The minimal modular extension conjecture for super-modular categories

A super-modular category is a premodular category whose Müger center is equivalent to $\sVec$. A spin modular category is a modular category containing a fermion. For a fusion category $\mathcal{B}$, write $\dim(\mathcal{B})$ for its categorical dimension. Minimal modular extension conjecture. Any super-modular category $\mathcal{B}$ is a ribbon subcategory of a spin modular category $\mathcal{C}$ such that

$$\dim(\mathcal{C})=2\dim(\mathcal{B}).$$

This is identified in the paper as the key outstanding conjecture for super-modular categories; it asserts the existence of a modular extension of the smallest possible dimension.