Baez–Dolan cobordism hypothesis for framed extended topological field theories

Let $\mathcal{C}$ be a symmetric monoidal $(\infty,n)$-category with duals. A framed extended $n$-dimensional TFT valued in $\mathcal{C}$ is a symmetric monoidal functor from the framed bordism $(\infty,n)$-category to $\mathcal{C}$, and $\mathcal{C}^{\sim}$ denotes its fully dualizable subcategory. Baez–Dolan's framed cobordism hypothesis. The evaluation functor $Z\mapsto Z(*)$ induces an equivalence

$$\operatorname{Fun}^{\otimes}(\mathbf{Bord}_n^{\mathrm{fr}},\mathcal{C})\simeq\mathcal{C}^{\sim}$$

between framed extended $n$-dimensional TFTs valued in $\mathcal{C}$ and the fully dualizable subcategory of $\mathcal{C}$. This conjecture asserts that a framed extended field theory is completely determined by its value on a point; the supplied text gives no evidence of resolution, so its status remains open.