This work presents a first-principles derivation of the fine-structure constant, α, within the Vortex Framework (VF), a model in which fundamental physical constantsand interactions emerge from a three-seed quantum substrate1, 2: the speed of light c, Planck’s constant ℏ, and the vacuum density ρ0. By modeling the quantum sub-strate as a 3D lattice of toroidal vortex rings with quantized circulation, we compute effective packing fractions and coarse-grained interactions that naturally produce thedimensionless electromagnetic coupling. The derivation incorporates lattice geometry, interlinking of vortex rings, IR coarse-graining, and substrate stiffness to reconcile naive continuum estimates with the observed value α ≈ 1/137. This framework demonstrates how electromagnetic and gravitational constants can emerge from topological and energetic constraints of a minimal vortex-based substrate, providing a unified, predictive approach to fundamental constants.
Alex Smith (Sat,) studied this question.