Whittaker–W-algebra braided equivalence for generic level

Let $G$ be the group associated with $\mathfrak{g}$, let $\operatorname{Gr}_G$ be its affine Grassmannian, and let $\operatorname{Whit}^c(\operatorname{Gr}_G)$ denote the Whittaker category. Let ${\mc W}_c(\mathfrak{g})\text{-mod}^0$ be the corresponding category of modules over the W-algebra. Whittaker–W-algebra equivalence conjecture. For generic $c$, the categories

$$\operatorname{Whit}^c(\operatorname{Gr}_G)\simeq {\mc W}_c(\mathfrak{g})\text{-mod}^0$$

are equivalent as braided tensor categories. The source derives this statement by combining the conjectural braided equivalence for quantum Drinfeld–Sokolov reduction with the theorem proving Lurie’s related conjecture; the displayed consequence itself is not stated as resolved in the supplied text.