Sign-vector determination of k-face Schubert arrangement cells

Show that, for any convex polytope, the cells in its k-face Schubert arrangement are determined by their sign vectors, as conjectured by Seemann–Zaffalon (Conjecture 3.5).

Background

Schubert-type arrangements in Grassmannians can be pulled back to arrangements on polytopes via stabbing and sign conditions. Whether sign vectors alone determine cells governs the combinatorial encoding of geometric incidences. Establishing this would streamline the paper of stabbing sets and amplituhedron-like semi-algebraic subsets via oriented matroid data.