The Gauge Parameters: Standard Model Constants from Cascade Geometry

The Standard Model of particle physics contains approximately nineteen free parameters whose numerical values appear to be arbitrary. Among these, the electroweak mixing angle (Weinberg angle), the fine structure constant, and the ratio of the strong to weak coupling constants are the defining numbers of the gauge sector. This paper demonstrates that all three are derivable, to within 0.4%, from the two universal Feigenbaum cascade constants α and δ. The primary result is sin²θ_W = 1/(2√δ) = 0.23139, matching the PDG MS-bar value of 0.23122 to 0.074%. The fine structure constant 1/α_em ≈ (α × δ)² = 136.576, within 0.336% of the measured 137.036. The coupling ratio α₃/α₂ ≈ δ²/α² = 3.4801, within 0.348% of the measured 3.4923. Three parameters. Two constants. The gauge sector is not arbitrary. The same cascade level architecture that explains why fermion masses do not appear at this level also predicts the boundary: Yukawa couplings are level-2 cascade observables, set by electroweak symmetry breaking which is itself a cascade transition. The gauge sector sits at level 1 because it encodes the geometry of the symmetry, not its breaking. Paper 44 of the Resonance Theory series.