The period-determines-b2 invariant 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 $c_2$ invariants are graph invariants defined from point counts of the associated graph hypersurfaces.

Period-determines-$c_2$ conjecture. If $G$ and $H$ have equal periods, then they have equal $c_2$ invariants.

The conjecture expresses the expectation that the $c_2$ invariant is preserved by completion followed by decompletion and by the Schnetz twist, operations known to preserve the period. It remains open.