Geometric-signature conjecture for Kasteleyn matrices of PBDTP graphs

Let $G$ be a planar bicoloured PBDTP graph, and let its edges carry the geometric signature. Form the associated sign matrix by assigning the corresponding geometric-signature signs to edges joining black and white vertices, with zero entries for nonedges. Geometric-signature conjecture. In the setting of PBDTP graphs, this sign matrix explicitly realizes Speyer's variant of the classical Kasteleyn theorem for planar bicoloured graphs. This would connect geometric signatures with dimer-counting Kasteleyn matrices; the supplied text gives no resolution.