The noncrossing matching ensemble realization conjecture

A matching ensemble is a collection of matchings satisfying the linkage axiom; it is noncrossing when its matchings are noncrossing. A generic simple polypositroid is a generic simple polypositroid $P$, and let ${\mathcal E}(P)$ denote the matching ensemble appearing in the paper's theorem.

Noncrossing matching ensemble realization conjecture. Every noncrossing matching ensemble appears as ${\mathcal E}(P)$ for some generic simple polypositroid $P$.

This conjecture asks whether the construction from generic simple polypositroids realizes all noncrossing matching ensembles. The supplied text gives no resolution status.