Uniform boundedness conjecture for Manin components

Let $\pi:\mathcal X\to B$ be a good Fano fibration, let $\lambda$ be an intersection profile, and let $\mathsf{S}_{\lambda,\mathbb Z}$ be the corresponding integral section classes. Uniform boundedness conjecture for Manin components. There exist uniform constants $\mathsf B'$ and $\mathsf C$ such that, for every $\alpha\in\mathsf{S}_{\lambda,\mathbb Z}$, the number of Manin components of class $\alpha$ is at most $\mathsf B'$, and every such component $M_{\alpha}$ satisfies

$$\#M_{\alpha}^{\circ}(k)\leq\mathsf Cq^{-K_{\mathcal X/B}.\alpha+n(1-g(B))}.$$

This uniform estimate is introduced to control the contribution of all Manin components to the standard counting function; the source gives no resolution status.