Period-determines-extended-graph-permanent conjecture for 4-point c6^4 graphs

Let $G$ and $H$ be $4$-point $c6^4$ graphs. Their Feynman periods are numerical invariants, and their extended graph permanents are sequences of finite-field residues associated with the graphs.

Period-determines-extended-graph-permanent conjecture. If $G$ and $H$ have equal periods, then they have equal extended graph permanents.

The conjecture seeks to recover the extended graph permanent from the Feynman period and would connect an integral invariant with an infinite residue sequence. The source states that the available results only suggest this connection and provides no method for resolving the conjecture; it remains open.