The closed-web Euler characteristic formula

Let $w$ be a closed web, meaning a web with no boundary, and let $D$ be its dual diskoid. Let $Q(D)$ be the variety of diskoid configurations associated with $D$, let $\Psi(w)$ denote the corresponding invariant in the geometric Satake model, and let $\chi$ denote Euler characteristic. Closed-web Euler characteristic conjecture. One has

$$\Psi(w)=\pm\chi(Q(D)).$$

This is presented as a corollary of the proposed Euler-characteristic geometric Satake equivalence and is therefore expected to follow from that broader conjecture.