Bridson–Reid conjecture on profinite rigidity of hyperbolic 3-manifold groups

Let $G$ and $H$ be lattices in $PSL_2(\mathbb{C})$, and let $\widehat{G}$ and $\widehat{H}$ denote their profinite completions. Bridson–Reid conjecture. If

$$\widehat{G}\cong\widehat{H},$$

then

$$G\cong H.$$

This is a profinite-rigidity question for lattices in $PSL_2(\mathbb{C})$. The conjecture has been proved for certain examples, but remains open in general; the source also notes a stronger version in which $H$ may be any finitely generated, residually finite group.