Nevo's Colin de Verdière stress-freeness conjecture

Let $G$ be a graph, let $k$ be a positive integer, and let $\mu(G)$ denote the Colin de Verdière parameter of $G$. A graph is generically $k$-stress free if it has no nonzero generic $k$-stress. Nevo's conjecture. If

$$\mu(G)\leq k,$$

then $G$ is generically $k$-stress free. This conjecture is proved in the source for $k=5$ and $k=6$, while the source gives no resolution for the general statement.