’s quasi-Riemann preprints: Liang Zhang (2610.36588, with UniDT’s UniMath model, GPT-6.1 Sol and GPT-6 Astra) bounds the arithmetic complexity of factorial multiples, τ(m_k k!) ≤ exp(C√(log k log log k)), assuming a zero-free half-plane, and notes that OpenAI’s unrefereed 7/8 and 11/12 results ‘supply the hypothesis’
- Agent systems: Infinity Machine (Harish S. Ganesan; 2610.35579), a self-improving harness that over 14 problems in six days and about $180 of model usage reports four results beyond the published state of the art in quantum information (e.g. stabilizer rank χ(T⁷) ≤ 10), and reports its failures (‘proposers gamed lenient scorers four times’)
- Meta-science: ‘Is the arXiv Apocalypse upon us?’ (Carlo Contaldi, Imperial; 2610.34449; analysis and first draft by an agentic AI): a second break in arXiv growth between Dec 2025 and Feb 2026; non-CS submissions 17% above trend; record 40,363 submissions in Sept 2026; maths submissions doubled within a year; solo-authored papers up 70% in maths and condensed matter
- Checked, no AI statement in the PDF: Andreadakis conjecture disproved for n ≥ 3, c ≥ 4 (C. E. Kofinas; 2610.36302); Carlet–Solé weight-spectrum conjecture refuted for RM(m−7, m) (Lou, Wang; 2610.36687)
- Writing help only: Wang’s planar D-coloring conjecture, sharp 2Δ−1 for Δ ≥ 6 (Harshit Verma; 2610.33322): ‘Generative AI tools were used to assist in the writing of this paper’
- Repositories: formal-conjectures added Erdős problems 777 (Claude-assisted PR, plby/lean-proofs proofs of known results), 1114, 284, 823 and others, proved the Tutte–Zykov variant of #627 (Mycielski graphs; main question open), linked Cambie’s n = 3 counterexample for #692 and marked Green’s problem 27 (lower bound) solved by Cao–Yuan; anthropics/formal-math added the ETH paper (own entry); openai/math update of 26 Oct added the ETH and all-dimension local smoothing papers and a Lean formalization for the CM Hodge paper (in those entries)
- 36Kr leads resolved: ‘Wang’s Conjecture fully cracked by AI overnight’ (27 Oct) is about Hong Wang’s Kakeya work and OpenAI’s all-dimension local smoothing claim (OpenAI claims local smoothing and Kakeya in all dimensions); ‘Zhang Yitang’s unsolved breakthrough … 5-page proof’ (26 Oct) is the Landau–Siegel zero story (Green, Banks, Kerr), already covered
What happened
The sweep listed 102 arXiv papers with an AI-use sentence and 69 conjecture papers without one. We read the abstracts and the PDFs’ AI statements for the 33 most relevant. The quotes above come from the PDFs. Five results got their own entries. The day’s biggest finds were not on arXiv: Axiom’s Classification of Finite Simple Groups in Lean, and OpenAI’s Haldane gap and De Giorgi manuscripts from 6 Oct, which we had not covered. The Haldane gap paper surfaced only because Tasaki cited it.
Why it matters
Models are now credited with specific discoveries in physics, not only maths. Claude found the TEMPO network structure, an agent swarm found the gap enhancement, and ChatGPT Astra found the separated-insertion argument in Tasaki’s paper. An agent-run study measured how far preprint volume has moved: maths submissions doubled in a year.
What is disputed or not yet verified
| Verification | Unrefereed arXiv preprints; Lean formalizations where stated |
|---|
Sources
21 sources from 3 sites. Numbers match the chips in the text.
21 sources: 19 primary, 2 press
Primary
- arXiv 2610.37125: A proof of the Bialostocki–Lotspeich conjecture (Wang, Zeng)arxiv.org, paper
- arXiv 2610.36377: Gross–Prasad conjecture in geometric Langlands (Chen, Wang)arxiv.org, paper
- arXiv 2610.36417: Fuglede’s conjecture holds in eight dimensions over 𝔽₂ (Ferguson, Iosevich)arxiv.org, paper
- arXiv 2610.37012: The TEMPO network can be made independent of the system size (Link)arxiv.org, paper
- arXiv 2610.35934: Agentic swarms discover enhancement of fractional Chern insulator gaps (MOSAIC)arxiv.org, paper
- arXiv 2610.36158: From boundary geometry to counterexamples in Smale’s mean value problem (Adamczewski, Colbrook)arxiv.org, paper
- arXiv 2610.36919: On the minimum speed for a fire blocking problem (Bressan, Talamini)arxiv.org, paper
- arXiv 2610.35819: The Erdős–Ginzburg–Ziv constant of C_nʳ for even n (Elsholtz)arxiv.org, paper
- arXiv 2610.34877: Rainbow maps and the number of graceful labelings of trees (Li)arxiv.org, paper
- arXiv 2610.34972: Membership in the cone of quantum states over time is NP-hardarxiv.org, paper
- arXiv 2610.34389: The ascending chain condition for radical well-mixed difference idealsarxiv.org, paper
- arXiv 2610.37187: Removing trace preservation from a universal spectral bound for 2-positive maps (Tanninen)arxiv.org, paper
Show all 19 sources
- arXiv 2610.37107: A counterexample to KL1 completenessarxiv.org, paper
- arXiv 2610.37018: Linear-time FPT rectilinear planarity testing of series-parallel graphs (Ortali)arxiv.org, paper
- arXiv 2610.36588: Square-root logarithmic bounds for the arithmetic complexity of factorial multiplesarxiv.org, paper
- arXiv 2610.35579: Infinity Machine: a self-improving AI agent for researcharxiv.org, paper
- arXiv 2610.34449: Is the arXiv Apocalypse upon us? (Contaldi)arxiv.org, paper
- arXiv 2610.36302: The Andreadakis conjecture (Kofinas; no AI statement)arxiv.org, paper
- formal-conjectures commit: Erdős Problem 627, Tutte–Zykov variant provedgithub.com, code
Press
- 36Kr: ‘Wang’s Conjecture Fully Cracked by AI Overnight’ (Kakeya)eu.36kr.com, press
- 36Kr: Zhang Yitang’s unsolved breakthrough (Landau–Siegel zeros)eu.36kr.com, press
Changes
- Filed (science agent; arXiv abstracts and PDFs, GitHub API, 36Kr)