The Orlik–Terao conjecture for graphical configuration spaces

Let $\Gamma$ be a directed graph, let $X(SU(2),\Gamma)$ be its graphical configuration space, and let $\overline{\operatorname{OT}}(\Gamma)$ be the reduced Orlik–Terao algebra associated with its graphical vector arrangement. Let $\operatorname{Aut}(\Gamma)$ be the automorphism group of the underlying undirected graph, acting on both the cohomology and the reduced Orlik–Terao algebra. Orlik–Terao conjecture. For any graph $\Gamma$, there exists a degree-halving isomorphism of graded $\operatorname{Aut}(\Gamma)$-representations

$$H^*(X(SU(2),\Gamma);\mathbb{Q})\cong\overline{\operatorname{OT}}(\Gamma).$$

This conjecture predicts that the cohomology representation of the graphical configuration space is encoded by the reduced Orlik–Terao algebra. The supplied source gives no evidence of a resolution, so the conjecture remains open.