A Structural Coherence Bound in the Higgs Sector: Geometric Derivation of λH ≈ e−2 from the Thales Variance Partition

The Higgs quartic coupling λ_H ≈ 0.129 satisfies λ_H e² ≈ 1 within ~5%. We show this is not numerological but structural: on a single Thales semicircle, h⁴ ≤ 1/16 = 0.0625, so e⁻² ≈ 0.135 exceeds the 1D bound by a factor of 2.17. The Standard Model Higgs doublet's two complex channels (four real degrees of freedom) raise the bound to 1/4, and the exact solution 4h₀⁴ = e⁻² yields h₀² = 1/(2e), with partition ratio a/b ≈ 3.12 — within 4% of the 3:1 Goldstone/Higgs DOF split after spontaneous symmetry breaking. Standard Model renormalization group running confirms λ(μ) passes through e⁻² at μ ≈ 116 GeV, reducing the apparent gap to ~1% at the Higgs mass scale. The h⁴ = a² − 2a³ + a⁴ decomposition is validated across hurricanes and binary black hole mergers as a diagnostic for surface- vs. volume-dominated regimes. Version 3 revision with 1D bound proof, doublet resolution, and RGE verification.