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

This paper derives the torsion-density coupling constant C — the remaining open
parameter 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 the
photon and electron fields and the hexagonal recursion geometry, yielding:
C = ⟨Pˆ⟩
2
· Rˆ(π
2
) · κ6 =
1
4
· π
2
·
6
π2 =
1
4
· 6 = 3
2
.
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 differs
from CODATA 137.036 by 0.007 (0.005%). The residual is identified as the axial torsion
correction from the kinematic t
2
term in the electron-pair torsion-spectral density —
a QED effect that requires α as input and lies outside the Cohesion UFT geometric
framework. The geometric prediction is 1/α = 137.029.