The Photon-Edge Gate: Uniqueness and Minimality of the Residual Five-Rail Complex for the Fine-Structure Constant

The residual five-rail gate for the fine-structure constant Concept DOI: 10.5281/zenodo.20628735 Author: Ali Attar Website: quantumtraction.org Main book anchor: Quantum Traction Theory: Main Book v10.01 This paper isolates the photon-edge gate in the QTT derivation of the electromagnetic coupling. The point is not to fit \(\alpha\), but to show why the residual rail has the minimal five-rail form allowed by the source grammar. The reader-facing target is the inverse-coupling form \[ \alpha^{-1}_{\mathrm{QTT}} =4\pi\left(8+\frac{\rho}{2}+\lambda_\gamma\right), \qquad \rho=2\pi\cos\left(\frac\pi8\right). \] The photon-edge theorem then asks why \(\lambda_\gamma\) is not a free decimal tail, but a closed residual packet with a declared minimality and no-smuggling test. Core labels: Σ-PHOTON-EDGE-GATE, Σ-FINE-STRUCTURE-RESIDUAL-FIVE-RAIL, Σ-ALPHA-NO-FIT-FIREWALL.