Xie–Zhang's real-rootedness conjecture for normalized inverse Kazhdan–Lusztig polynomials

Let $\mathsf{M}$ be a matroid, and write its inverse Kazhdan–Lusztig polynomial as

$$Q_{\mathsf{M}}(x)=q_0+q_1x+\cdots+q_sx^s,$$

where $s=\deg Q_{\mathsf{M}}\leq\left\lfloor\frac{\operatorname{rk}(\mathsf{M})-1}{2}\right\rfloor$. Define the normalization of $Q_{\mathsf{M}}(x)$ by

$$\mathcal{B}(Q_{\mathsf{M}})(x)=\binom{s}{0}q_0+\binom{s}{1}q_1x+\cdots+\binom{s}{s}q_sx^s.$$

Xie–Zhang's conjecture. For every matroid $\mathsf{M}$, the polynomial $\mathcal{B}(Q_{\mathsf{M}})(x)$ is real-rooted.

This conjecture refines the log-concavity conjecture for the coefficients of $Q_{\mathsf{M}}(x)$ by applying binomial normalization and predicting the stronger property of real-rootedness. Its status is open in the supplied text.