The combinatorial characterization conjecture for the matroid invariant

Let $M$ be a loop- and co-loop-free matroid, let $\operatorname{Poly}_M$ be its matroid polytope, and let $G_M$ be a polynomial assigned to each isomorphism class of such matroids. For a polyhedral decomposition $\mathcal{D}$ of $\operatorname{Poly}_M$ into smaller matroid polytopes, let $\mathring{\mathcal{D}}$ denote the set of interior faces. A series-parallel matroid is understood in the standard sense.

Combinatorial characterization conjecture. If the assignment $M\mapsto G_M$ satisfies

1. for every such decomposition,

$$G_M=\sum_{\operatorname{Poly}_F\in\mathring{\mathcal{D}}}G_F,$$

2. if $M$ is a direct sum of $c$ series-parallel matroids, then

$$G_M=t^c,$$

then $G_M=g_M$.

This conjecture asks whether the stated valuation and normalization properties uniquely determine the invariant $g_M$. The source calls it essentially combinatorial and supplies no resolution evidence, so it remains open.