Proudfoot–Xu–Young negative-root conjecture for matroid Z-polynomials

Let $M$ be a matroid with lattice of flats $L(M)$, and let $M_F$ and $M^F$ denote the corresponding localization and restriction notation used in the source. Its $Z$-polynomial is

$$Z_M(t):=\sum_{F\in L(M)}t^{\operatorname{rk} M_F}P_{M^F}(t).$$

Proudfoot–Xu–Young's conjecture. The polynomial $Z_M(t)$ has only negative zeros for every matroid $M$. The source gives no resolution of this conjecture for arbitrary matroids.