Positivity conjecture for connected matroids with series-parallel subdivisions

Let $\mathsf{M}$ be a connected matroid whose base polytope admits a subdivision into direct sums of series-parallel matroids, and define

$$\wwtilde{g}_{\mathsf{M}}(t):=\frac{1}{t}g_{\mathsf{M}}(t).$$

Connected series-parallel subdivision conjecture. The polynomial $\wwtilde{g}_{\mathsf{M}}(t-1)$ has non-negative coefficients. This is a stronger positivity statement beyond Schubert matroids and is accompanied in the source by the open challenge of characterizing all matroids admitting such subdivisions; no resolution status is supplied.