The semi-simplification conjecture for strongly-finite VOAs

Let $\mathcal{V}$ be a strongly-finite VOA, and let $\mathrm{Mod}^{g.r}(\mathcal{V})$ be its category of grading-restricted generalized modules. Its semi-simplification is obtained by quotienting by negligible morphisms and restricting to the full subcategory generated by simple modules. Semi-simplification conjecture. The semi-simplification is a modular tensor category, and its Grothendieck ring is the quotient of the Grothendieck ring of $\mathrm{Mod}^{g.r}(\mathcal{V})$ by the image of the $\mathcal{V}$-modules that are both simple and projective. This would connect the non-semisimple representation category to an ordinary modular tensor category and its fusion rules; the source presents it among consequences of the log-modularity conjecture.