Zilber's Zilber–Pink conjecture for distinguished categories

Let $K$ be an algebraically closed field and let $\mathfrak{C}$ be a distinguished category over $K$. A distinguished variety is an object of $\mathfrak{C}$, and $\operatorname{ZP}(X,m,d)$ denotes the corresponding Zilber–Pink assertion for a distinguished variety $X$ and non-negative integers $m$ and $d$. Zilber's conjecture. For every distinguished variety $X$ and all non-negative integers $m$ and $d$, $\operatorname{ZP}(X,m,d)$ holds. This is Zilber's version of the Zilber–Pink conjecture, formulated by Habegger and Pila; the paper explains that it is equivalent to Pink's formulation in the presence of the stated axioms.