Broustet–Höring's log canonical model conjecture for polarized endomorphisms

Let $X$ be a normal projective complex variety admitting a non-invertible polarized endomorphism $f: X \longrightarrow X$. Suppose that $X$ has a log canonical model $\mu: Y \longrightarrow X$.

Broustet–Höring's conjecture. The morphism $\mu$ is an isomorphism in codimension one.

This is a precise formulation of the conjectural extension of Broustet and Höring's result to varieties that are not necessarily $\mathbb{Q}$-Gorenstein. In the paper's setting, the broader log canonical singularities conjecture is proved using valuative log canonical singularities, while this log canonical model formulation is not separately identified as resolved.