The Colin de Verdière stress-freeness conjecture

Let $G$ be a graph, and let $\mu(G)$ denote the Colin de Verdière parameter of $G$. A graph is generically $k$-stress free when its generic $k$-dimensional rigidity stress space is trivial.

Colin de Verdière stress-freeness conjecture. If $\mu(G)\leq k$ for a positive integer $k$, then $G$ is generically $k$-stress free.

This would extend the known implications for planar and linklessly embeddable graphs, corresponding to $\mu(G)\leq 3$ and $\mu(G)\leq 4$. The source presents the general statement as open.