Blanc–Van Santen's Perron conjecture for polynomial automorphisms

Let $K$ be a field of characteristic $0$, let $d$ be a positive integer, and let $f\colon \mathbb{A}^d_K\to\mathbb{A}^d_K$ be a polynomial automorphism. Blanc–Van Santen's conjecture. The dynamical degree of $f$ is a Perron number of degree at most $d-1$. This is the automorphism counterpart to the preceding conjecture and is a stronger degree restriction in the invertible case. The source gives no resolution, so the conjecture remains open.