The QCA–Witt group homomorphism conjecture

Let $k$ be a field, let $\mathbf Q(\mathbb Z^3)$ be the QCA space in dimension three, and let $\mathrm{Witt}_k$ denote the Witt group of braided fusion $k$-linear categories. The QCA–Witt group homomorphism conjecture. There exists a natural group homomorphism

$$\pi_0\mathbf Q(\mathbb Z^3)\longrightarrow \mathrm{Witt}_k.$$

This conjecture would connect three-dimensional QCA with the Witt group of braided fusion categories, relating the computation of QCA groups to tensor-categorical structures. It is proposed as a direction for future work, and no resolution is stated in the source.