The cluster structure conjecture for open positroid varieties

Let $Gr_{d,n}(k)$ be the Grassmannian of $d$-planes in $k^n$, and let a positroid variety be the matroid variety associated with a point of the totally non-negative Grassmannian $Gr_{d,n}(\mathbb R)$. An open positroid variety is the corresponding open matroid variety, and a reduced plabic graph is a reduced plabic graph associated with that positroid variety.

Cluster structure conjecture. The coordinate ring of an open positroid variety has a cluster structure obtained from the quiver associated to any of its reduced plabic graphs.

This conjecture proposes a cluster-algebraic structure on open positroid varieties and relates it to the combinatorics of reduced plabic graphs. The source gives no resolution status.