The $c_2=-1$ multiple-zeta-value conjecture

Let $G$ be a primitive log-divergent graph with loop number $h_G$ and $c_2$-invariant $-1$. $c_2=-1$ MZV conjecture. Its period is a multiple zeta value of weight $2h_G-3$:

$$P(G)\in\mathcal{Z},\qquad \operatorname{wt}(P(G))=2h_G-3.$$

The periods of all such graphs were known through eight loops at the time of the paper. The all-orders assertion remains open.