Geometric-stratum conjecture for tensegrity fibers

Let $G$ be a graph and let $k$ be a positive integer. The $(G,k)$-stratum is the set of frameworks $G(P)$ for which the dimension of the fiber $W(G,P)$ is at least $k$. Such a stratum is geometric when it is a finite union of sets of conditional solutions of systems of geometric conditions, with the points in the systems corresponding to vertices of $G$. Geometric-stratum conjecture. For any graph $G$ and integer $k$, the $(G,k)$-stratum is geometric. The conjecture proposes that every stratum of the tensegrity configuration space has a finite geometric-incidence description; the paper establishes semialgebraicity of these strata but leaves this stronger description open.