Fiber functors for finite symmetric tensor categories in positive characteristic

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 ${\mathrm{Ver}}_{p^n}(k)$. The result includes characteristic two, and the level n may depend on the category.