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 matches the CODATA value to seven significant digits, with the minor variance Δ ≈ 1. 2 × 10⁻⁵ interpreted as arising from interface dynamics. 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. This framework derives α from interface geometry rather than treating it as an empirical input. The exact identity is excluded at current experimental precision (~560σ) ; the residual defines a forward target (c₃ ≈ -0. 22) for a geometric derivation of the third-order term. Keywords: fine‑structure constant; dual‑domain cosmology; entanglement topology; 4D lattice; action principle; vacuum polarization; entanglement strain; Planck scale; interface geometry
Risto Vanhanen (Fri,) studied this question.