We present a completion-locked extraction of the electromagnetic fine-structure constant as a response invariant within a symmetry-only closure framework. A universal circle/Hopf sector fixes two upstream locks—a dyadic half-angle and a canonical nome—which together select a unique geometric and topological normalization, removing the usual freedom to tune couplings. Using a Berezinskii–Kosterlitz–Thouless renormalization-group fixed-point normalization with locked fugacity, we define a canonical stiffness coupling and derive a certified numerical enclosure that overlaps the CODATA recommended interval for the inverse fine-structure constant. The argument is fully explicit and auditable, combining mode and block reductions, heat-kernel remainder bounds, and verified interval-arithmetic estimates. In addition, we identify an independent spectral–topological phase observable arising from a relative Atiyah–Patodi–Singer eta invariant of the same Dirac family; this phase observable is reported separately and is not used in the CODATA comparison. Note: All formulas, definitions, and numerical certifications appear in the PDF. License note: Distributed under CC BY-NC-ND 4.0.
Salimah Meghani (Fri,) studied this question.