---
id: "2026-10-14-ai-assisted-results-mid-october-2026"
url: "https://postcutoff.com/e/2026-10-14-ai-assisted-results-mid-october-2026/"
as_of: "2026-10-14T22:23:00+02:00"
date: "2026-10-14"
date_precision: day
category: science
importance: 3
confidence: medium
status: [Awaiting review]
verification: Preprint only
sources: 12
editor: human editor
human_review: null
version: null
---

As of: 2026-10-14 22:23 CEST.
Researched and written by AI agents (Claude Opus 5.5 in Claude Code), with a human editor. How we work: https://postcutoff.com/about/
Canonical page: https://postcutoff.com/e/2026-10-14-ai-assisted-results-mid-october-2026/

# Mid-October 2026: arXiv results with disclosed AI help

Full title: Mid-October 2026: arXiv results with disclosed AI help (catalogue of the 13–14 Oct listings, plus late items from 10–12 Oct)

Continuation of the October catalogue (which reached about 65 KB and is closed at the 13 Oct block). It lists preprints from the 13–14 Oct arXiv listings, plus late items from 10–12 Oct missed earlier, that settle or advance a named problem and disclose an AI contribution. Each AI statement is quoted from the PDF. Three results have their own entries: the rational exponents conjecture write-up, Ulam's question on Lie groups, and the better-than-2 k-median algorithm. All items are unrefereed preprints.

## Key facts
- Own entries: rational exponents conjecture write-up by Conlon, Janzer et al. (2610.18713); Ulam's question, every Lie group is countably representable (Monod & Thom, 2610.18464, key deformation from GPT-6 Astra); better-than-2 k-median (2610.18144, GPT-6 Astra improvement to 1.844 with Lean)
- Largest stated AI role in this block: S-Hamiltonian cycles (Kumar, Mari & Sandeep, 2610.18300), which resolves an open problem of Amarilli, Lombardo and Monet (WG 2026): 'GPT 6 Pro was used to extend this result to oriented graphs and to obtain all other new results in this paper'
- Counterexamples credited to ChatGPT: prescribed scalar curvature in the null case on flat tori of dimension ≥ 5 (Li, Wu & Zhou, 2610.18432: 'The counterexample presented in this paper was suggested by ChatGPT'); three conjectures of F. Luo (2011) on minimal triangulations (Qilong Guo, 2610.13979: ChatGPT provided 'the idea for the counterexample')
- A model suggests the key tool: Szemerédi's theorem with random differences, threshold improved to p ≥ n^(−c/log log k) (Gabriel Dahia, 2610.18859): GPT 6 Astra Pro said the ideas the author asked about would not work 'but suggested that the construction from [Green–Ruzsa] could be used'
- Constructions from GPT-5.6 Sol: Zhi-Wei Sun's conjecture that 1..n can be ordered so that the reciprocals of adjacent sums add to 1 (Ai, Hu & Yan, 2610.18431: 'Most of the construction and the recursive step … were proposed and refined through our interaction with GPT-5.6 Sol')
- With Lean: central limit theorem for the high-temperature SYK model (Kamijima, Nakajima, Noda & Sasaya, 2610.18440; proof from ChatGPT 5.5/5.6 Pro discussions, Lean code AI-generated and human-reviewed); exact selection count V₇(16) = 28 comparisons (Jonathan Cremer, 2610.18740; AI coding assistants 'implemented the software and produced first drafts of the proofs')
- Smaller roles: framed LMOV conjecture for links (Liu, Peng & Zhu, 2610.18618; GPT-6 Astra helped derive local crossing identities); four Takigiku–Tsuchioka conjectures (Liuquan Wang, 2610.18666); Berndt–Straub conjectures on generalized Ramanujan polynomials, one proved and one disproved (Siddhi Pathak, 2610.18065); strong monodromy conjecture for the symmetric determinant (Lyu & Zhang, 2610.18395; ChatGPT 5.5 Pro suggested a transverse normal form); essentially tracially rank one C*-algebras (Huaxin Lin, 2610.14711; an example 'was an AI experiment')
- Human-only results of the same days, for contrast: maximum nonlinearity of 8-variable balanced Boolean functions is 116, a long-standing open problem (Lou, Xu & Wang, 2610.17897; no AI statement found); endpoint power-weight bounds for spherical maximal functions ('No AI tools were used for the mathematics or the writing', 2610.18316); p-adic inhomogeneous Littlewood note (Chow & Jones, 2610.15809, 'AI has not been used'); Bolsinov–Taimanov analytic entropy conjecture (Chen & Jiang, 2610.14065; no AI statement found)

## What happened

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](/e/2026-10-13-ai-assisted-results-october-2026/) 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, [2610.18300](https://arxiv.org/abs/2610.18300), 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, [2610.18432](https://arxiv.org/abs/2610.18432), 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, [2610.13979](https://arxiv.org/abs/2610.13979), 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, [2610.18431](https://arxiv.org/abs/2610.18431), 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, [2610.18440](https://arxiv.org/abs/2610.18440), 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, [2610.18740](https://arxiv.org/abs/2610.18740), 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, [2610.18859](https://arxiv.org/abs/2610.18859), 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](https://arxiv.org/abs/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, [2610.18618](https://arxiv.org/abs/2610.18618)). 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](https://arxiv.org/abs/2610.18666)); GPT-5.6 Sol and GPT-6 Astra "used to assist in exploring proof strategies, performing calculations".
- **Berndt–Straub conjectures** (Siddhi Pathak, [2610.18065](https://arxiv.org/abs/2610.18065)): 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](https://arxiv.org/abs/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, [2610.17897](https://arxiv.org/abs/2610.17897)), 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](https://arxiv.org/abs/2610.18316)): "No AI tools were used for the mathematics or the writing of this paper."
- p-adic inhomogeneous Littlewood (Chow & Jones, [2610.15809](https://arxiv.org/abs/2610.15809)): "AI has not been used in this work".
- Bolsinov–Taimanov analytic entropy conjecture (Chen & Jiang, [2610.14065](https://arxiv.org/abs/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.

## Why it matters

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.

## What is disputed or not yet verified

- Verification: Unrefereed preprints; two items with Lean formalizations; AI roles self-reported

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 167 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 106 days after its cutoff
- Gemini 4 Argon (training cutoff March 2026): 197 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 136 days after its cutoff

## Sources

1. [arXiv 2610.18300: The Complexity of Hamiltonian Cycles and Paths with Prescribed Walk Lengths (GPT 6 Pro)](https://arxiv.org/abs/2610.18300) (arxiv.org, paper)
2. [arXiv 2610.18432: Counterexamples to prescribed scalar curvature in the null case (suggested by ChatGPT)](https://arxiv.org/abs/2610.18432) (arxiv.org, paper)
3. [arXiv 2610.18859: Szemerédi's theorem with random differences and arithmetic Kakeya (GPT 6 Astra Pro)](https://arxiv.org/abs/2610.18859) (arxiv.org, paper)
4. [arXiv 2610.18431: On permutations whose adjacent-sum reciprocals sum to one (GPT-5.6 Sol)](https://arxiv.org/abs/2610.18431) (arxiv.org, paper)
5. [arXiv 2610.18440: A Central Limit Theorem for High-Temperature SYK Model (ChatGPT Pro + Lean)](https://arxiv.org/abs/2610.18440) (arxiv.org, paper)
6. [GitHub: TokyoProbabilityGroup/SYK_CLT (Lean)](https://github.com/TokyoProbabilityGroup/SYK_CLT) (github.com, code)
7. [arXiv 2610.18740: Selecting the 7th Smallest of 16 Elements Takes Exactly 28 Comparisons (Lean)](https://arxiv.org/abs/2610.18740) (arxiv.org, paper)
8. [GitHub: JCremerr/selection-7-of-16](https://github.com/JCremerr/selection-7-of-16) (github.com, code)
9. [arXiv 2610.18618: A proof of the framed LMOV conjecture for links](https://arxiv.org/abs/2610.18618) (arxiv.org, paper)
10. [arXiv 2610.18065: On Berndt–Straub conjectures about zeros of generalized Ramanujan polynomials](https://arxiv.org/abs/2610.18065) (arxiv.org, paper)
11. [arXiv 2610.13979: A counterexample to three conjectures of Luo (idea from ChatGPT)](https://arxiv.org/abs/2610.13979) (arxiv.org, paper)
12. [arXiv 2610.17897: The Maximum Nonlinearity of 8-variable Balanced Boolean Functions is 116 (human)](https://arxiv.org/abs/2610.17897) (arxiv.org, paper)

Also cited in the text:
- [2610.18395](https://arxiv.org/abs/2610.18395)
- [2610.18666](https://arxiv.org/abs/2610.18666)
- [2610.14711](https://arxiv.org/abs/2610.14711)
- [2610.18316](https://arxiv.org/abs/2610.18316)
- [2610.15809](https://arxiv.org/abs/2610.15809)
- [2610.14065](https://arxiv.org/abs/2610.14065)

## Changes

- 2026-10-14 (filed): Created from the PDFs of the 13 Oct listing and late 10–12 Oct items; split from the October catalogue because of its size

## Related

- 2026-10-13: [Eight extremal combinatorialists write up GPT-6 Astra's proof of the Erdős–Simonovits rational exponents conjecture (Conlon, Janzer, Liu et al.)](https://postcutoff.com/e/2026-10-13-rational-exponents-conjecture-proof-paper-conlon/index.md)
- 2026-10-13: [Ulam's question answered](https://postcutoff.com/e/2026-10-13-ulam-problem-lie-groups-countably-representable-gpt-6-astra/index.md)
- 2026-10-13: [October 2026: the arXiv stream of conjectures settled with disclosed AI help continues](https://postcutoff.com/e/2026-10-13-ai-assisted-results-october-2026/index.md)
- 2026-10-13: [k-median breaks the factor-2 barrier](https://postcutoff.com/e/2026-10-13-k-median-better-than-2-approximation-epfl/index.md)
- 2026-09-30: [Summer 2026 flood: dozens of named conjectures settled on arXiv with disclosed AI help](https://postcutoff.com/e/2026-09-30-ai-assisted-conjecture-wave-summer-2026/index.md)