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 pressure–recursion–torsion operator algebra of the photon-electron interface without using α as an input.The derivation proceeds from the pressure operator Pˆ through the pressure ratio of thephoton and electron fields and the hexagonal recursion geometry, yielding:C = ⟨Pˆ⟩2· Rˆ(π2) · κ6 =14· π2·6π2 =14· 6 = 32.With C = 3/2 the full Cohesion UFT chain gives:1/α = 360/φ2 − 12κ6/ωC· (3α/2)3/2· 180/π = 137.029.This is a transcendental equation for α with no free parameters. Its solution differsfrom CODATA 137.036 by 0.007 (0.005%). The residual is identified as the axial torsioncorrection from the kinematic t2term in the electron-pair torsion-spectral density —a QED effect that requires α as input and lies outside the Cohesion UFT geometricframework. The geometric prediction is 1/α = 137.029.