The arbitrary-position rigidity conjecture for 2-triangulations

Let $P$ be a convex $n$-gon, and place $n$ distinct points on the moment curve in $\mathbb{R}^{4}$. The associated bar-and-joint rigidity matroid is represented by the rigidity matrix of these points. The arbitrary-position rigidity conjecture. Every $2$-triangulation of the $n$-gon is isostatic, that is, a basis of this bar-and-joint rigidity matroid, for arbitrary distinct points on the moment curve. The paper proves the corresponding assertion for generic positions along the moment curve, which motivates this stronger conjecture; its status beyond that theorem is open.