Novik–Zheng affine-stress support conjecture for simplicial spheres

Let $2\leq i\leq d/2$. Let $\Delta$ be either the boundary complex of a simplicial $d$-polytope with its natural embedding $p$, or a simplicial $(d-1)$-sphere with a generic embedding $p$. Assume that $\Delta$ has no missing faces of dimension at least $d-i+1$. The affine-stress support conjecture. Every $(i-1)$-face of $\Delta$ participates in some affine $i$-stress on $(\Delta,p)$. In particular, the space of affine $i$-stresses of $(\Delta,p)$ determines the $(i-1)$-skeleton of $\Delta$. The $i=2$ case is known by the cited results, but all other cases remain wide open.