Quadrelli–Weigel's Bloch–Kato conjecture for right-angled Artin pro-$p$ groups

Let $\Gamma$ be a finite simplicial graph, and let $G=G_{\Gamma}$ be the associated right-angled Artin pro-$p$ group. The graph contains an induced subgraph of type $C_4$ when it has an induced square, and of type $L_3$ when it has an induced path of length $3$. Quadrelli–Weigel's conjecture. The group $G$ is a Bloch–Kato pro-$p$ group if and only if $\Gamma$ has no induced subgraph of either type $C_4$ or type $L_3$. The conjecture is presented as a characterization of Bloch–Kato right-angled Artin pro-$p$ groups; the source gives no resolution status.