Amenable minimal matchbox manifolds are affable

Let ${\mathfrak{M}}$ be a minimal matchbox manifold. Assume that its associated equivalence relation is amenable in the sense of Anantharaman-Delaroche and Renault.

Affability conjecture. Then ${\mathfrak{M}}$ is affable.

This concerns the extension of affability results from minimal ${\mathbb Z}^n$-actions on Cantor sets to amenable minimal matchbox manifolds. The supplied source does not indicate whether the assertion has been proved or disproved.