Gedeon–Proudfoot–Young interlacing conjecture for matroid Kazhdan–Lusztig polynomials

Let $M$ be a matroid and let $e$ be an element of its ground set. Let $M/e$ be the contraction of $M$ at $e$. A matroid is non-degenerate if its rank is $0$ or its Kazhdan–Lusztig polynomial has degree $\left\lfloor \frac{\operatorname{rk} M-1}{2}\right\rfloor$. For real-rooted polynomials with positive leading coefficients, write $g(t)\preceq f(t)$ when the zeros interlace in the sense defined in the source. Gedeon–Proudfoot–Young's conjecture. If both $M$ and $M/e$ are non-degenerate, then

$$P_{M/e}(t)\preceq P_M(t).$$

The conjecture is known for uniform matroids of rank $n-1$ on $n$ elements and is proved in this paper for fan matroids; it remains open in general.