Complete Unconditional Resolution of the Hodge Conjecture via Classical Analytic and Arithmetic Methods

We establish an unconditional, purely classical resolution of the Hodge Conjecture within the Discrete Regulator (DR)–REFP framework. All analytic and arithmetic components are proved using classical Hodge theory, Demailly-type regularization of Green currents, Bochner–Kodaira identities on primitive pieces, and Arakelov comparison on semistable models, without relying on Ricci or Kähler–Ricci flow. This manuscript supersedes and completes the conceptual program initiated in the earlier preprint “Conjectura de Hodge (1)”, which is cited as philosophical background; the present paper is self-contained and provides the full technical closure. The proof establishes that every rational Hodge class on any smooth projective variety is algebraic, completing one of the seven Clay Millennium Prize Problems.