Kazhdan–Lusztig positivity conjecture for matroids

Let $M$ be a matroid, and let $P_M(t)\in\mathbb{Z}[t]$ be its Kazhdan–Lusztig polynomial, characterized by the recursive conditions in the paper. Kazhdan–Lusztig positivity conjecture. For any matroid $M$, the coefficients of $P_M(t)$ are non-negative. This was proved for representable matroids using an intersection cohomology interpretation, but remains open for arbitrary matroids.