Pappas recently formulated universal properties called canonicity to characterize integral models of Shimura varieties defined by Kisin and himself. This modifies the canonicity introduced by Milne, and this applies to the cases of parahoric levels. On the other hand, Rapoport, Smithling and Zhang have conjectured interactions, including a variant of Arithmetic Gan--Gross--Prasad conjecture, of the intersection theory on some Shimura varieties or on their integral models and automorphic representation theory. We show that the integral models showing up here are canonical in the sense of Pappas, being isomorphic to the models of Kisin and Pappas in particular.

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