Helme-Guizon–Przytycki–Rong torsion conjecture for chromatic homology

Let $G$ be a graph, and let ${{H_{*,*}}^{\mathcal{A}_m}(G)}$ denote its chromatic cohomology over the algebra $\mathcal{A}_m$. A graph has a loop if it contains an edge whose endpoints coincide, and a cycle has order equal to its number of edges.

Helme-Guizon–Przytycki–Rong torsion conjecture. The cohomology ${{H_{*,*}}^{\mathcal{A}_m}(G)}$ contains a torsion part if and only if $G$ has no loops and contains a cycle of order at least $3$. In this case, ${{H_{*,*}}^{\mathcal{A}_m}(G)}$ has torsion of order dividing $m$.

This conjecture concerns the existence and order of torsion in chromatic homology over $\mathcal{A}_m$. The supplied text identifies it as a conjecture posed by Helme-Guizon, Przytycki, and Rong, but gives no resolution status.