The Theory of Harmonic Quantization: Resolving the Vacuum Catastrophe and Information Paradox via Geometric Resonance

Abstract Physics currently treats the fundamental constants of the Standard Model—such as the Fine Structure Constant and the Proton-to-Electron Mass Ratio—as arbitrary "free parameters" that cannot be derived from theory. This paper proposes the Theory of Harmonic Quantization (THQ), which redefines these constants as necessary geometric impedance factors of the vacuum itself. By modeling the vacuum as a high-Q resonator constrained by volumetric geometry (\pi), we derive the fundamental constants with extreme precision using only geometric integers. Key Results: The Fine Structure Constant (\alpha^{-1}): Derived via the sum of spatial dimensions relative to \pi. Formula: 4\pi^3 + \pi^2 + \pi \approx 137.036 Accuracy: 99.9998% relative to CODATA 2018. The Proton-to-Electron Mass Ratio (\mu): Derived via the volumetric impedance scalar. Formula: 6\pi^5 \approx 1836.118 Accuracy: 99.9981% relative to CODATA 2018. This paper suggests that the "constants" of nature are not random settings, but are the inevitable result of a self-referential geometric structure. The model provides a unified framework connecting Quantum Electrodynamics (QED) to Vacuum Geometry.