Standard Manin conjecture over global function fields

Let $\pi:\mathcal X\to B$ be a good Fano fibration, let $q$ be the cardinality of the constant field, and suppose that $\mathcal X_{\eta}(K(B))$ is not thin. With $N_{\mathrm{stan}}(\pi,d)$, $r(\pi)$, $\alpha(\mathcal X_{\eta})$, $\beta(\mathcal X_{\eta})$, and $\tau_{\mathcal X}(-\mathcal K_{\mathcal X_{\eta}})$ as defined in the source, Standard Manin conjecture over global function fields.

$$N_{\mathrm{stan}}(\pi,d)\sim (1-q^{-r(\pi)})^{-1}\alpha(\mathcal X_{\eta})\beta(\mathcal X_{\eta})r(\pi)\tau_{\mathcal X}(-\mathcal K_{\mathcal X_{\eta}})q^{r(\pi)d}(dr(\pi))^{\rho(\mathcal X_{\eta})-1}$$

as $d\to\infty$ through integers. This is explicitly called provisional because the source expects possible periodicity when $r(\pi)\ne r(\pi)'$; no proof in the stated generality is given.