Cobordism hypothesis for topological quantum field theories with moduli level $m$

Let $m\geq 0$, and let ${\rm Bord}^{G}(n)$ denote the symmetric monoidal bordism $(\infty,n)$-category with $G$-structure. Let $(m+n)\text{-}\mathrm{Vect}$ be the symmetric monoidal $(\infty,m+n)$-category of higher vector spaces, and let $((m+n)\text{-}\mathrm{Vect})_{\mathrm{fd}}^{G\\, (\infty,m)}$ denote its fully dualizable objects equipped with the relevant $G$-homotopy fixed-point data. The evaluation functor sends a theory $Z$ to its value $Z({\rm pt}^{+})$. Cobordism hypothesis for TQFTs with moduli level $m$. For any $m\geq 0$ there is an equivalence of $\infty$-categories

$${\rm Fun}^{\otimes}({\rm Bord}^{G}(n),(m+n)\text{-}\mathrm{Vect})\simeq((m+n)\text{-}\mathrm{Vect})_{\mathrm{fd}}^{G\\, (\infty,m)}$$

induced by the evaluation functor $Z\to Z({\rm pt}^{+})$. This would characterize fully extended TQFTs with moduli level greater than zero, a case for which the authors state that no characterization is currently known.