Affine stress reconstruction conjecture for spheres without large missing faces

Assume $u\leq d/2$. Let $(\Delta,p)$ be a $(d-1)$-sphere in $S(d-u,d-1)$, with $p$ a generic or natural embedding in $\mathbb{R}^d$. Let $\mathcal{S}^a_i(\Delta,p)$ denote the space of affine $i$-stresses and let $R_{i-j}$ denote the corresponding space of differential operators. Affine stress reconstruction conjecture. For all $1\leq j<i\leq u$,

$$\mathcal{S}^a_j(\Delta,p)=\{\partial_\mu\omega:\omega\in\mathcal{S}^a_i(\Delta,p),\ \mu\in R_{i-j}\}.$$

The conjecture was proposed as a structural description of affine stress spaces, but the paper gives counterexamples showing that it fails when $d=2u\geq 6$; it is therefore refuted.