Tate–Voloch conjecture on torsion points and subvarieties

Let $K$ be a field complete with respect to a non-archimedean absolute value, let $A/K$ be a semiabelian variety, and let $X \subset A$ be a closed subvariety. Tate–Voloch conjecture. There exists $c > 0$ such that for every torsion point $P \in A(K)$, either $P \in X$ or $d(P,X) \ge c$. This conjecture predicts a uniform non-archimedean separation of torsion points from closed subvarieties when they do not lie on the subvariety; the supplied text attributes it to Tate and Voloch but gives no resolution status.