2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153990We show that the algebra A of a commutative unital spectral triple (A,H,D) satisfying several additional conditions, slightly stronger than those proposed by Connes, is the algebra of smooth functions on a compact spin manifold.67 pages, no figures, Latex; major changes, a new Appendix AOperator AlgebrasHigh Energy Physics - Theory58B34text