Transcendence of conjugacy growth series outside virtually abelian groups

Let $G$ be a finitely presented group that is not virtually abelian, and let a finite generating set mean any finite generating set of $G$. The general conjugacy-growth transcendence conjecture. The conjugacy growth series of $G$ with respect to any finite generating set are transcendental. This generalizes the conjecture for the soluble Baumslag–Solitar groups and is stated as a broader form of a conjecture attributed to Evetts; it remains open in general.