Weak Bombieri–Lang conjecture for C-pairs

Let $(X, \Delta)$ be a smooth C-pair over $\overline{\mathbb{Q}}$. Say that $(X, \Delta)$ satisfies potential density of integral points if, for some number field $K$, finite set of finite places $S$, and model $(\mathcal{X},\Delta_{\mathcal{X}})$ over $\mathcal{O}_{K,S}$, its integral points are Zariski-dense in $X$. Assume that $(X, \Delta)$ is of general type, that $X$ is projective, and that $X$ is positive-dimensional. Weak Bombieri–Lang conjecture for C-pairs. The C-pair $(X, \Delta)$ does not satisfy potential density of integral points. This is the weak, C-pair version of the Bombieri–Lang conjecture; it is stated as a special case of Campana's conjecture and is used in the paper to deduce Campana-specialness from potential density of integral points. Its status is not resolved in the supplied source.