The bounded isomorphism conjecture for box spaces of residually finite groups

Let $G$ be a residually finite group and let $(G_n)$ be a nested sequence of finite-index normal subgroups with trivial intersection. The associated box space is the coarse disjoint union $\bigsqcup_n G/G_n$. The bounded isomorphism conjecture. The bounded isomorphism conjecture is true for box spaces of residually finite groups. This is presented as the main conjectural assertion of the paper; the supplied context gives no evidence that it has been resolved.