The UWSCP characterization by bounded virtual-endomorphism growth

Let $f$ be a hyperbolic rational map, and let $\phi$ be its virtual endomorphism. Write $N[\phi^n]$ for the corresponding complexity quantity at the $n$th iterate, and say that it is uniformly bounded if there is a constant $C$ such that $N[\phi^n]\leq C$ for every $n\geq 1$. UWSCP characterization. The Julia set of $f$ satisfies the uniformly well-spread cut points property (UWSCP) if and only if $N[\phi^n]$ is uniformly bounded independently of $n$. This proposes a dynamical-combinatorial characterization of UWSCP for hyperbolic rational maps; the supplied text does not indicate whether the assertion has been proved or disproved.