The singlet quantum-group correspondence

Let $\overline{U}_{q}^{H}s\ell(2)$ be the unrolled restricted quantum group, and let $\mathrm{\bf Rep}_{\!\mathrm{wt}\,}\overline{U}_{q}^{H}s\ell(2)$ denote its finite-dimensional weight-module category. Let $\mathcal{M}(p)$ be the singlet vertex operator algebra, and let $\mathrm{\bf Rep}_{\langle\mathrm{s}\rangle}\mathcal{M}(p)$ be the full subcategory generated by its simple modules under tensor products, finite sums, and subquotients. The singlet correspondence conjecture. There is an equivalence

$$\mathrm{\bf Rep}_{\!\mathrm{wt}\,}\overline{U}_{q}^{H}s\ell(2)\cong \mathrm{\bf Rep}_{\langle\mathrm{s}\rangle}\mathcal{M}(p)$$

as ${\mathbb C}$-linear ribbon categories. This is part of the proposed quantum-group description of the singlet VOA; the source does not state that it has been proved.