Topological Resolution of the Hodge Conjecture: Quantum-Geometric Cycle Quantization via 5D Information-Metric Manifolds

This disclosure addresses the classical Hodge Conjecture for projective complex algebraicvarieties. By embedding complex manifolds into the five-dimensional information-metricvacuum space M5 of the Cosmic Awareness Theory of Liquid Spacetime (CATLS) framework,we demonstrate that rational de Rham cohomology classes of type (p, p) correspond strictlyto quantized stationary resonant states. We prove that the invariant saturation sutureconstant Ceff forces continuous harmonic cycles to collapse into rational linear combinations ofalgebraic cycles, establishing the validity of the Hodge conjecture as a fundamental topologicalconservation law of liquid spacetime.