Unipotent Frobenius divisibility conjecture for spetses

Let $\mathbb{G}=(W\phi,\Lambda)$ be a simply connected $\mathbb{Z}_\ell$-spets and let $q\in\mathbb{Z}_\ell^\times$. Let $S$ be the Sylow $\ell$-subgroup of $(\mathbb{G},q)$, let $\mathcal F$ be its saturated fusion system, and let $\chi\in\operatorname{Uch}(\mathbb{G})$ be a unipotent character. Unipotent Frobenius divisibility conjecture.

$$\left(\sum_{t\in S/\mathcal F}|\mathbb{G}:C_{\mathbb{G}}(t)|\chi(t)\right)_{x=q}\equiv0\pmod{|S|}.$$

This is the unipotent-character analogue of the Frobenius divisibility property and is known when $W$ is rational; it remains open in general.