Rigidity conjecture for modules over self-dual quasi-lisse vertex operator algebras

Let $V$ be a finitely strongly generated, self-dual, quasi-lisse vertex operator algebra of CFT type, and let $\mathcal{C}_V^{\mathrm{ord}}$ denote its category of ordinary modules. Rigidity conjecture for quasi-lisse vertex operator algebras. The category $\mathcal{C}_V^{\mathrm{ord}}$ has the structure of a vertex tensor category in the sense of Huang and Lepowsky. Huang established this for rational, lisse vertex operator algebras, while the corresponding statement for non-rational lisse and more general quasi-lisse algebras remains open.