The Harmonic Resonance of the KnoWellian Vacuum: Unifying the CMB and SGWB through Cairo Q-Lattice Dispersions

This paper presents the culmination of the KnoWellian Universe Theory (KUT) series, proposing a fundamental unification of cosmology, quantum mechanics, and information theory. By modeling the vacuum as the KnoWellian Resonant Attractor Manifold (KRAM)—a structured, aperiodic medium tiled according to a Cairo Q-Lattice—we demonstrate that the universe acts as a massively parallel optical computer. We derive the Cross-Correlation Theorem, which asserts that the Cosmic Microwave Background (CMB) and the Stochastic Gravitational Wave Background (SGWB) are spectrally linked by the topological harmonic sequence of the (3,2) Torus Knot (the fundamental topology of the Event-Point). This theoretical synthesis offers a precise, falsifiable resolution to the Hubble Tension and provides a new road map for experimental gravitational and cosmological research.