Open Orbit Conjecture for dual canonical and dual semicanonical bases

Let $\Lambda_d$ be the relevant variety of $d$-dimensional modules over the preprojective algebra $\Lambda$, and let $Z$ be an irreducible component of $\Lambda_d$. Let $b_Z$ and $\rho_Z$ be the associated dual canonical and dual semicanonical basis vectors of $\mathcal M^*$. Open Orbit Conjecture. If $Z$ contains an open $\operatorname{GL}_d$-orbit, then

$$b_Z=\rho_Z.$$

The conjecture proposes a class of elements common to the dual canonical and dual semicanonical bases, whose difference is otherwise known in general. Its resolution status is not specified in the source.