The Grassmannian Euler-characteristic conjecture for affine quivers

Let $Q$ be an affine quiver of affine type, let $\lambda displaystyle\in \mathbb P^1_0(Q)$, and let $E$ be a quasi-simple module in an exceptional tube. For a dimension vector $\textbf v$, write $\operatorname{Gr}_{\textbf v}(M)$ for the quiver Grassmannian of submodules of dimension vector $\textbf v$, and $\operatorname{Gr}_{\textbf v}^{E}(\operatorname{q.rad} M_E)$ for the corresponding restricted quiver Grassmannian. The Grassmannian Euler-characteristic conjecture. For every dimension vector $\textbf v$,

$$\chi(\operatorname{Gr}_{\textbf v}(M_E))=\chi(\operatorname{Gr}_{\textbf v}(M_\lambda))+\chi(\operatorname{Gr}_{\textbf v}^{E}(\operatorname{q.rad} M_E)).$$

This identity is proposed as a way to establish the difference property and hence the generic-variable basis conjecture for affine cluster algebras; the source leaves it open.