The quiver flag variety reconstruction conjecture

Let $Y$ be any quiver flag variety, and let $E$ be the tilting bundle from cite[Theorem~4.5]{Cra11}.

Quiver flag variety reconstruction conjecture. The morphism

$$f_E:Y\rightarrow \mathcal{M}(E)$$

is an isomorphism.

The conjecture is motivated by the proved Grassmannian case for $\operatorname{Gr}(n,2)$, the analogous result for toric quiver flag varieties, and work identifying quiver flag varieties with connected components of the relevant moduli space. A proof for arbitrary quiver flag varieties is not supplied and remains open.