Rational invariants as invariants of isogenies of interval exchange systems

Let $(X,\operatorname{\sigma})$ be an interval exchange system (IES) with an invariant decomposition into ergodic probability measures, and let its rational invariants consist of the associated rational measure spaces and SAF invariants, as defined above. Rational invariants conjecture. If two IES with invariant decomposition are isogenous, then they have the same rational invariants. This proposes rational invariants as invariants of the isogeny class of an interval exchange system; the source does not state a resolution.