Rationality conjecture for simple Virasoro VOAs in positive characteristic

Let $\mathbb{F}$ be a field of characteristic $p>2$, let $c\in\mathbb{F}$, and let $L_{\operatorname{Vir}}(c,0)_{\mathbb{F}}$ denote the simple quotient Virasoro vertex operator algebra. A module is called simple if it has no nonzero proper submodules, and the adjoint module is the module given by the vertex operator algebra itself. Rationality conjecture. The vertex operator algebra $L_{\operatorname{Vir}}(c,0)_{\mathbb{F}}$ is rational, and the adjoint module is the only simple module up to isomorphism. The conjecture is motivated by computations establishing this conclusion in several small-characteristic cases, while the cases not covered by those computations remain open.