The Photon-Electron Coupling Derivation and the Fine-Structure Constant

This paper derives the torsion-density coupling constant C — the remaining openparameter in the Cohesion UFT fine-structure chain — from the spin geometry of thephoton-electron interface without using α as an input. The derivation proceeds fromthe pressure axiom through the spin ratio of the photon and electron fields and thehexagonal packing geometry, yielding:C =SeSγ2· π2· κ6 =ℏ/2ℏ2· π2·6π2=14· 6 =32.With C = 3/2 the full Cohesion UFT chain gives:1α=360φ2−12κ6ωC3α2m2e3/2·180π= 137.029.This is a transcendental equation for α with no free parameters. Its solution differs fromCODATA 137.036 by 0.007 (0.005%). The residual is identified as the axial torsioncorrection from the kinematic t2term in the electron-pair spectral density — a QEDeffect that requires α as input and lies outside the Cohesion UFT geometric framework.The geometric prediction is 1/α = 137.029.