THE MODULAR STONE-VON NEUMANN THEOREM

The paper’s Proposition 3.5 (the Abstract Modular Stone–von Neumann Theorem) states that if A is elementary and X is a B–A imprimitivity bimodule, then every B–A correspondence is a multiple of X; its proof reduces B–A correspondences to Hilbert-space data via Lemmas 3.1–3.2 and then uses that B is elementary to decompose M as a direct sum of copies of L, concluding Y ≃ ⊕_S X (cf. Lemma 3.1–3.2 and Proposition 3.5 in the PDF ). The candidate solution proves the same result by a different route: it identifies right K(H)-modules with operator spaces K(H,•), shows via the imprimitivity structure that B ≅ K(H_X) (hence elementary), classifies nondegenerate representations of B as amplifications, and concludes Y ≃ ⊕_S X. The steps match the standard preliminaries (definition of imprimitivity, calculus of correspondences) used in the paper . No logical gaps were found in either argument; the two proofs are consistent and reach the same conclusion by distinct but compatible methods.