The complete electroweak spectrum from the Planck mass and the golden ratio: L4 spectral formulas for MZ, MW, MH, and predictions

Technical Addendum to the Artosphere series. We derive the complete electroweak boson spectrum from two inputs: the Planck mass MPl and the golden ratio φ = (1+√5) /2. Zero free parameters. The five L4 formulas (defining η = 719/9 and ξ = 8φ−3): vEW = MPl·φ−η = 245. 97 GeV (Δ=0. 10%) MW = MPl·φ2−η/8 = 80. 50 GeV (Δ=0. 16%) MZ = MPl·φ5/2−η/√ (8ξ) = 91. 84 GeV (Δ=0. 71%) MH = MPl·φ1/2−η/√ (2π) = 124. 82 GeV (Δ=0. 34%) Mχ = MPl·φ−3−η = 58. 1 GeV (prediction) The exponent shifts from vEW are −3, 0, +1/2, +2, +5/2, traced to Cl (6) representation dimensions. With 1-loop RG running (boundary at Λ = MPl/φ80), MZ improves to 0. 12%. The Higgs quartic coupling λH = φ/ (4π) is derived from VArt curvature: V″ (s0) = φ3. Three independent routes to MH converge at 0. 24–0. 91%. All quantities trace to the single axiom Ψ∈Cl (9, 1) through: VArt from Z3 Fibonacci fusion, g2 = φ2/4 from Cl (6) Casimir, sin2θW = 3/ (8φ) from Fermat descent, and η = 719/9 from E8→SU (9) hierarchy.