The stress-flex conjecture for coned polytope frameworks

Let $P$ be a convex polytope with $n$ vertices and full-dimensional span in $\mathbb R^d$. Let $(G^*,\hat{\bf p})$ be the tensegrity framework on $n+1$ vertices obtained by putting cables on the one-skeleton of $P$ and struts from the vertices of $P$ to a selected cone point in the interior of $P$. Let $\Omega$ be its Izemstiev stress, and let $\hat{\bf p}'$ be an infinitesimal flex of its bar framework. The stress-flex conjecture. The last row of $\Omega\hat{\bf p}'$ equals zero. Numerical experiments in three dimensions support this conjecture, and the condition has also been observed in broader examples, but no proof or resolution is given here.