The Fine‑Structure Constant as Interface Geometry

Derivation Within the Dual-Domain Cosmology Framework 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 six decimal places, with the minor variance Δ ≈ 1.2 × 10⁻⁵ interpreted as arising from interface dynamics. Formalizing the interface as a normalized action principle, S_DDC=137α+(π²/2)α^2=1, partitions the coupling between discrete network microstates and continuous 4D volumetric propagation. The Electron-Planck identity redefines α as the scale-invariant transduction ratio between the Planck-scale vacuum and macroscopic fields. This framework derives α from interface geometry rather than treating it as an empirical input, with the remaining variance constituting a direction for future quantitative derivation. Keywords: fine‑structure constant; dual‑domain cosmology; entanglement topology; 4D lattice; action principle; vacuum polarization; entanglement strain; topological quantization; Planck scale; interface geometry