Ab Initio Derivation of the Fine Structure Constant from Density Field Dynamics

We present numerical evidence that the electromagnetic fine structure constant α ≈ 1/137 emerges from first principles within the gauge-emergence microsector of Density Field Dynamics (DFD). Four independent topological constraints — all fixed by the geometry of the internal manifold CP² × S³ with no continuous free parameters in the topological input sector — uniquely determine the lattice parameter point (βU(1), βSU(2)) = (3.80, 22.80). At this point, lattice Monte Carlo simulations yield α within 1% of the physical value across lattice sizes L = 6, 8, 10, 12, 16. Key results: k_max = 60 derived from a closed Spin^c index on CP² (Bridge Lemma) βU(1) = 3.7969 from the Chern-Simons weighted average at k_max = 60 βSU(2)/βU(1) = 6 derived from the stiffness ratio and generation count The fully converged sum (k_max → ∞) gives α = 1/303, ruled out at >50σ Wilson ratio 6 uniquely correct: ten ratios tested (3–9 including fractional), all others fail Result independent of simulation parameters (proposal size ε, background field k₀) Simulation code and data: https://doi.org/10.5281/zenodo.19173548 Parent theory: Density Field Dynamics (DFD) unified theory v3.2, https://doi.org/10.5281/zenodo.18066593 Version history: v1 deposited December 24, 2025 (priority timestamp). This version (v2.0) incorporates corrections and extensions through March 2026, including the Bridge Lemma derivation of k_max, proper beta/kappa distinction, L=16 results, and alignment with DFD unified theory v3.2.