Geometric Manin's conjecture on the number of Manin components

Let $X$ be a smooth Fano variety over $\mathbb C$ with Brauer group $Br(X)$. Let $C$ be a smooth connected genus $g$ curve. A component of $\operatorname{Mor}(C,X,\alpha)$ is understood to be a Manin component when it is one of the components distinguished by Geometric Manin's conjecture from exceptional components. Geometric Manin's conjecture (IV). There exists a curve class $\beta \in Nef_1(X)_{\mathbb Z}$ such that for all $\alpha \in \beta + Nef_1(X)_{\mathbb Z}$, there are exactly $|Br(X)|$ many Manin components in $\operatorname{Mor}(C, X,\alpha)$. This conjecture is part of the geometric analogue of Manin's conjecture: Manin components are intended to capture the expected contribution of dominant families of curves, while exceptional components are ignored. Its resolution status is not specified in the source.