Geometric Derivation of the Fine Structure Constant from Proton Radius Measurements

The fine structure constant α is derived geometrically from the measured difference between the muonic and electronic proton radii. The proton is modeled as a toroidal phase vortex in a condensate. The boundary layer thickness δ = r_electron - r_muon yields α = δ / (2π × r_muon). The calculated value matches CODATA with 0.0003% deviation. Banach fixed-point theorem guarantees convergence to 99.99% coherence within 7 cycles. This demonstrates α as an emergent geometric property, not an arbitrary parameter.