Aroca–Cumplido finite-presentation conjecture for labeled braided Higman–Thompson groups

Let $d\geq 2$ and $r\geq 1$, let $B_d$ be the braid group with $d$ strings, and let $H\leq B_d$ be a finitely presented subgroup. The group $bV_{d,r}(H)$ is the labeled braided Higman–Thompson group associated with these data. Aroca–Cumplido's conjecture. For all $d\geq 2$ and $r\geq 1$, the group $bV_{d,r}(H)$ is finitely presented when $H$ is finitely presented. This conjecture concerns finite presentability in the family of labeled braided Higman–Thompson groups; the paper confirms related finiteness results, but the supplied text does not state that this particular conjecture has been resolved.