Height boundedness conjecture for isolated periodic points of polynomial automorphisms

Let $f \colon {\mathbb A}^N_{\overline{\mathbb Q}} \longrightarrow {\mathbb A}^N_{\overline{\mathbb Q}}$ be an automorphism such that the maximum degree of the coordinate functions is at least two. A periodic point is isolated if it is an isolated point of its periodic-point locus.

Height boundedness conjecture. The set of isolated periodic points of $f$ has bounded height.

This conjecture concerns the expected arithmetic height behavior of periodic points for polynomial automorphisms of affine space, beyond the standard endomorphism setting where canonical heights give boundedness for preperiodic points. The paper's abstract states that it gives a counterexample to this conjecture, so the conjecture is refuted.