The Fine‑Structure Constant as Interface Geometry

This paper presents a geometric and number-theoretic derivation of the fine-structure constant α within the Dual-Domain Cosmology (DDC) framework. In this ontology, stable matter emerges from discrete three-quanta anchors in an atemporal Quantum Domain (QD) that project into the continuous 4-dimensional Spacetime Domain (SD). The projection interface is constrained by a non-degenerate discrete lattice triad, forcing an effective radius R=√5. Exact number theory applied to this 4D hyper-ball yields 137 integer lattice points, providing a geometric interpretation of the reciprocal coupling constant. The resulting bare value α^ (-1) ≈137. 03601 reproduces the CODATA value to within 8. 6×10^ (-8) in relative terms—a match to seven significant digits with no fitted parameters. The relation is excluded as an exact identity at 562 experimental standard deviations; the residual is a stated open problem, not a fitted parameter. Formalizing the interface as a normalized action principle, SDDC=137α+π²/2 α²=1, partitions the coupling between discrete network microstates and continuous 4D volumetric propagation. The framework derives α from interface geometry with no fitted parameters; the 8. 6 × 10⁻⁸ residual is a quantified open problem, not a tuned correction. Keywords: fine‑structure constant; dual‑domain cosmology; entanglement topology; 4D lattice; action principle; vacuum polarization; entanglement strain; Planck scale; interface geometry