Ostrik's fiber-functor conjecture for semisimple symmetric tensor categories

Let $\mathcal{C}$ be a semisimple symmetric tensor category over a field $\mathbb K$ of characteristic $p>0$ and of moderate growth. Here $\operatorname{Ver}_p$ denotes the Verlinde symmetric tensor category, and a fiber functor is a symmetric tensor functor.

Ostrik's conjecture. The category $\mathcal{C}$ admits a fiber functor

$$\mathcal{C}\to\operatorname{Ver}_p.$$

This extends Ostrik's theorem for symmetric fusion categories by removing the finiteness assumption. The source notes that it is unknown whether moderate growth is necessary. The conjecture is disproved without the semisimplicity hypothesis.