The c_2 residue conjecture for primitive log-divergent graphs

Let $G$ be a graph with graph polynomial $cPsi_G$, and let $I_G$ denote its Feynman residue when $G$ is primitive and overall logarithmically divergent. For graphs with at least three vertices, let $c_2(G)$ be the point-counting invariant defined by

$$[X_G]_q \equiv c_2(G)_q q^2 \pmod{q^3},$$

where $X_G\subset \mathbb{A}^{N_G}$ is the affine graph hypersurface defined by $cPsi_G=0$.

The $c_2$ residue conjecture. If $I_{G_1}=I_{G_2}$ for two primitive log-divergent graphs $G_1$ and $G_2$, then

$$c_2(G_1)=c_2(G_2).$$

This conjecture says that the $c_2$ invariant depends only on the Feynman residue whenever it is defined. It was verified for all graphs with at most $14$ edges, but its general status is not resolved in the supplied source.