Sazdanovic–Scofield homological span conjecture for chromatic homology

Let $G$ be a graph with $v$ vertices and $b$ blocks, and let $\mathcal{A}_m$ be the algebra used to define its chromatic homology. Write $H_{*,*}^{\mathcal{A}_m}(G)$ for the resulting bigraded chromatic homology and let $hspan$ denote its homological span.

Sazdanovic–Scofield conjecture. The homological span satisfies

$$hspan\left(H_{*,*}^{\mathcal{A}_m}(G)\right)=v-b.$$

The paper states that it proves this conjecture using the spanning tree model, so the conjecture is resolved in the setting considered. The result gives a graph-theoretic description of the homological span of chromatic homology over $\mathcal{A}_m$.