Favre's algebraic-integrality conjecture for dynamical degrees

Let $k$ be a field, let $n$ be a positive integer, and let $f\in\operatorname{End}(\mathbb{A}^n_k)$. Its dynamical degree is

$$\lambda(f):=\lim_{r\to\infty}\bigl(\deg(f^r)\bigr)^{1/r},$$

where $\deg(f)$ is the maximum of the degrees of the coordinate polynomials of $f$. Favre's conjecture. The dynamical degree $\lambda(f)$ of any element $f\in\operatorname{End}(\mathbb{A}^n_k)$ is an algebraic integer of degree at most $n$. This would constrain the possible asymptotic degree growth of polynomial self-maps in arbitrary dimension; the statement is posed as a natural question after known low-dimensional examples, but its resolution is not supplied here.