Non-Archimedean Campana's specialness conjecture

Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let $X/K$ be a smooth projective variety. Write $X^{\operatorname{an}}$ for its non-Archimedean analytification, and call it $K$-analytically special when it admits the dense analytic parametrization described in the paper. Non-Archimedean Campana's conjecture. The following conditions are equivalent: $X$ is special, and $X^{\operatorname{an}}$ is $K$-analytically special. The paper presents this as a non-Archimedean analogue of Campana's characterization of special varieties; the source gives no resolution status.