Ferroni–Schröter's real-rootedness conjecture for Chow polynomials

Let $\mathrm{M}$ be a matroid, and let its Chow polynomial be the polynomial invariant associated with its lattice of flats. Ferroni–Schröter's conjecture. The Chow polynomial of $\mathrm{M}$ has only nonpositive real roots. This is a central real-rootedness question for matroid invariants; the source presents it as a motivating conjecture, without stating a resolution.