Orlik–Solomon Koszulness conjecture

Let $\mathcal{L}$ be a geometric lattice, and let $\mathrm{OS}(\mathcal{L})$ be its Orlik–Solomon algebra. Orlik–Solomon Koszulness conjecture. The algebra $\mathrm{OS}(\mathcal{L})$ is Koszul if and only if $\mathcal{L}$ is supersolvable.

This is described as a classical conjecture and is attributed to Yuzvinsky. The source does not state a resolution; the paper aims to shed new light on the problem.