Campana's generalized Lang conjecture

Let $(X,\sum_{i=1}^r (1-\frac{1}{m_i})D_i)$ be a smooth proper C-pair of general type over a number field $K$. Let $S$ be a finite set of finite places of $K$, let $\mathcal{X}\to \operatorname{Spec}\mathcal{O}_{K,S}$ be a smooth proper model of $X$, and let $\mathcal{D}_i$ be the closure of $D_i$ in $\mathcal{X}$. Write

$$\Delta =\sum_{i=1}^r\left(1-\frac{1}{m_i}\right)\mathcal{D}_i.$$

Campana's generalized Lang conjecture. If $\dim X \geq 1$, then $(\mathcal{X},\Delta)(\mathcal{O}_{K,S})$ is not dense in $X$.

This is the orbifold and C-pair analogue of Lang's conjecture on non-density of integral points on varieties of general type. The source gives no resolution.