Kapustin–Rozansky's Hochschild cohomology conjecture for Lagrangian intersections

Let $X$ be a smooth algebraic symplectic variety, and let $Y,Z\subset X$ be smooth Lagrangian submanifolds. Write $H\!H^{\bullet}(\mathscr{C})$ for the Hochschild cohomology of a triangulated category $\mathscr{C}$, and let $\mathscr{C}at_X(Y,Z)$ denote the triangulated category associated with the pair $(Y,Z)$. The groups $\operatorname{Tor}^{\mathcal{O}_X}_{\bullet}(\mathcal{O}_Y,\mathcal{O}_Z)$ carry the canonical Gerstenhaber bracket referred to in the source. Kapustin–Rozansky's conjecture. There is an associated triangulated category $\mathscr{C}at_X(Y,Z)$ such that

$$H\!H^{\bullet}(\mathscr{C}at_X(Y,Z))\cong \operatorname{Tor}^{\mathcal{O}_X}_{\bullet}(\mathcal{O}_Y,\mathcal{O}_Z).$$

Moreover, under this isomorphism, the standard Gerstenhaber bracket on Hochschild cohomology agrees with the canonical Gerstenhaber bracket on $\operatorname{Tor}^{\mathcal{O}_X}_{\bullet}(\mathcal{O}_Y,\mathcal{O}_Z)$. The claim is attributed to A. Kapustin and L. Rozansky and concerns the categorical and Gerstenhaber-algebra structure expected from intersections of Lagrangian submanifolds. The supplied text does not establish the assertion or provide evidence that it has been resolved, so its database status remains open.