Finite symmetric tensor categories and the Verlinde tower

What OpenAI claims

Proves that every finite symmetric tensor category over an algebraically closed field k of characteristic p > 0 admits a k-linear exact faithful strong symmetric monoidal fiber functor to a higher Verlinde category Ver_pⁿ. The level may depend on the category, and the theorem includes characteristic two, resolving the finite case of the Benson–Etingof–Ostrik conjecture.

Paper

1. Fiber functors for finite symmetric tensor categories in positive characteristic

   24 September 2026 · Preprint, not peer reviewed · PDF

   We prove the finite case of the Benson–Etingof–Ostrik conjecture: every finite symmetric tensor category over an algebraically closed field k of characteristic p > 0 admits a k-linear exact faithful strong symmetric monoidal functor to a finite higher Verlinde category Ver _pⁿ(k). The result includes characteristic two, and the level n may depend on the category.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.