2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70913This article presents a new and more elementary proof of the main Seiberg-Witten-based obstruction to the existence of Einstein metrics on smooth compact 4-manifolds. It also introduces a new smooth manifold invariant which conveniently encapsulates those aspects of Seiberg-Witten theory most relevant to the study of Riemannian variational problems on 4-manifolds.21 pages, LaTeX2eDifferential GeometryGeometric Topology53C25, 57R57text