Loop-number bound for motivic Feynman amplitudes

Let $G$ be a Feynman graph with $h_G$ loops, and let $I_G$ be a convergent Feynman amplitude. Write $I_G^{\mathfrak{m}}$ for its motivic version, and let its weight mean the motivic period weight.

Loop-number weight conjecture. The weight of $I_G^{\mathfrak{m}}$ is less than or equal to $4h_G$.

The conjecture would bound the weight in terms of the number of loops rather than the number of edges. In even space-time dimension $D$, the analogous proposed bound is $Dh_G$; in the paper the discussion specializes to $D=4$.