Hovey–Strickland: author says OpenAI’s paper matches his ChatGPT-uploaded draft
Awaiting review
The takeaway
OpenAI’s 6 Oct maths release includes a paper dated 24 Sept that proves Chai’s invariant-ideal conjecture and, through Barthel–Heard–Naumann, the Hovey–Strickland classification of thick tensor ideals of dualizable K(n)-local spectra (family 311). The next day Copenhagen mathematician Chenglong Ma posted his own proof on arXiv. In it he writes that OpenAI’s ‘proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.’ OpenAI’s paper does not mention him. He also reports an independent proof by Ningyi Li. We found no response from OpenAI as of 29 Oct. The allegation has not been examined publicly beyond a GitHub label and a one-comment Hacker News thread.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 29 October 2026
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None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 99 days before it.
Key facts
- Ma’s statement (arXiv 2610.10072, introduction, verbatim): ‘After the paper was written, the author learned that the same result was also proved independently and by a different method by Ningyi Li [7]. The result is also contained in a paper [8] released by OpenAI on October 6, 2026, in which the proof strategy and specific choices of notation are identical to a preliminary version of the present paper that was uploaded to ChatGPT on September 8, 2026.’
- Ma’s own AI statement: ChatGPT ‘was used on September 8, 2026 to check that the author’s method works in height-3 case’; on 10 Sept it ‘identified a problem in the original proof of theorem 6.1 concerning the passage from infinite Cartier-coordinate data to finite jets’ and suggested the fixed-jet repair of Appendix A, ‘the only part of the proof whose initial argument was generated by AI’. The idea of applying Chai’s rigidity results came from his work on Shimura varieties
- Dates: Ma’s upload to ChatGPT 8 Sept; OpenAI’s manuscript dated 24 Sept; OpenAI release 6 Oct; Ma’s arXiv posting 7 Oct. OpenAI’s paper (family 311, no Lean) names neither Ma nor Li; history.md records no change to it
- Claim of both papers: the invariant prime ideals are exactly the height ideals, which proves Chai’s invariant-ideal conjecture and, via Barthel–Heard–Naumann (Selecta Math. 2022, which settled height two), the Hovey–Strickland conjecture: n + 2 thick tensor ideals, Balmer spectrum a chain of n + 1 points
- Independent proof: Ningyi Li, ‘Invariant Ideals and the Hovey–Strickland Conjecture’ (shared as a Google Drive PDF, cited by Ma)
- Reactions found: mahrud/openai-math-comments PR #311 (9 Oct) labels the family ‘2nd-proof’ and quotes Ma; a Hacker News submission of Ma’s paper (8 Oct, 4 points) whose submitter writes there is ‘at least a non-zero probability’ that the chat was turned into OpenAI’s paper. No statement from OpenAI found
- Not established: whether OpenAI’s research models had any access to ChatGPT conversations. Ma reports similarity, not a mechanism. OpenAI has not said how its maths model’s inputs were chosen
What happened
The Hovey–Strickland conjecture predicts that the thick tensor ideals of dualizable K(n)-local spectra are only the obvious chromatic ones. Barthel, Heard and Naumann reduced it in 2022 to a conjecture of Chai about ideals of the Lubin–Tate ring that are invariant under the Morava stabilizer group, and proved the height-two case.
OpenAI’s release of 6 Oct contains a manuscript dated 24 Sept that proves both at every height. On 7 Oct Chenglong Ma posted his own proof on arXiv. In his introduction he writes that the OpenAI paper’s strategy and notation are identical to a preliminary version he uploaded to ChatGPT on 8 Sept, when he used it to check the height-three case. Two days after the upload, he says, ChatGPT found a gap and proposed the repair he kept in Appendix A. He also credits Ningyi Li with an independent proof by a different method.
Why it matters
This is a different kind of credit dispute from Jihao Liu’s priority remark or the Penrose authors’ complaint. It suggests that work a user shared with ChatGPT may have ended up, unattributed, in the lab’s own research output. Similar strategy and notation are not proof of copying. OpenAI’s maths model may have arrived at the same route independently, and Ma states no mechanism. OpenAI has not explained how it chose the inputs for its maths runs or whether ChatGPT conversations were among them, and has not credited Ma, as it did Carenini for random k-SAT.
What is disputed or not yet verified
| Verification | Unrefereed preprints; no formalization |
|---|
Sources
6 sources from 4 sites. Numbers match the chips in the text.
6 sources: 3 primary, 3 reactions
Primary
- arXiv 2610.10072: Invariant Primes in Lubin–Tate Space and Hovey–Strickland at Every Height (Chenglong Ma)arxiv.org, paper
- OpenAI: Stabilizer orbits and thick tensor ideals of dualizable K(n)-local spectra (24 Sept 2026, PDF)github.com, paper
- Background: Barthel, Heard, Naumann, On conjectures of Hovey–Strickland and Chai (Selecta Math. 2022)link.springer.com, paper
Reactions
- oai-math-revised: community notes on the OpenAI paper (follow-ups, comments)github.com, discussion
- mahrud/openai-math-comments PR #311: The Hovey–Strickland and Chai conjecturesgithub.com, discussion
- Hacker News: Invariant Primes in Lubin–Tate Space and Hovey–Strickland at Every Height (8 Oct)news.ycombinator.com, discussion
Changes
- Filed (arXiv PDF and metadata of 2610.10072, oai-math-revised AGENT_NOTES, HN Algolia)