The ancestor weight-drop conjecture for $\phi^4$ periods

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and completion $\overline{G}$, and suppose $P(G)\in\mathcal{Z}_N[\xi_N]$ for some $N$. Let $\operatorname{anc}(\overline{G})$ be the ancestor obtained from the completion by a maximal sequence of product and double-triangle reductions. Ancestor weight-drop conjecture. The weight drop of $\operatorname{anc}(\overline{G})$ exists and equals the weight drop of $P(G)$, namely $2h_G-3$ minus the maximum weight of $P(G)$.

The claim concerns periods known to be multiple polylogarithms at roots of unity. The weight filtration exists more generally, but the source reports supporting data only in this restricted setting; it remains open.