arXiv results with disclosed AI help, 16 Oct 2026 announcement

On 17 Oct the sweep’s arXiv API step was still blocked (HTTP 429 on export.arxiv.org since the 16 Oct fetch), and arXiv’s RSS feeds were empty because arXiv does not announce on Saturdays. The HTML listing pages (/list/<category>/new, with abstracts) still worked. They gave 615 new submissions from the 16 Oct announcement; 32 were already cited in the dataset. 119 matched keywords (conjecture, counterexample, open problem, Erdős, Lean, model names); their PDFs and those of the remaining uncited maths, CS and hep papers were read with pdftotext and searched for AI statements. Each statement below is quoted or closely paraphrased from the PDF. None of the papers is refereed, and no Hacker News thread was found for any of them.

Named problems settled or advanced

• Suffridge’s conjecture and two Brevig–Saksman conjectures (Ole Fredrik Brevig & Øistein Søvik, 2610.217881). If 0 < p < 1, every norm-attaining element of the unit sphere of H^p for a bounded linear functional is an outer function; this complements Duren–Romberg–Shields on the failure of Hahn–Banach in H^p. AI: “An initial proof of Theorem 1 was found by Claude Opus 5.5 when it was tasked with resolving the conjectures from [1]. That proof was variational and based on ideas going back to F. Riesz … Corollary 2 (b) led the authors to the work of de Leeuw and Rudin [2], where they found the main idea in the much simpler proof presented below.”
• Wahl’s Main Conjecture for ℚ-Gorenstein singularities (Heesang Park & Dongsoo Shin, 2610.210922). Δ ≥ 0 with equality exactly in the quasi-homogeneous case, also proving Wahl’s ℚ-Gorenstein and Rational Conjectures; Δ + 4p_g ≥ 0 in general. AI: ChatGPT-6 Astra searched and analysed Wahl’s and Lima-Pereira et al.’s work; “The authors proposed various approaches to generalizing the ideas in these papers and used ChatGPT-6 Astra to examine their feasibility.” Companion 2610.21093 builds singularities with arbitrarily negative Wahl defect; there Astra also helped by “finding explicit gluing maps for the construction of the counterexamples”.
• Wahl’s conjecture on rational homology disk smoothings (Márton Beke, Heesang Park, Dongsoo Shin & András I. Stipsicz, 2610.20991). A normal surface singularity whose minimal good resolution graph has at least two nodes has no rational homology disk smoothing; with earlier work this completes the classification of singularities admitting such smoothings “and proves Wahl’s conjecture”, and also his Rational Conjecture. AI: “The authors used large language models in proving some statements, drafting the paper, and identifying errors.”
• Six-dimensional Tarski problem (Kristóf Zólomy, 2610.217853). Lower bound Ω((log n)^(2+⌊log₃(d/2)⌋)), giving the optimal Θ((log n)³) deterministic query complexity for d = 6. “ChatGPT-6 Astra was used to assist in developing the lower-bound argument, working out the technical details of the manuscript, preparing the figures, and checking the arguments.” The abstract says “several papers obtained improved lower bounds using AI-assisted proofs” (the references include Chen, Gao, Li, Rubinstein & Yannakakis, arXiv 2610.07055, and Liu & Wang).
• Points on spanned lines; questions of Basit–Dvir–Saraf–Wolf and Averkov–Schymura (Matthew E. Kroeker & Ben Lund, 2610.214154). Some point lies on at least n + 1 − 2n/(d+1) spanned lines (sharp in every dimension), removing the large-rank assumption from Geelen–Nelson–Walsh; n²/40 ordinary lines in ℂ³ under a plane condition. AI: “The authors used GPT-6 Astra to assist with proof development and writing.”
• Exponential sums with multiplicative coefficients (Haozhe Gou, 2610.223455). Optimal constants 4/√6 (multiplicative) and 1 (completely multiplicative), confirming “a folklore conjecture … motivated by the work of Montgomery and Vaughan (1977)”. AI: “ChatGPT 5.6 Sol suggested modifying this reduction to impose complete multiplicativity only at the primes not dividing q … and also suggested the subsequent Fourier expansion”; “ChatGPT 6 Astra also helped construct the second counterexample in Proposition 1.1(ii).” Ramaré’s identity and the pretentious large sieve were the author’s ideas.
• Lévy-process dichotomy (Jorge González Cázares, David Kramer-Bang & Aleksandar Mijatović, 2610.209166). Every infinite-variation Lévy process is abrupt or strongly eroded, resolving a conjecture from Ann. IHP 2024; counterexamples to Vigon’s point-hitting conjecture. AI: “ChatGPT-5.6 and 6.1 and Gemini Flash 3.6 were used to develop the ideas, particularly from Fourier analysis, needed and used in the proof … and in the construction of the examples.”
• Matroid cotangent cohomology (Qihang Wang, 2610.206499). T² vanishes exactly when the matroid has no U₁,₄-minor, “settling the conjecture of Constantinescu, Klein, Nguyen, Singh, and Venturello”, plus obstructions of every order. AI: “A generative-AI workflow using OpenAI GPT-5.6 Sol, Anthropic Claude Fable 5, Grok 4.6, and OpenAI GPT-6 Astra developed the hyperplane-graph and cup-product formulas, higher-order obstruction constructions, and primary-quotient module calculations … The results await further verification by domain experts.” Acknowledges Gewu Intelligence Lab.
• Undecidability in dynamics (Jason Bell, 2610.221237). Extending Lee and Nam, the set of n with φⁿ(Y) meeting Z gives an undecidable problem for a fixed variety and map, and a counterexample to a Bell–Satriano–Sierra conjecture. In the acknowledgments: “ChatGPT offered me one free month of what they call a ‘Plus’ subscription … gave it some of my rough mathematical thoughts on this problem and asked it to turn them into a paper. Aside from the fact that I could not initially understand much of what it had written, it was largely a success.” He then rewrote it.
• Hegselmann–Krause dynamics (S. Rasoul Etesami & Behrouz Touri, 2610.20783). A six-agent counterexample to convergence of scalar heterogeneous HK dynamics (after Hegarty, Ognissanti & Wedin’s counterexamples in arXiv 2610.03229). “Generative AI models ChatGPT and Claude have been used for the refinement of the counterexample and the exposition.”
• Crossing numbers of simplicial complexes (Alfredo Hubard, Cheikh Saliou Ndiaye & Oriol Solé-Pi, 2610.2101710). Higher-dimensional crossing lemma, a generalised Harary–Hill conjecture, and a simple proof of Harary–Hill for antipodal drawings. “An LLM, after being given our calculations for B2,S, discovered the upper bound on B2. Prompted with the suggestion to use Gale duality, an LLM found the proof Theorem 24.”
• Eccentricity Shortest Path (Anand Babu, Ashwin Jacob, H. Kumar & R. B. Sandeep, 2610.207698). FPT and XP algorithms for many structural parameters, answering two published questions. “All results obtained in this paper were developed using OpenAI’s GPT-5.6/6 Pro. These models were also used to generate, refine, and write the proofs and exposition.”
• Lacunary maximal operators (Xiaojing Zhou, 2610.21197). Negative answer to the weak-type (1,1) question of Seeger and Wright (2011) and Wright’s Open Problems 14 and 15 (2016). Minor AI role: “The idea of applying Markov’s inequality to obtain (2.3) in the proof of Lemma 2.1 arose from discussions with ChatGPT.”

Other substantive AI contributions

• Yukich’s 1989 question (Weitao Huang, Yichen Wu, Renzhen Wang & Deyu Meng, 2610.2107011). Exact leading constant c* = κ₁/(2√π) for the bounded-Lipschitz (W₁) distance of 2-D uniform empirical measures, in expectation and almost surely. AI: “we developed a reusable AI-agent workflow for mathematical research, which we plan to release, and applied it to Yukich’s question. The agents assisted in exploring proof strategies, testing conjectures through counterexample search, and refining mathematical arguments … The final proof has been formally verified in Lean.”

• Fermionic n-representability (Nicholas C. Rubin, Google Quantum AI, & A. Eugene DePrince III, 2610.2073712). A complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy (exponential cost, as the authors say). AI: “The key components of the constructive solution are the work of humans, but some key proofs come from LLMs. Specifically, the reduction of degree-4 multiplier polynomials to degree-2 multiplier polynomials … along with the proof for the sufficiency of wnΣη,≤2 in Section III B were derived by OpenAI’s Astra-6 pro model.” Gemini 3.1 Pro suggested a counterexample to an earlier completeness claim.

• Duffus’s A^A question, two short proofs (George Grätzer, 2610.2080213). One proof is his, the other is ChatGPT’s (Section 4), set as a challenge: “My conclusion from this experiment is that ChatGPT is fully competitive with my own mathematical research abilities. If I look just a year ahead … I expect the comparison will be overwhelmingly in ChatGPT’s favor.”

• An auto-research system writes an optimisation paper (Wendao Wu, …, Zhouchen Lin, Peking University, 2610.2220814). Matching gradient–Hessian query lower bounds. “Nearly the entire research pipeline for this paper was carried out by Colombo, our laboratory’s internal auto-research system, powered by GPT-5.6 Sol.” Similar in convex optimisation: Rudomanov, Fomin, Gasnikov & Stonyakin’s (L₀,L₁)-smooth oracle complexity (2610.21461: “The models Codex Astra 6 and Claude Opus 5.5 were used in obtaining the theoretical results”); Liang & Luo’s matching stochastic bound (2610.21692: “The construction in the lower-bound was discovered with the assistance of ChatGPT 5.5 Pro”).

• Lean-checked physics lemma (Sarang Gopalakrishnan & Romain Vasseur, 2610.20724). A bound on long-lived local coherences in quantum-group-symmetric spin chains; the overlap-inequality proof “was generated with the assistance of large language models with minimal human input, and has been formalized and machine-checked in Lean 4 (Mathlib)”.

• Zeta second moment along Gram points (Dundulis, Garunkštis, Laurinčikas & Šimėnas, 2610.22107). Proofs “developed with assistance from ChatGPT in exchanges on 21 August 2026”; the authors note their 7/8 and 11/12 thresholds also appear in OpenAI’s “Quasi-Riemann Hypothesis” preprints released on 6 Oct.

• Heegaard Floer pillowcase (Eaman Eftekhary & Marzieh Souri, 2610.21153): “The bi-grading theorem (Theorem 2.6) was formulated and proved through correspondence with GPT-6”, and “GPT-6 provided a counterexample to this conjecture” (the authors’ own guess about all slope pairs).

• Gewu Intelligence Lab again (Qihang Wang & Weiye Li, 2610.22082): exact exponent 2^⌊k/2⌋ for the integral saturation of Bouc’s hook cycles; “OpenAI GPT-6.1 Sol developed the saturation, integral-action, finite-state and fixed-space arguments … and drafted the expanded manuscript”.

• Preprocessed 3SUM from reals to integers (Nick Fischer & Jonas Schmidt, 2610.21961): ChatGPT 5.6 Sol “suggested the general approach based on linear algebra”, the rest was developed without AI.

• Optimal gap-majority lemma for bounded-round communication (Pachara Sawettamalya, 2610.22313): GPT 5.6 Sol proposed an entropy bound and “identified the need for the ‘smoothing’ assumption, addressing a gap that the author had missed”.

• Quantum no-signalling-assisted zero-error capacity (Xin Li & Yinan Li, 2610.21071): ChatGPT used “in developing the mathematical arguments and proofs in IV-E and V-B–V-G”.

• Range weighted LIS queries (Keisuke Korogi, 2610.20983): ChatGPT “assisted with literature searches, algorithm design, proof development and checking, counterexample searches, implementation”.

• Lotka–Volterra fixed-point abundances (Ph. Jacquod, 2610.22183): free GPT-5.6 Luna, Claude Sonnet 5.5 and Gemini 3.6 Flash, chats public; Gemini linked the expansion to Catalan and Narayana numbers, and “Claude spontaneously suggested to instead use the cavity method”.

• Gravitational-wave tails to all orders (Debanjan Karan & Babli Khatun, 2610.20770): ChatGPT-6 Astra and Claude Opus 5.5 for algebra; “Claude Opus 5.5 identified the agreement of eq.(3.12) with ref.[59]”.

• Star-ordered rotor loops in Clifford algebras (Nik Jenzer, 2610.21593): “the content authorship lies with the language model” (Claude Sonnet/Opus), the author holding editorial control.

• Quantum McKay correspondence in type D (Andrea Brini & Jingxiang Ma, 2610.22359): Claude Code (Fable 5.1) review of their Wolfram code “identified for us the source of the discrepancy” in the literature; detailed disclosure following “the AIxMaths upheaval of the summer of 2026”.

• Two-variable logic on 2-D structures, settling three finite-satisfiability cases open for two decades (Bednarczyk, Kojelis & Szymański, 2610.20937): results human (“We developed the main results and first versions of most proofs without AI assistance”), but Claude Opus 5.5 “found an error in an earlier version of Lemma 3.4”.

• Interchange-process mixing (Gil Alon, 2610.22151): proofs “partially assisted by ChatGPT Pro and Astra models, and so were the simulations behind Conjecture 1.5”.

• cscK metrics near the canonical class (Frederick Tsz-Ho Fong & Junbang Liu, 2610.21934): ChatGPT 6 asked “to produce counterexamples or proofs in special cases”; key estimates human.

• Also: ballistic deposition gaps with a Claude-assisted Lean formalisation of the combinatorial lemmas (2610.21094); triple Schubert coefficients with GPT 5.6 Sol through Codex (2610.21053); friends-and-strangers graphs, ChatGPT found Example 7.4 (2610.20648); BCOV quantisation with ChatGPT 6 Astra (2610.21927); Bergman spaces with Astra (2610.21749); exchange networks with a Claude coding agent checked by DeepSeek-V4-Flash and Codex (2610.22093).

Explicitly no AI

• A stronger spectral bound for the clique number, where the Elphick–Wocjan conjecture holds in an example (2610.21388): “The authors declare that no AI tools were used to conduct this research.” Incremental exact vertex connectivity (2610.21531): results “obtained without the use of artificial intelligence” (Gemini 3.1 Pro for TikZ only).

One day’s listing again holds a dozen named conjectures or published questions where a model contributed the first proof, a key reduction, a counterexample or the whole result. Two patterns are new here: small companies running multi-model “research frameworks” (Altifina, Gewu Intelligence Lab) as co-authors, and senior physicists handing whole derivations to a model with a second model as referee. Several items (6-D Tarski, Hegselmann–Krause) build on AI-assisted papers from earlier weeks.