Speyer's non-negativity conjecture for matroid g-polynomials

Let $\mathsf{M}$ be a matroid, and let $g_{\mathsf{M}}(t)\in\mathbb{Z}[t]$ denote its $g$-polynomial. Speyer's conjecture. For every matroid $\mathsf{M}$, the polynomial $g_{\mathsf{M}}(t)$ has non-negative coefficients. This conjecture concerns positivity of the covaluative $g$-polynomial, which is known in the source for the Schubert-matroid setting but is asserted here for arbitrary matroids; its general resolution status is not specified.