Weak Green–Griffiths–Lang conjecture for C-pairs

Let $(X, \Delta)$ be a smooth C-pair over $\mathbb{C}$, where a dense entire curve means a holomorphic C-pair map $\mathbb{C} \to (X, \Delta)^{\an}$ whose image is Zariski-dense in $X$. Assume that $(X, \Delta)$ is of general type, that $X$ is projective, and that $X$ is positive-dimensional. Weak Green–Griffiths–Lang conjecture for C-pairs. The C-pair $(X, \Delta)$ does not admit a dense entire curve. This is the weak, C-pair version of the Green–Griffiths–Lang conjecture; it is stated as a special case of Campana's conjecture and is used in the paper to deduce Campana-specialness from the existence of dense entire curves. Its status is not resolved in the supplied source.