Mid-October 2026: arXiv results with disclosed AI help

This block was read from the PDFs of the arXiv papers the 14 Oct evening sweep listed as disclosing AI use (112 papers) or claiming to settle conjectures without a disclosure (86). Most 7–12 Oct items had already been processed in the morning run and are in the October catalogue or in the leads file. Below are the new items, grouped by how large the stated AI role is.

Results where the AI did most of the new work

• S-Hamiltonian cycles and paths (Kumar, Mari & Sandeep, 2610.183001, 13 Oct). The paper completes the complexity classification for undirected graphs, including NP-completeness for every finite set of odd walk lengths, which was an open problem of Amarilli, Lombardo and Monet (WG 2026), and treats digraphs. Declaration: “A preliminary version of Theorem 12 was obtained manually using a construction with loops. GPT 6 Pro was used to extend this result to oriented graphs and to obtain all other new results in this paper.”
• Prescribed scalar curvature, null case (Yuxiang Li, Yunqing Wu & Jie Zhou, 2610.184322, 13 Oct). Smooth sign-changing functions with negative mean on flat tori Tⁿ, n ≥ 5, that are not the scalar curvature of any metric in the conformal class. “The counterexample presented in this paper was suggested by ChatGPT. The authors have verified its correctness.”
• Three conjectures of F. Luo (2011) (Qilong Guo, 2610.1397911, 11 Oct). One counterexample to all three: a minimal two-tetrahedron triangulation of the lens space L(3,1) with a null-homotopic loop edge. The author thanks ChatGPT “for providing the idea for the counterexample”.
• Zhi-Wei Sun’s permutation conjecture (Jinggao Ai, Dingsheng Hu & Junmin Yan, 2610.184314, 13 Oct). For n > 6 (line) and n > 7 (circle), 1, …, n can be arranged so that the reciprocals of adjacent sums add up to 1. “Most of the construction and the recursive step in this paper were proposed and refined through our interaction with GPT-5.6 Sol”; the authors checked every case by hand.
• SYK central limit theorem (Kamijima, Nakajima, Noda & Sasaya, 2610.184405, 13 Oct). A CLT for log Z_N(β) of the q-body SYK model at high temperature. The paper is written as a case study: direct attempts with ChatGPT 5.5 Pro failed; after the humans proposed working with the partition function instead, the discussion produced proofs; ChatGPT 5.6 Pro later helped replace a complicated analytic step with a combinatorial one. “In parallel, we formalized the refined proofs in Lean: the AI generated the code, and we reviewed it.” Code at github.com/TokyoProbabilityGroup/SYK_CLT.
• Exact selection complexity (Jonathan Cremer, 2610.187407, 13 Oct). V₇(16) = 28 and V₅(17) = 27 comparisons, with better upper bounds for other ranks; V₇(16) was one of the two 16-element entries left open after Dörrer et al. settled n ≤ 15 (previous range 28–30, from Gasarch–Kelly–Pugh’s table). Every bound has a certificate checked by an independent checker and in Lean 4. “The assistants implemented the software and produced first drafts of the proofs.”

A model suggested the key tool

• Szemerédi’s theorem with random differences (Gabriel Dahia, 2610.188593, 13 Oct). The threshold is improved from p ≥ n^(−2/k+o(1)) (Briët–Castro-Silva) to p ≥ n^(−c/log log k) for large k. The author asked GPT 6 Astra Pro whether an Alon–Pham-style idea could give a small cover; “It replied that it could not use those ideas, but suggested that the construction from [Green–Ruzsa, arithmetic Kakeya] could be used”, and the proof “crucially relies” on that construction.
• Strong monodromy conjecture for the symmetric determinant (Renjie Lyu & Xiping Zhang, 2610.18395). ChatGPT 5.5 Pro helped connect the resolution to complete quadrics, computed Euler characteristics and “suggests the following transverse normal form” (Lemma 2.3).
• Framed LMOV conjecture for links (Kefeng Liu, Pan Peng & Shengmao Zhu, 2610.186189). Built on Liu–Peng’s 2012 strategy; “GPT-6 Astra assisted in deriving the local crossing identities (4.1) and (4.2)”.

Exploration, computation and checking

• Takigiku–Tsuchioka conjectures: eight Rogers–Ramanujan-type identities (Liuquan Wang, 2610.18666); GPT-5.6 Sol and GPT-6 Astra “used to assist in exploring proof strategies, performing calculations”.
• Berndt–Straub conjectures (Siddhi Pathak, 2610.1806510): the conjecture for R_k is proved; the one for S_2n is disproved (S₆(x; χ₁₆₃, χ₁₆₃) has four zeros off the unit circle), so the “Riemann hypothesis for period polynomials” can fail for Eisenstein newforms. ChatGPT (GPT-5.6 Sol, GPT-6 Astra) helped with exploration and examples.
• C-algebras of essentially tracial rank one* (Huaxin Lin, 2610.14711), which the abstract says “completes a long-standing project”: “The example in Section 14 was an AI experiment”; an argument “was initially suggested by ChatGPT-5.6-sol”.

Human-only results of the same days (for contrast)

• Maximum nonlinearity of 8-variable balanced Boolean functions is 116 (Lou, Xu & Wang, 2610.1789712), a negative answer to the existence of nonlinearity 118, “a famous and long-standing open problem”; no AI statement found. Same group: covering radius of RM(1,9) is 242 (2610.17871).
• Endpoint power-weight inequalities for spherical maximal functions (Fraccaroli, Lee, Lei, Roos & Seeger, 2610.18316): “No AI tools were used for the mathematics or the writing of this paper.”
• p-adic inhomogeneous Littlewood (Chow & Jones, 2610.15809): “AI has not been used in this work”.
• Bolsinov–Taimanov analytic entropy conjecture (Chen & Jiang, 2610.14065): no AI statement found.

No Hacker News threads on any of these were found on 14 Oct (Algolia search); X was not searched directly.

One day’s listing now routinely holds several AI-assisted resolutions of named problems. Their disclosures are increasingly specific, naming which lemma, construction or counterexample came from the model. The rational exponents write-up and Monod–Thom paper show leading experts publishing and crediting AI-originated arguments under their own names.