The Satake-basis Euler characteristic expansion conjecture

Let $w$ be a minuscule web with boundary $\vec{\lambda}$ and dual diskoid $D$. Let $F(\vec{\lambda})$ be the Satake fibre, let $Q(D)$ be the diskoid-configuration variety, and let

$$\pi:Q(D)\to F(\vec{\lambda})$$

be the restriction map to the boundary. For each irreducible component $X$ of $F(\vec{\lambda})$, choose a generic point $x\in X$, and let $[X]$ denote its Satake-basis element. Satake-basis Euler expansion conjecture. Then

$$\Psi(w)=\pm\sum_{X\in\operatorname{Irr}(F(\vec{\lambda}))}\chi(\pi^{-1}(x))[X].$$

This formula is proposed as a consequence of the Euler-to-homological convolution conjecture and generalizes the closed-web Euler characteristic formula.