---
id: "2026-11-03-ai-assisted-results-november-3-listing"
url: "https://postcutoff.com/e/2026-11-03-ai-assisted-results-november-3-listing/"
as_of: "2026-11-09T21:13:00+01:00"
date: "2026-11-03"
date_precision: day
category: science
importance: 2
confidence: medium
status: [Awaiting review]
verification: Lean-verified
sources: 13
editor: human editor
human_review: null
version: "2026-11-03"
---

As of: 2026-11-09 21:13 CET.
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/2026-11-03-ai-assisted-results-november-3-listing/

# AI-assisted results, 3 Nov: arXiv of 3 Nov and Hexagon of 2–3 Nov

Full title: AI-assisted results in the 3 Nov 2026 sweep: a second Erdős–Hajnal proof for paths, D₄ as optimal 4D lattice quantizer, the Díaz–Park sharpness conjecture in Lean and Rocq, unitaryQIP = unitaryPSPACE, no bound helium dianion, R(k) ≤ 3.7698^k, plus 45 Hexagon works

Catalogue of AI-disclosing papers from the arXiv announcement of 3 Nov 2026 (and late items of 30 Oct–2 Nov), Hexagon works of 2–3 Nov not cited before, 10 lines of the Hexagon backlog and the result-repository commits of 1–3 Nov, beyond the items with own entries. AI statements are quoted from PDFs or Hexagon provenance records (Hexagon does not judge correctness); none of these papers is refereed.

## Key facts
- Own entries from this sweep: [2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt](https://postcutoff.com/e/2026-11-03-kronheimer-mrowka-dodecahedron-web-instanton-homology-64-chatgpt/index.md) (Hexagon 2611.00021), [2026-11-03-alon-seymour-thomas-separator-conjecture-gpt-6-astra-two-proofs](https://postcutoff.com/e/2026-11-03-alon-seymour-thomas-separator-conjecture-gpt-6-astra-two-proofs/index.md) (arXiv 2611.00663, 2610.40270), [2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra](https://postcutoff.com/e/2026-11-03-mixed-volume-fpras-gurvits-conjecture-disproved-gpt-6-astra/index.md) (arXiv 2611.01368), [2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs](https://postcutoff.com/e/2026-11-03-reed-muller-rm19-covering-radius-242-three-proofs/index.md) (arXiv 2611.00890, 2611.00070)
- Erdős–Hajnal for every path, second proof: Shenwei Huang, Yidong Zhou, Yuwen Zhou (arXiv 2611.01963): 'The proof presented in this paper was developed through an interactive dialogue with Claude Opus 5.5 (Anthropic) and ChatGPT-6 (OpenAI) … the AI generated the initial draft under the authors' guidance' (see [2026-10-17-erdos-hajnal-all-paths-nguyen-astra-deepmind](https://postcutoff.com/e/2026-10-17-erdos-hajnal-all-paths-nguyen-astra-deepmind/index.md))
- Lattice quantizers: Tianle Liu (arXiv 2611.00100) proves D₄ uniquely minimizes the normalized second moment among 4-dimensional lattices (computer-assisted, secondary cones and sums of squares) and proves Ajjanagadde's circular-cone concavity conjecture; 'Generative AI tools were used to discuss research ideas and to assist with verification code'
- Fusion systems: Baoyu Zhang and Shengmin Zhang (arXiv 2611.02043) prove the Díaz–Park sharpness conjecture for all saturated fusion systems; 'Shengmin Zhang first found a candidate proof … via interacting with ChatGPT'; checked in 61,849 lines of Lean and 99,857 lines of Rocq, with Claude Code examining the check logs
- Quantum complexity: Entong He, Fengning Ou, Mingnan Zhao (arXiv 2611.02819) prove unitaryQIP = unitaryPSPACE (Rosenthal–Yuen classes); 'GPT-6 helped sketch the argument that, for unitaryPSPACE families, the oracles … can be replaced by a PSPACE language'
- Dynamics: Barthelmé, Salmoiraghi, Tsang (arXiv 2611.00977), 'There is only one transitive Anosov flow' (dim 3, orientable foliations, up to bicontact padding and Goodman surgeries): an LLM proofreading pass found an error and 'The model (ChatGPT-6 Astra, using a "plus" subscription) was then asked for a fix … which is now Proposition 5.1'. Also Ding–Tong, finite-regularity counterexamples to Katok's periodic-point conjecture (2611.01980, GPT-6 for 'certain details'); Caby (CNRS), SRB measures for Rössler systems near c = 5.7 (Hexagon 2610.00676, 'Primarily AI-generated', all checked by a human, Claude Opus 5.5)
- Mathematical physics: Alec Shelley and Daniel Tartakovsky (Stanford), 'A Bound Helium Dianion Does Not Exist' (Hexagon 2611.00041): E₄(Z=2) = E₃(Z=2), so a helium nucleus binds at most three electrons; approach developed 'in conversation with Anthropic's Claude (Claude Fable)', a second Claude instance ran the certification on Stanford's Sherlock cluster (~560 CPU core-hours); only some parts human-checked. Basu–Midha (arXiv 2611.03624) prove Okuyama's Lee–Yang conjectures for q-deformed oscillators and doubly-scaled SYK; Theorem 1.7 'proven in multiple sequential interactions with ChatGPT-5.6-Sol-Plus'. Masaki Oshikawa (arXiv 2610.41256), faster-than-power-law decay in the 2D RP² model, 'a rigorous result by vibe-proving'
- Ramsey numbers: Ella Puerto (Hexagon 2611.00026) iterates the Gupta–Ndiaye–Norin–Wei method to a computer-verified R(k) ≤ 3.7698^{k+o(k)} (GNNW had 3.7992 and an unverified AI-suggested 3.78233); 'Claude wrote the Python software, ran the parameter searches and interval-arithmetic checks, and drafted the manuscript'; two independent verifiers, two lemmas in Lean
- Other arXiv items with AI-originated proofs: Gan–Xie–Zhou, inverse hybrid Kazhdan–Lusztig positivity, 'proofs … developed almost entirely by GPT-6 Astra' (2611.00882); Yair Lavi proves his 2018 conjecture on the maximum diagonal product of bounded-rank stochastic matrices, 'carried out by GPT-5.6-sol, GPT-6 Astra, Claude Fable 5, and Claude Fable 5.1' (2611.01763); Shunia, deterministic primality test with one binomial congruence, proofs written by GPT-6 Astra (2611.02280); online carpooling (2611.00388, approach first proposed by GPT-6 Astra); parity decision trees of depth O(4^d log‖f̂‖₁) with GPT Astra (2611.03452); sharp Stein–Tomas on S¹ with GPT-6 Pro (2611.01318); Krzyż's conjecture for a₇ (2611.00397, GPT-6.1 Sol for code and checks); Topping's diameter conjecture for immersed surfaces (2611.01589); Duke–Erdős question on intersecting hypergraphs answered (2611.01915); NP-hardness reduction for Gromov–Wasserstein found with Claude Opus 5 (2611.00479); two Bergeron conjectures (2611.00629); Wooley's L¹ question for Beatty sequences, counterexample (2611.01494); Calvert–Vamanamurthy local-to-global minimum problem (2611.02068); irrationality exponent of ζ(5) ≤ 171 and of Γ(1/4), Γ(1/3) by David Niedbala Giraudin with Claude (2611.01708, 2611.01711); Cao–Păun, 'Human Variations on AI Mathematics', an alternative proof of a theorem in an OpenAI manuscript on log abundance (2611.03225)
- Hexagon 2–3 Nov (provenance quoted from the records): Qiyue Tang (Tsinghua; ChatGPT-6-Pro sessions, Codex, Rethlas-OSV review) claims Hilton's 1977 conjecture on cycle multiplicities (2611.00028, ~56 min session), Kourovka Problem 21.3 second question on soluble subgroup pairs for n ≥ 21 (2611.00042), Castronovo–Gorsky–Simental–Speyer Conjecture 4.45 (2611.00022) and Banaian–Huang Question 35 (2611.00023); Uskov, Chervov, Levkovich-Maslyuk et al., exact diameter of S_n with LX generators, a question from the 1960s, proof 'obtained by our agentic system' with GPT-6 Astra, formalization attached (2611.00039); Lucas Almeida, inverse problem for connected induced subgraphs with Claude Opus 5.5 and Lean (2611.00029); twinheterodox, linear independence of even Dirichlet beta values with Codex 'Astra-6-Max' (2611.00044); Arhancet, Haagerup symmetries of the E₈ theory (2611.00034) and column rigidity (2611.00038, human); Nikzad–Frinkle–Bagherzadeh, Collatz reciprocal-sum bounds, not a proof of the conjecture (2611.00033)
- Hexagon, Claude-run deposits by David Niedbala Giraudin with 'None of this contribution has been checked and understood by any human' and 'No professional mathematician has reviewed the note yet' (claims only): Hatada's 1981 question answered for a ≤ 10, negative for a = 11–13 (2611.00035); Allouche–Han–Niederreiter Hankel-determinant question (2611.00032); two Gallardo–Rahavandrainy conjectures on binary Collatz trinomials (2611.00031) and c_M at Mersenne exponents (2611.00025); odd perfect polynomials over F₂ (2611.00030); Casas-Alvero type descent (2611.00040). Frank Vega with Claude Opus 5.5: Nicolas's question on 2^{v₂} sums (2611.00027) and a MIDS heuristic (2611.00043). Human-written, out of AI scope: Zeng Chunping (2610.00712, 2610.00691, 2610.00687), K. Mahesh Krishna (2611.00024), Kaminsky (2610.00678)
- Hexagon backlog (10 lines processed): Cédric Arhancet, Pisier's operator Hilbert space OH embeds completely isometrically into the predual of a QWEP von Neumann algebra, 'answering a longstanding question', primarily human-written (2610.00555); Peter Lim, a connectedness-preserving bijection of Rⁿ whose inverse is not, 'read by Willie Wong, the person who posed the question' (2610.00543, primarily AI-generated); Deep Bhattacharjee, a survey of 36 statements of Ashoke Sen with Claude and GPT tools (2610.00564); Machado Manhães de Castro, edge multiset dimension (2610.00562); Almeida, finite cardinalities of the hyperspace of regular subcontinua (2610.00546); Y. T. Miah with GPT-6 Pro (2610.00541); human: Mahesh Krishna (2610.00547), Zhenyu Sun (2610.00557, 2610.00556), Zeng Chunping (2610.00544)
- Result repositories: formal-conjectures added a formalization of Maxwell's point-charge conjecture and its refutation by Arathoon–Ball–Kvalheim (arXiv 2607.27197; see [2026-07-29-maxwell-point-charge-conjecture-false](https://postcutoff.com/e/2026-07-29-maxwell-point-charge-conjecture-false/index.md)) and linked a Palomar-registered Lean proof of Luca's abc-conditional variant of Erdős 393 (veljjanoski/erdos393-palomar); mathcommunity/oai-math-revised commits are About/Contribute site text. GitHub: AxiomMath/CFSGCorollary (Lean proof that every finite simple group is 2-generated, on top of Axiom's CFSG; see [2026-10-27-axiom-cfsg-classification-finite-simple-groups-lean](https://postcutoff.com/e/2026-10-27-axiom-cfsg-classification-finite-simple-groups-lean/index.md)); google-deepmind/gbench, detectorscope, anthropics/FlashProve and QwenLM/BlenderWorld are tooling
- Checked, no AI statement among conjecture papers: Zariski closure conjecture (2611.00757), counterexample to Lee's conjecture on pseudo-Einstein structures (2611.02718), 1-2-3 conjecture for Borel combinatorics (2611.03320), Yang–Koolen conjecture (2611.00591), K-theory torsion counterexamples for crystallographic groups (2611.00493), Hilton–Zhao vertex-splitting for triangle-free graphs (2610.41984), Paine conjecture model (2611.02246)

## What happened

See key facts. Beyond the four own entries, the items of note are a second, independent AI-assisted proof of the Erdős–Hajnal property for all paths, Liu's proof that D₄ is the optimal 4D lattice quantizer, the Lean- and Rocq-checked Díaz–Park proof that began with a ChatGPT candidate, and a Stanford computer-assisted proof, partly run by Claude, that helium cannot bind four electrons.

## What is disputed or not yet verified

- Verification: Unrefereed preprints and Hexagon deposits; Lean/Rocq for some

## Your AI and this story

- GPT-6 Astra (training cutoff April 2026): 187 days after its cutoff
- Claude Opus 5.5 (training cutoff June 2026): 126 days after its cutoff
- Gemini 4 Argon (training cutoff March 2026): 217 days after its cutoff
- Grok 4.7 (training cutoff May 2026): 156 days after its cutoff

## Sources

1. [arXiv 2611.01963: The Erdős–Hajnal property for paths (Huang, Zhou, Zhou)](https://arxiv.org/abs/2611.01963) (arxiv.org, paper)
2. [arXiv 2611.00100: The optimal four-dimensional lattice quantizer (Liu)](https://arxiv.org/abs/2611.00100) (arxiv.org, paper)
3. [arXiv 2611.02043: A proof of the sharpness conjectures for all saturated fusion systems](https://arxiv.org/abs/2611.02043) (arxiv.org, paper)
4. [arXiv 2611.02819: unitaryQIP = unitaryPSPACE](https://arxiv.org/abs/2611.02819) (arxiv.org, paper)
5. [arXiv 2611.00977: There is only one transitive Anosov flow](https://arxiv.org/abs/2611.00977) (arxiv.org, paper)
6. [Hexagon 2611.00041: A bound helium dianion does not exist (Shelley, Tartakovsky)](https://hexagonmath.org/abs/2611.00041) (hexagonmath.org, paper)
7. [Hexagon 2611.00026: R(k) ≤ 3.7698^{k+o(k)} (Puerto)](https://hexagonmath.org/abs/2611.00026) (hexagonmath.org, paper)
8. [Hexagon 2611.00028: Hilton's conjecture on cycle multiplicities (Tang)](https://hexagonmath.org/abs/2611.00028) (hexagonmath.org, paper)
9. [Hexagon 2611.00039: Exact diameter of the symmetric group with LX generators](https://hexagonmath.org/abs/2611.00039) (hexagonmath.org, paper)
10. [Hexagon 2611.00035: Hatada's question (Niedbala Giraudin)](https://hexagonmath.org/abs/2611.00035) (hexagonmath.org, paper)
11. [Hexagon 2610.00555: OH embeds into a noncommutative L¹-space (Arhancet)](https://hexagonmath.org/abs/2610.00555) (hexagonmath.org, paper)
12. [AxiomMath/CFSGCorollary](https://github.com/AxiomMath/CFSGCorollary) (github.com, code)
13. [formal-conjectures commit: Maxwell conjecture and refutation](https://github.com/google-deepmind/formal-conjectures/commit/7bdc4a42f24c0316f81c73b26121794b2bed96a3) (github.com, code)

## Changes

- 2026-11-03 (filed): Created

## Related

- 2026-11-02: [AI-assisted results, 2 Nov: arXiv of 2 Nov and Hexagon of 1–2 Nov](https://postcutoff.com/e/2026-11-02-ai-assisted-results-november-2-listing/index.md)