Deriving the Fine Structure Constant from Dimensional Geometry: A Lagrangian Formulation

Deriving the Fine Structure Constant from Dimensional Geometry: A Lagrangian Formulation

The fine structure constant α ≈ 1/137 has been measured to 12 significant figures and explained by nothing. This paper proposes that α—and all fundamental constants—emerge from the geometry of dimensional structure itself.

The polynomial family x^n = x + 1 defines dimensional constants: ρ = 1.3247 (the plastic constant, n=3) governs three-dimensional classical structure; Q = 1.2207 (the quantum constant, n=4) governs four-dimensional quantum spacetime. From conformal symmetry and holographic structure:

α = π²/(ρQ)^15 = 1/137.06

matching the measured fine structure constant to 0.02% with zero free parameters.

The framework extends to 39 predictions across particle physics and cosmology. Monte Carlo validation (10 million trials) yields combined significance of 20.0σ. Supplementary materials include complete validation code, prediction tables, and statistical analysis.