Period-determines-$c_2$ conjecture for primitive-divergent graphs

Let $G_1$ and $G_2$ be primitive-divergent graphs in $\phi^4$ theory, let $I_{G_i}$ denote their residues, and let $c_2(G_i)$ be their graph invariants. Period-determines-$c_2$ conjecture. If

$$I_{G_1}=I_{G_2},$$

then

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

The source states this as a stronger conjecture implying invariance under the completion relation. Its status is not resolved in the supplied text.