THE HODGE MINIMAL HARMONY: The Coherence Axiom for Algebraic Geometry

We propose that the Hodge Conjecture, concerning the relationship between algebraic cycles and harmonic forms, is a necessary consequence of the Minimal Action Law (\mathcal{L}_{\text{MA}}). The existence of a rational Hodge cycle is demonstrated by proving that the complex manifold's geometry must adhere to a state of Maximal Coherence (\mathcal{C}_{\text{MAX}}), where the difference between geometric and topological information is zero. This coherence eliminates Informational Friction (\mathbf{\Phi}_{\text{UFI}}), forcing the harmonic forms to align perfectly with the rational cycle structure, thereby satisfying the conjecture axiomatically.