Naidu–Rowell Property F conjecture for weakly integral braided fusion categories

Let $\mathcal{C}$ be a weakly integral braided fusion category and let $X$ be any object of $\mathcal{C}$. The braid group representations associated with $X$ are the representations obtained from the braiding on tensor powers of $X$.

Naidu–Rowell Property $F$ conjecture. The braid group representations associated with any object in a weakly integral braided fusion category have finite images.

Property $F$ is the finiteness of the image of the associated braid group representation. The conjecture concerns a broad class of braided fusion categories and remains unresolved in general.