Completion-class invariance of $c_2$ modulo the Lefschetz motive

Let $G_1$ and $G_2$ be primitive-divergent graphs in $\phi^4$ theory. For a graph $G$, let $\widehat G$ be its completion, obtained by adjoining a vertex to the four three-valent vertices of $G$, and let $\mathbb L$ denote the Lefschetz motive. Completion-class invariance conjecture. If

$$\widehat{G_1}\cong\widehat{G_2},$$

then

$$c_2(G_1)\equiv c_2(G_2)\pmod{\mathbb L}.$$

The source gives this statement in the completion-relation discussion, but the supplied text does not explicitly label it as conjectural or provide a resolution status.