The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories
In characteristic zero, Deligne's theorem gives every symmetric tensor category of moderate growth a fiber functor to supervector spaces. In characteristic , Benson, Etingof and Ostrik constructed the tower of higher Verlinde categories and conjectured that every symmetric tensor category of moderate growth over an algebraically closed field of characteristic admits a fiber functor to the union of this tower. Ostrik proved it for fusion categories (to ). Does every finite symmetric tensor category in characteristic , including , admit a fiber functor to some ?
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Tensor categories; positive characteristic, Verlinde categories
- Posed by
- D. Benson, P. Etingof and V. Ostrik, New incompressible symmetric tensor categories in positive characteristic, Duke Math. J. 172 (2023), Conjecture 1.4
- Year posed
- 2023
- Years open
- 3y
- Solved
- 2026-09-24
- Model
- Unreleased internal OpenAI model
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Collection
- OpenAI math release (October 2026), version adc7f12
- Significance
- 28 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Theorem 1.1: every finite symmetric tensor category over an algebraically closed field of characteristic has a fiber functor to a single finite level , including . Consequences stated: classification of finite incompressible categories (the finite case of Coulembier-Etingof-Ostrik's Conjecture B), uniqueness of the functor in characteristic two via their subterminality theorem, and a generalized Tannakian realization. The full conjecture for non-finite categories of moderate growth is not addressed.
What the AI did
The release README says all results were produced by an unreleased internal OpenAI model with a fixed procedure, on average about three hours of ChatGPT Pro thinking compute per result. This result is not among the README's exceptions (the Hodge conjecture for CM abelian varieties and the Re(s) > 11/12 zero-free region). The manuscript is authored 'OpenAI' and names no human author.
Verification
No independent mathematician has checked this yet. Checked here: Theorem 1.1 was read against BEO Conjecture 1.4 as the paper states it; it claims a -linear exact faithful strong symmetric monoidal functor for every finite symmetric tensor category, every prime including 2, with depending on . The proof was not refereed and is not formalized. The paper itself limits the claim to finite categories and makes no assertion for general moderate-growth categories.