Quasi-fractal intersection conjecture for algebraic varieties

Let $X$ be an irreducible variety defined over a finitely generated field $K$, and let $Q\subset X(\bar K)$ be a quasi-fractal on $X$ with respect to correspondences $Y_i$ in $X\times X$, each having finite and surjective projection maps. Let $Z$ be any reduced subscheme of $X$ defined over $K$.

Quasi-fractal intersection conjecture. The Zariski closure of $Z(\bar K)\cap Q$ is a union of finitely many points and finitely many components $B_i$ such that, for each $i$, the intersection $B_i(\bar K)\cap Q$ is a quasi-fractal in $B_i$ with respect to correspondences induced by the $Y_i$.

This extends the arithmetic-fractal framework by allowing self-similarities induced by geometric self-correspondences rather than self-maps. The source does not state a resolution or known general cases.