Classification of invertible bosonic GQLs by modular extensions

Let $G$ be a symmetry group and let $\cE=\operatorname{Rep}(G)$. A modular extension $\cM$ of $\cE$ is a UMTC containing $\cE$ fully faithfully and satisfying the defining centralizer condition. Bosonic GQL classification conjecture. Invertible bosonic GQLs with symmetry $\cE=\operatorname{Rep}(G)$ are classified by $(\cM,c)$ where $\cM$ is a modular extension of $\cE$ and $c=0$ modulo $8$. This is intended to capture gauged symmetry data and the vanishing-modulo-$8$ central charge of invertible bosonic phases; the source gives no resolution of the conjecture.