Framework Foundations for the Alpha Spiral: Dirac–Coulomb Boundary Roles, Recoil-Capacity Selection, and Failure-Route Analysis

This framework preprint provides the technical foundations behind the published Alpha Spiral preprint, The Alpha Spiral: A Spinor-Boundary and Recoil-Capacity Route to the Fine-Structure Constant. The paper expands the compact branch-selection route m_e/m_p -> K = 35 -> N = 137 -> alpha_model^(-1) ≈ 137.035999178290 by giving the supporting Dirac–Coulomb boundary-role construction, the recoil-capacity selector, the structural tiling route to K = 35, the continuous correction terms, the numerical recalculation, and the failure routes rejected during development. The work is intended as an auditable companion framework. It does not claim an accepted first-principles QED derivation of the fine-structure constant. The claim is narrower: the Alpha Spiral is presented as a Dirac–Coulomb-compatible, failure-tested branch-selection framework in which the observed low-energy electromagnetic branch of alpha is selected by spinor closure, finite-anchor recoil capacity, and continuous boundary corrections.