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 algebraic
varieties. By embedding complex manifolds into the five-dimensional information-metric
vacuum 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 strictly
to quantized stationary resonant states. We prove that the invariant saturation suture
constant Ceff forces continuous harmonic cycles to collapse into rational linear combinations of
algebraic cycles, establishing the validity of the Hodge conjecture as a fundamental topological
conservation law of liquid spacetime.