Substitution Delone sets with pure point spectrum are inter-model sets

The paper establishes an equivalence between pure point diffraction and certain types of model sets, called inter-model sets, in the context of substitution point sets and substitution tilings. The key ingredients are a new type of coincidence condition in substitution point sets, which we call algebraic coincidence, and the use of a recent characterization of model sets through dynamical systems associated with the point sets or tilings.