Ehrhart equivalence conjecture for discrete equidecomposability

Let Ehrhart-equivalent rational polytopes be rational polytopes whose Ehrhart functions agree. Discrete equidecomposability is allowed to use an arbitrary number of simplices, and the simplices need not be rational. Ehrhart equivalence conjecture. Ehrhart equivalence is a necessary and sufficient condition for discrete equidecomposability under these unrestricted decompositions. This would extend the paper's finite rational theory: Ehrhart equivalence is not sufficient for rational discrete equidecomposability, but the conjecture allows irrational simplices and infinitely many pieces. The source gives no resolution.