Moment-graph character formula conjecture for intersection sheaves

Let ${\widehat{\mathcal G}}_k$ be the affine moment graph over the field $k$, let $\mathscr B_k(w)$ be the intersection sheaf attached to $w\in{\widehat{\mathcal W}}$, and let $\mathscr B_k(w)^x$ be its graded stalk at $x$. For a graded free module $M\cong\bigoplus_i S[l_i]$, write $\underline{\operatorname{rk}}\,M=\sum_i v^{l_i}$, and let $h_{x,w}$ be the Kazhdan–Lusztig polynomial. Intersection-sheaf multiplicity conjecture. If ${\widehat{\mathcal G}}_{k,\le w}$ is a GKM-graph, then for every $x\le w$,

$$\underline{\operatorname{rk}}\,\mathscr B_k(w)^x=v^{l(x)-l(w)}h_{x,w}.$$

This is presented as a natural generalization of the affine Kazhdan–Lusztig conjecture and connects stalk data on moment graphs with Kazhdan–Lusztig polynomials. Its status is left unresolved by the supplied source context.