VTT-HODGE CONJECTURE: A Reformulation Through Informational Persistence

Abstract

We propose an informational reformulation of the classical Hodge Conjecture within the frame-work of Viscous Time Theory (VTT), introducing informational persistence as a principle extending classical harmonicity. In this formulation, harmonic representatives are reinterpreted as persistent informational configurations (∆C-stable structures) on compact K¨ahler manifolds. We define the informational coherence gradient ∆C on M × R, where M is a compact K¨ahler manifold and R denotes the informational axis, and establish a ∆C-inner product via a deformed Hodge star operator. Within this setting, ∆C-harmonic forms arise as the natural generalization of classical harmonic forms, capturing equilibrium informational flows under tempo-
ral evolution. We further show that bounded informational flows converge toward ∆C-harmonic equilibrium, and we prove correspondence between ∆C-harmonic representatives and algebraic cycles under ∆C-preserving deformations. A worked example on the complex torus illustrates the feasibility of the framework, yielding explicit ∆C-harmonic representatives with algebraic support. This formulation embeds the classical Hodge setting as the limiting case (κ → 0) while opening broader perspectives for informational geometry, with implications for algebraic cycles, quantum coherence, and informational models of gravitation.