Infinite periodic asymptotic dimension of nonabelian free groups

Let $F$ be a nonabelian free group, and let $\operatorname{pdim}(F)$ denote its periodic asymptotic dimension. Free-group periodic-dimension conjecture. Nonabelian free groups have infinite periodic asymptotic dimension, that is, $\operatorname{pdim}(F)=\infty$. This concerns the behavior of periodic asymptotic dimension for free groups, following the paper's discussion of finiteness under extensions and examples of virtually polycyclic groups and Baumslag–Solitar groups.