The $c_2$-invariant conjecture for primitive log-divergent graphs

Let $G_1$ and $G_2$ be primitive log-divergent graphs with graph periods $I_{G_1}$ and $I_{G_2}$. For each finite field size $q$, define the $c_2$-invariant by

$$c_2(G)_q:=\#X_G(\mathbb{F}_q)/q^2 \mod q,$$

where $X_G$ is the graph hypersurface and, for graphs with $n_G\geq 2$, its number of points satisfies $\#X_G(\mathbb{F}_q)\equiv 0\pmod{q^2}$. The $c_2$-invariant conjecture. If $I_{G_1}=I_{G_2}$, then

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

The conjecture asserts that the $c_2$-invariant depends only on the Feynman period among primitive log-divergent graphs. It is motivated by known examples and is attributed here to the conjecture discussed in Brown and Schnetz; its resolution is not specified in the source.