A Geometric Framework for Vacuum Impedance, the Derivation of Fundamental Constants, and the Electromagnetic Wave as Topological Phase Transition

This preprint presents a unified geometric model of the vacuum as a structured electromagnetic impedance network. We define a 1-radian impedance metric and distinguish between an unconstrained 4π solid-angle free space and a confined 2π von Klitzing phase space. The fine-structure constant α emerges as the radial contraction factor governing the topological transition between these states. Key results include: Derivation of the vacuum impedance Z₀ and the von Klitzing constant R_K from geometric topology Identification of the elementary charge e as the charge quantum of confined phase space Independent recovery of the volumetric ratio (1/α)³ via capacitance, inductance, and electric potential Derivation of the Rydberg constant, Bohr radius, and classical electron radius A novel interpretation of all electromagnetic waves, including photons, as topological phase transitions: a confined 2π state relaxing to the 4π free space, with frequency encoding the confined potential difference and wavelength preserved across the transition The framework offers a geometric interpretation of the fine-structure constant and provides a unified, mechanistic description of electromagnetic radiation.