Orbifold Fano bound conjecture for locally soluble fibres

Let $\pi:X\to\mathbb{P}^1$ be a standard fibration, meaning a smooth, proper, geometrically irreducible variety over $\mathbb{Q}$ with dominant morphism to $\mathbb{P}^1$ and geometrically integral generic fibre. For each closed point $D\in(\mathbb{P}^1)^{(1)}$, let $m_D$ be the minimum multiplicity of the irreducible components of $\pi^{-1}(D)$, and define

$$\partial_\pi=\sum_{D\in(\mathbb{P}^1)^{(1)}}\left(1-\frac{1}{m_D}\right)[D].$$

Orbifold Fano bound conjecture. If the $\mathbb{Q}$-divisor $-(K_{\mathbb{P}^1}+\partial_\pi)$ is ample, then, for every $\varepsilon>0$,

$$N_{\text{loc}}(\pi,B)=O_{\varepsilon}\left(B^{2-\deg\partial_\pi+\varepsilon}\right).$$

This conjecture predicts a power-saving upper bound governed by the degree of the orbifold boundary. The paper presents it as a proposed extension of known sparsity results to standard fibrations with multiple fibres; the excerpt does not state that it has been proved or disproved.