The derivation constraints for $c_2=-z_3$ $\phi^4$ periods

Let $G$ be a primitive log-divergent $\phi^4$ graph with loop number $h_G$ and $c_2(G)=-z_3$, and let $\delta_m$ be the derivation with respect to the modified parity basis in the source. Derivation constraint conjecture.

$$\delta_mP(G)\in\mathcal{Z}\quad\text{if $m>2h_G-16$ is even},$$

and

$$\delta_mP(G)=0\quad\text{if $m>2h_G-17$ is odd}.$$

This is motivated by the expected absence of weight-drop periods in the relevant imaginary sixth-root-of-unity space below weight $14$. It remains open.