2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94750We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26 which admit a codimension 3 immersion in Euclidean space.This paper has been withdrawn due to a sign error in proposition 6.5Differential Geometrytext