The sign-vector reconstruction conjecture for affine stresses

Let $P\subset\mathbb R^d$ be a simplicial $d$-polytope, with boundary complex $\partial P$. For $2\leq i\leq d/2$, let $\mathcal V_i(P)$ be the set of sign vectors of the coefficients of affine $i$-stresses on $P$.

Sign-vector reconstruction conjecture. The $(i-1)$-skeleton of $\partial P$ together with $\mathcal V_i(P)$ determines the combinatorial type of $P$, equivalently the entire abstract simplicial complex $\partial P$.

This is presented as a strengthening of Kalai's reconstruction conjecture, replacing the full affine-stress space by its sign-vector data. The source gives no resolution.