Nonnegativity conjecture for the matroid polynomial g-invariant

Let $M$ be a matroid, and let $g_M(t)\in\mathbb{Z}[t]$ be the covaluative matroid invariant described in the paper. Nonnegativity conjecture for $g_M(t)$. For any matroid $M$, the coefficients of $g_M(t)$ are nonnegative. This conjecture would imply the f-vector conjecture for matroidal decompositions of uniform matroids; its resolution is not established in the supplied text.