Small arithmetic non-density conjecture

Let $K$ be a number field, let $X$ be a projective variety over $K$, and let $f:X\to X$ be a surjective endomorphism. For a positive constant $d$, let $X(d)$ denote the degree-bounded set used in the source and define

$$Z_f(d):=\{x\in X(d)\mid \alpha_f(x)<d_1(f)\}.$$

Here $\alpha_f(x)$ is the arithmetic degree of $x$ and $d_1(f)$ is the first dynamical degree of $f$. Small arithmetic non-density conjecture. For every positive constant $d$, the set $Z_f(d)$ is not Zariski dense in

$$X_{\overline K}=X\times_K\overline K.$$

This conjecture strengthens the non-density assertion by imposing a bounded-degree condition on the points. It is cited in the paper as one of the two main arithmetic dynamical conjectures; the parser provides no evidence that it has been resolved.