Squiggly-and-double-edge formula for cosmological polytopes

Let $G$ be a graph, let $\mathbb{C}_G$ be its cosmological polytope, and let $T$ be a triangulation of $\mathbb{C}_G$ arising from a good term order on $R_G$. For each simplex $S\in T$, let $G_S$ be its associated graph, and let $\operatorname{sq}(G_S)$ and $\operatorname{db}(G_S)$ denote respectively the numbers of squiggly and double edges in $G_S$. Squiggly-and-double-edge formula.

$$h^*(\mathbb{C}_G;z)=\sum_{S\in T}z^{\operatorname{sq}(G_S)+\operatorname{db}(G_S)}.$$

The formula is proposed as a general expression supported by the preceding visibility results for cycles and trees. The supplied text gives no proof or resolution, so its validity for all graphs and all triangulations arising from good term orders remains open.