Equivalence of minimal rigidity and rigidity for generic conic frameworks

Let $(\Gamma,p)$ be a generic conic framework, meaning that its placement satisfies the genericity condition used for conic frameworks. A framework is minimally rigid when it is rigid and ceases to be rigid after removing any edge.

Generic rigidity equivalence conjecture. The framework $(\Gamma,p)$ is minimally rigid if and only if it is rigid.

For generic Euclidean frameworks, infinitesimal rigidity and rigidity are equivalent; the corresponding equivalence for generic conic frameworks is presented as a conjecture because the necessary differential-geometric proofs are not supplied.