Geometric Manin's conjecture for non-nef sections

Let $\pi:\mathcal{X}\to B$ be a Fano fibration, and let $\operatorname{Sec}(\mathcal{X}/B)$ be its moduli space of sections. A component is accumulating when it is governed by the exceptional-set contribution predicted by the Fujita invariant. Geometric Manin's conjecture for non-nef sections. The components parametrizing non-nef sections satisfy: (1) there is a Zariski-closed proper subset $\mathcal{Y}\subsetneq\mathcal{X}$ containing every non-nef section; and (2) all but finitely many such irreducible components are accumulating.

Over a field of characteristic zero, the source states that this claim is established by its main theorem and proof; thus this is a solved conjectural statement in that setting.