Positivity conjecture for Mather classes and local Euler obstructions

Let $X=G/P$ be a cominuscule space, and let $v,w\in W^P$. Write the Mather class of the Schubert variety $X_w^P$ as

$${c_{\operatorname{Ma}}}(X_w^P)=\sum_{v\leq w}a_{w,v}[X_v^P].$$

The local Euler obstruction coefficients $e_{w,v}$ are non-negative. Moreover, the Schubert coefficients $a_{w,v}$ are non-negative, and the analogous positivity statement holds equivariantly. This conjecture predicts positivity for characteristic classes and singularity invariants of Schubert varieties in cominuscule spaces; the source gives no resolution status.