Lusztig's microlocal characterization conjecture for perverse sheaves

Let $Q$ be a finite quiver without loops, let $E$ be a variety of representations of $Q$, and let $\mathcal{F}$ be an equivariant simple perverse sheaf on $E$. Let the singular support of $\mathcal{F}$ be its microlocal singular-support variety, and let Lusztig's Lagrangian variety be the variety of nilpotent representations of the preprojective algebra of $Q$. Lusztig's conjecture. The sheaf $\mathcal{F}$ is a Lusztig perverse sheaf if and only if its singular support is contained in Lusztig's Lagrangian variety. This conjecture is the quiver-representation analogue of the microlocal characterization of character sheaves for reductive groups. It is proved in the paper from which this statement is taken, although the supplied parser status is unknown.