The coherent-sheaf category conjecture for the two-block Springer construction

Let $\mathcal{C}$ be the heart of the $t$-structure on coherent sheaves on the smooth compactification $Z_n$, and let $A$ be the corresponding highest-weight algebra. Coherent-sheaf category conjecture. There is an isomorphism of categories between $\mathcal{C}$ and the category of finite-dimensional modules over $A$.

The surrounding text describes this as a structural identification of the coherent-sheaf heart with the module category of the highest-weight algebra, but gives no resolution status.