The equivalence conjecture for the functors from quiver Hecke modules

Let $R$ be the symmetric quiver Hecke algebra, let $Q$ be the chosen quiver datum, and let $\mathrm{Rep}(R)$ be the category of finite-dimensional $R$-modules. For $t=1,2$, let $\mathscr{C}_Q^{(t)}$ be the corresponding full subcategory of representations of the quantum affine algebra, and let ${\mathcal F}_Q^{(t)}$ be the functor constructed in the paper.

Equivalence conjecture. For $t=1,2$, the functor

$${\mathcal F}_{Q}^{(t)}\colon\mathrm{Rep}(R)\to\mathscr{C}_Q^{(t)}$$

is an equivalence of categories.

These functors are intended to identify the representation categories of the symmetric quiver Hecke algebra with the corresponding monoidal subcategories of quantum affine algebra representations. The supplied text does not state whether this conjecture has been resolved.