Zhang's fixed-point growth conjecture for polarized endomorphisms

Let $X$ be a projective variety over $\mathbb{C}$ and let $\varphi:X\to X$ be an endomorphism with $\varphi^*L\cong L^{\otimes q}$ for some ample line bundle $L$ on $X$. Suppose that $Y\subset X$ is a subvariety of dimension $r$ such that $\varphi^m(Y)=Y$. Zhang's fixed-point growth conjecture. Then

$$\#\{P\in Y(\mathbb{C}):\varphi^{ml}(P)=P\}=q^{rml}(1+o(1))$$

as $l\to\infty$. This conjecture predicts the asymptotic growth of periodic points on invariant subvarieties under polarized endomorphisms; the supplied source identifies it as Zhang's conjecture, but gives no resolution status.