Schnetz's prime reduction conjecture for $c_2$ invariants

Let $G_1$ and $G_2$ be graphs, and for a prime power $q=p^s$ let $c_2^{(q)}(G)$ denote their $c_2$ invariants. Schnetz's prime reduction conjecture. If

$$c_2^{(p)}(G_1)\equiv c_2^{(p)}(G_2)\pmod p$$

for every prime $p$, then

$$c_2^{(q)}(G_1)\equiv c_2^{(q)}(G_2)\pmod q$$

for every prime power $q=p^s$. The conjecture would reduce comparisons of $c_2$ invariants at all prime powers to comparisons at primes. The source attributes this conjecture to Oliver Schnetz and presents it as an open question.