Ordinary Weight Conjecture for spetses

Let ${\mathbb{G}}$ be a simply connected ${\mathbb{Z}}_\ell$-spets, let $\ell>2$ be very good for ${\mathbb{G}}$, and let $q$ be a power of a prime different from $\ell$. Let $B_0$ be the principal block of ${\mathbb{G}}(q)$, and let $\mathcal F({\mathbb{G}}(q))$ be its associated fusion system. Ordinary Weight Conjecture for spetses. For every integer $d\ge 0$, one has

$$|{\operatorname{Irr}}^d(B_0)|=\mathbf m(\mathcal F({\mathbb{G}}(q)),d).$$

This is an analogue for spetses of Robinson's Ordinary Weight Conjecture; when the spets is associated to a finite group of Lie type, it is equivalent to the ordinary weight conjecture for the principal block of that group.