Minimal rigidity implies rigidity for conic frameworks

Let $(\Gamma,p)$ be a conic framework. A framework is minimally rigid when it is rigid and ceases to be rigid after removing any edge.

Minimal rigidity conjecture. If $(\Gamma,p)$ is minimally rigid, then $(\Gamma,p)$ is rigid.

For Euclidean frameworks, infinitesimal rigidity implies rigidity, but the analogous implication for conic frameworks is only conjectured because the relevant differential-geometric arguments are beyond the scope of the paper.