Benson–Etingof–Ostrik conjecture: full proof generated by GPT-6 Astra
Awaiting review
Importance: major (4 of 5)The takeaway
A month after the finite case, the full 2023 conjecture on symmetric tensor categories in positive characteristic is claimed in a paper ‘generated by GPT-6 Astra’, posted by a team that includes Etingof and Ostrik, who posed it.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Expert-checked
- Importance
- Major (4 of 5)
- Last verified
- 12 November 2026
Your AI and this story
- GPT-6 Astra195 days after its cutoff
- Claude Opus 5.5134 days after its cutoff
- Gemini 4 Hydrogen225 days after its cutoff
- Grok 4.7164 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 134 days before it.
Key facts
- Claim: the conjecture ‘in full generality’ ([BEO23, Conjecture 1.4]): moderate-growth symmetric tensor categories in characteristic p > 0 fibre over higher Verlinde categories Ver_{p^∞}
- Method (abstract): maximal nilpotence and geometric reductivity reduce it to showing that finitely generated maximally nilpotent tensor categories are finite; main ingredients are generic points built from alternating norms and a Frobenius reduction of the fundamental coend to an ordinary Hopf subalgebra
- Provenance (Hexagon): ‘The paper was generated by GPT-6 Astra. The contributors asked questions, suggested reduction arguments, and shared proof ideas based on their experience from previous projects and on discussions among the contributors.’ Text ‘Primarily AI-generated’; human understanding ‘some’
- Comment on the record: ‘The authors plan to turn this AI generated proof into a human paper.’
- Earlier step: Coulembier and Flake proved the finite case (arXiv 2610.04096, Oct 2026), with the main ideas of Sections 3–4 ‘originally obtained using GPT-6 Astra’; OpenAI’s 6 Oct release also claimed the finite case
- People: Pavel Etingof (MIT) and Victor Ostrik (Oregon) are two of the three authors of the conjecture (with Dave Benson); Etingof also deposited a ChatGPT-produced answer to the Etingof–Gelaki finiteness question on 10 Nov
- Status: unrefereed, no Lean; no outside reaction found by 12 Nov
What happened
On 11 Nov 2026 Hexagon published a paper claiming the full Benson–Etingof–Ostrik conjecture. Its five listed contributors are specialists in tensor categories, and two of them, Etingof and Ostrik, posed the conjecture with Dave Benson in 2023. The provenance statement says the paper itself was generated by GPT-6 Astra, with the humans asking questions and proposing reductions; they say they will turn it into a human-written paper.
Why it matters
The conjecture describes all “reasonable” symmetric tensor categories in positive characteristic, an analogue of Deligne’s theorem in characteristic zero. It is unusual that the conjecture’s own authors co-sign a deposit that they describe as written by a model. The claim has not been refereed.
What is disputed or not yet verified
| Verification | Unrefereed Hexagon deposit; partly checked by the contributors |
|---|
Sources
2 sources from 2 sites. Numbers match the chips in the text.
2 sources: 2 primary
Primary
- Hexagon 2611.00301: The Benson–Etingof–Ostrik conjecturehexagonmath.org, paper
- arXiv 2610.04096: finite case (Coulembier, Flake)arxiv.org, paper
Changes
- Filed (science agent; Hexagon record and PDF read)