Finiteness conjecture for braid group representations from $(d,3,1)$-gYBE objects

A generalized Yang–Baxter equation object (gYBE object) is an object in a unitary ribbon fusion category that produces braid group representations through the associated $(d,3,1)$-gYBE solution. Finiteness conjecture. Images of resulting braid group representations from $(d,3,1)$-gYBE objects in unitary ribbon fusion categories are always finite groups. This conjecture proposes a uniform finiteness property for braid group representations arising from $(d,3,1)$-gYBE objects; the source presents it as a conjecture without stating a resolution.