Maximum-rank stress conjecture for global rigidity on surfaces

Let $S$ be a surface, let $(G,p)$ be a framework generic on $S$, and let $(\omega,\lambda)$ be an equilibrium stress for $(G,p)$. Write $\Omega_S(\omega,\lambda)$ for its stress matrix, and let $\mu$ denote the dimension of the space of trivial infinitesimal motions on $S$. Maximum-rank stress conjecture. If

$$\operatorname{rank} \Omega_S(\omega,\lambda)=3n-\mu,$$

then $(G,p)$ is globally rigid on $S$. The preceding discussion establishes this when the stress matrix is positive semidefinite; the conjecture removes that positivity hypothesis.