mass_ratio_from_couplings
plain-language theorem explainer
The declaration asserts that the W to Z boson mass ratio equals the cosine of the Weinberg angle as required by electroweak symmetry breaking. A researcher embedding the Standard Model into Recognition Science would cite this when linking gauge couplings to the golden ratio φ. The proof is a one-line wrapper that reduces the claim to the trivial proposition.
Claim. In the Standard Model the boson masses satisfy $m_W / m_Z = g / √(g² + g'²) = cos(θ_W)$, where g and g' are the SU(2) and U(1) gauge couplings and θ_W is the Weinberg angle.
background
Recognition Science models the electroweak sector through φ-quantized gauge couplings inside RS-native units where c = 1. The W and Z masses arise from the Higgs vacuum expectation value v via m_W² = (g² v²)/4 and m_Z² = ((g² + g'²) v²)/4, so the ratio equals cos(θ_W) by definition of the mixing angle. The module targets derivation of the observed ratio ≈ 0.881 from the φ-constraint on g'/g.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to assert the definitional identity between the mass ratio and cos(θ_W).
why it matters
This declaration fills the SM-003 slot by recording the gauge-symmetry origin of the mass ratio inside the φ-structured electroweak sector. It supports the paper proposition on electroweak parameters from RS and connects to the eight-tick octave through gauge mixing. No downstream uses are recorded, leaving open the explicit computation of the ratio from φ.
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