The singlet VOA rigidity conjecture

Let $\mathcal{M}(p)$ be the singlet vertex operator algebra, and let $\mathrm{\bf Rep}\,\mathcal{M}(p)$ be its representation category equipped with the $P(1)$-tensor product. The singlet rigidity conjecture. The category $\mathrm{\bf Rep}\,\mathcal{M}(p)$ is a rigid vertex tensor category, and hence in particular a ribbon category. The conjecture depends on establishing the relevant vertex tensor category structure and rigidity; the source records no resolution.