Weak non-Archimedean Green–Griffiths–Lang–Vojta conjecture

Let $X$ be a $K$-variety. Weak non-Archimedean Green–Griffiths–Lang–Vojta conjecture. The following are equivalent:

$$\begin{aligned} &\text{Every integral subvariety of $X$ is of log-general type},\\ &\text{$X$ is groupless},\\ &\text{$X$ is $K$-analytically Brody hyperbolic}. \end{aligned}$$

This is the weak form of the non-Archimedean Green–Griffiths–Lang–Vojta conjecture, asserting that logarithmic general type for all integral subvarieties is equivalent to grouplessness and analytic Brody hyperbolicity. The supplied source does not state whether it is known or remains open.