Arzhantseva's residual finiteness conjecture for Gromov hyperbolic groups

A Gromov hyperbolic group is a group satisfying the usual metric hyperbolicity condition; a group is residually finite if its nontrivial elements survive in finite quotients, and it is sofic if it admits asymptotically multiplicative, asymptotically free finite symmetric-group approximations. Arzhantseva's conjecture. All Gromov hyperbolic groups are residually finite if and only if all Gromov hyperbolic groups are sofic.

The statement is attributed in the source to Conjecture 2.8 of Arzhantseva and collaborators. The preceding question asks whether an embedding into an ultrapower of the unitary group of the hyperfinite factor implies an embedding into that unitary group; a positive answer would establish this conjecture.