Chirotropical Dressian versus chirotropical Grassmannian

Determine whether, for any uniform oriented matroid M whose realization space is diffeomorphic to an open ball, the chirotropical Dressian of M equals the chirotropical Grassmannian of M.

Background

Chirotropical analogues of classical Grassmannians and Dressians capture combinatorial and tropical structures governing scattering equations and positive geometries. For oriented matroids with particularly simple realization spaces (open balls), an equality between these two chirotropical objects is conjectured. Establishing this equivalence would clarify the foundations of chirotropical geometry and its role in positive geometry and CEGM theory.