Stratified dimension conjecture for enhanced quiver varieties

Let $\Xi$ index the strata $\Lambda_{(r_i),I}^{\xi}$ of the enhanced quiver variety $\Lambda_{(r_i),I}$, let $d_{(r_i),I}$ be its expected dimension, and let $\Lambda^\circ$ be the specified open locus. Stratified dimension conjecture.

1. For any $\xi\in\Xi$,

$$\dim\Lambda_{(r_i),I}^{\xi}\leq d_{(r_i),I}.$$

2. Equality holds in (1) for a unique $\xi$; the corresponding stratum consists of those $(u_i,A_i,B_i)$ such that $A_i$ is injective and $B_i$ is surjective for all $i$, and $u_{i+1}\notin\operatorname{im}(A_i)$ for all $i\in I$.
3. If $\dim\Lambda_{(r_i),I}^{\xi}=d_{(r_i),I}-1$, then $\Lambda_{(r_i),I}^{\xi}\subset\Lambda^\circ$.

The conjecture is motivated by the Kraft--Procesi stratification theorem and would imply the dimension-bound conjecture, hence the normal complete-intersection conjecture. The supplied text gives no resolution of these assertions.