ADE singularity derived-category equivalence conjecture

Let $W$ be a regular weight system corresponding to an ADE singularity, and let $f$ be a quasi-homogeneous polynomial attached to $W$. Write $D^b_{\mathbb Z}({\mathcal A}_f)$ for the ${\mathbb Z}$-equivariant derived category of the matrix-factorization category associated with $f$, and let the Dynkin quiver corresponding to the singularity type of $f$ be $Q$. ADE derived-category equivalence conjecture. The category $D^b_{\mathbb Z}({\mathcal A}_f)$ should be equivalent, as a triangulated category, to the bounded derived category of finite-dimensional representations of $Q$:

$$D^b_{\mathbb Z}({\mathcal A}_f)\simeq D^b(\operatorname{rep}_{\mathrm{fd}} Q).$$

This conjecture expresses the expected correspondence between ADE matrix factorizations and representations of Dynkin quivers; the source gives no further evidence of resolution.