The completion-invariance conjecture for the graph invariant $c_2$

Let $G$ be a primitive-divergent graph in $\phi^4$ theory, and let $c_2(G)$ denote its graph invariant. The completion relation identifies graphs whose completions are isomorphic; write $G_1\sim G_2$ for this relation. Completion-invariance conjecture. The invariant $c_2(G)$ is invariant under the completion relation:

$$G_1\sim G_2\Longrightarrow c_2(G_1)=c_2(G_2).$$

The invariant $c_2(G)$ is introduced through point counts of graph hypersurfaces modulo powers of $q$ and is more tractable than the full Grothendieck class. The source presents completion invariance as conjectural and cites work relating it to Feynman periods.