The Benson-Etingof-Ostrik conjecture for finite symmetric tensor categories

Theorem 1.1: every finite symmetric tensor category over an algebraically closed field of characteristic $p>0$ has a fiber functor to a single finite level $\mathrm{Ver}_{p^n}(k)$, including $p=2$. 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.

Theorem 1.1: every finite symmetric tensor category over an algebraically closed field of characteristic $p>0$ has a fiber functor to a single finite level $\mathrm{Ver}_{p^n}(k)$, including $p=2$. 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.