Generalized Lang-type conjecture for arithmetic fractals

Let $X$ be an irreducible variety over a finitely generated field $K$, let $F\subset X(\bar K)$ be an arithmetic fractal on $X$, and let $Z$ be a reduced subscheme of $X$. The Zariski closure of $Z(\bar K)\cap F$ is a union of finitely many components $B_i$.

Arithmetic-fractal intersection conjecture. For each such component $B_i$, either $B_i$ is a point, or $B_i(\bar K)\cap F$ is an arithmetic fractal with respect to some induced endomorphisms of $B_i$.

This conjecture is presented as a common framework for the theorems of Raynaud and Faltings, and would imply a generalized Lang conjecture for arithmetic fractals. Its resolution status is not specified in the source.