Witt-space functor conjecture for extended symmetric multifusion categories

Let $\mathds{k}$ be a field, and let $\widehat{\mathbf{SMF1C}}^{\mathrm{dom,faith}}_{\mathds{k}}$ be the $(2,1)$-category of extended symmetric (multi)fusion $1$-categories over $\mathds{k}$ and faithful dominant symmetric tensor functors. Let $\mathbf{Spaces}$ denote the $(\infty,1)$-category of spaces. Witt-space functor conjecture. There is a functor

$$\mathcal{W}itt:\widehat{\mathbf{SMF1C}}^{\mathrm{dom,faith}}_{\mathds{k}}\rightarrow \mathbf{Spaces}$$

that preserves homotopy limits of profinite groups. The conjecture proposes a generalization over an arbitrary field of the corresponding expectation over an algebraically closed field; its status and the required limit-preservation argument are not established in the supplied text.