The Alpha Spiral: A Spinor-Boundary and Recoil-Capacity Route to the Fine-Structure Constant

The fine-structure constant alpha is one of the most important dimensionless constants in physics, yet its numerical value is not derived from standard quantum electrodynamics. In accepted practice, alpha is measured experimentally and then used as an input parameter. This paper proposes a candidate semiclassical spinor-boundary closure model in which the observed low-energy electromagnetic branch of alpha is selected by a combination of Dirac-Coulomb boundary structure, spinor 4pi closure, finite electron-proton recoil, and a recoil-capacity branch condition. The model begins from a low-energy electron-proton electromagnetic system and introduces a boundary-sector basis B = r, Omega, s, corresponding to radial Coulomb structure, angular/orbital closure, and spinor-frame participation. This gives an active boundary-sector count nch = 3. A spinor closure-index condition then requires N + nch = 4K, so that, for the three-sector branch, N = 4K - 3. The branch variable K is selected by a recoil-capacity condition CK = (nch/2) (mₑ/mₚ) K² ≈ 1. For nch = 3, this gives K_* ≈ 34. 987, selecting the nearest integer branch K = 35. The corresponding base closure integer is therefore N = 4 (35) - 3 = 137. Using this selected branch, the model proposes a self-consistent equation for alpha whose solution is alpha^-1 ≈ 137. 035999178290, in close agreement with the measured inverse fine-structure constant. The claim of this paper is not that standard QED is replaced, nor that a completed first-principles QED derivation has already been established. The claim is narrower: the route mₑ/mₚ -> K = 35 -> N = 137 -> alpha is proposed to arise from spinor-boundary closure and finite-anchor recoil capacity.