Panzer's Hepp-period identity conjecture

Let $G_1$ and $G_2$ be graphs with Feynman periods $P(G_1)$ and $P(G_2)$, and let $H(G)$ denote the Hepp period of a graph $G$.

Panzer's Hepp-period identity conjecture. Equality of Feynman periods is equivalent to equality of Hepp periods:

$$P(G_1)=P(G_2)\Leftrightarrow H(G_1)=H(G_2).$$

The conjecture would imply that the Hepp period detects all identities between Feynman periods. The source notes that, at eight loops, it requires two specific period identities, for which no sequence of twists or Fourier identities was known.