Antolín–Ciobanu conjecture on formal growth in acylindrically hyperbolic groups

Let $G$ be a finitely generated acylindrically hyperbolic group, meaning a group acting non-elementarily and acylindrically by isometries on a hyperbolic space. Let $\mathcal G_{cj}$, $\mathcal G_{pc}$, and $\mathcal G_{cm}$ denote respectively the formal conjugacy, primitive conjugacy, and commutator growth series. Antolín–Ciobanu's conjecture. The three series

$$\mathcal G_{cj},\qquad \mathcal G_{pc},\qquad \mathcal G_{cm}$$

are transcendental.

This is proposed as a natural extension of Rivin's conjecture from word-hyperbolic groups to the broader class of acylindrically hyperbolic groups, which includes many hyperbolic, relatively hyperbolic, mapping class, outer automorphism, and right-angled Artin groups. The source does not state whether the conjecture has been resolved.