Functorial Alperin weight conjecture

Let $k$ be an algebraically closed field of characteristic $p>0$, let $\mathbb{F}$ be an algebraically closed field of characteristic $0$, and let $(G,b)$ be a group-block pair over $k$. Let $\mathcal{F}\mathcal{B}\ell_{\mathbb{F},k}$ be the category of diagonal $p$-permutation functors, let $K_0(\mathcal{F}\mathcal{B}\ell_{\mathbb{F},k})$ be its Grothendieck group, and write $[\![G,b]\!]_{\mathbb{F}}$ for the class of the functor associated with $(G,b)$. Let $\mathcal{S}_p(G)$, $G_\sigma$, $|\sigma|$, $b_\sigma$, and $d(b)$ be as in Alperin's blockwise weight conjecture. Finally, $S_{\mathbf{1},1,\mathbb{F}}$ denotes the simple diagonal $p$-permutation functor indexed by the trivial $p$-group, the identity automorphism, and the trivial module.

Functorial Alperin weight conjecture. In $K_0(\mathcal{F}\mathcal{B}\ell_{\mathbb{F},k})$,

$$\sum_{\sigma\in [G\backslash \mathcal{S}_p(G)]}(-1)^{|\sigma|}[\![G_\sigma,b_\sigma]\!]_{\mathbb{F}}=\begin{cases}[S_{\mathbf{1},1,\mathbb{F}}]&\text{if }d(b)=0;\\0&\text{if }d(b)>0.\end{cases}$$

The paper formulates this as a functorial version of Alperin's blockwise weight conjecture and states that it is equivalent to the original conjecture. The source gives no independent resolution status.