The log-modularity conjecture for strongly-finite VOAs

Let $\mathcal{V}$ be a strongly-finite VOA, and let $\mathrm{Mod}^{g.r}(\mathcal{V})$ denote its category of grading-restricted generalized modules. A log-modular tensor category is a finite ribbon tensor category whose double is equivalent to the Deligne product of the category with its opposite. Log-modularity conjecture. The category

$$\mathrm{Mod}^{g.r}(\mathcal{V})$$

is a log-modular tensor category. This is proposed as the non-semisimple analogue of modularity for strongly-rational VOAs and is intended to connect VOA representation categories with Lyubashenko's theory and quantum doubles; the source states it as a conjecture.