weak_coupling_approx
plain-language theorem explainer
The weak coupling constant g satisfies |g - 0.653| < 0.01. Electroweak modelers would cite this bound when confirming consistency between the W boson mass and the Higgs vacuum expectation value. The proof reduces the coupling expression directly from those two definitions via simplification followed by numerical evaluation.
Claim. The absolute difference between the weak coupling constant g and 0.653 is less than 0.01, where g is obtained from twice the W boson mass divided by the vacuum expectation value.
background
The module derives W and Z boson masses from electroweak symmetry breaking in Recognition Science. The Higgs field acquires a vacuum expectation value v ≈ 246 GeV, breaking SU(2)_L × U(1)_Y to U(1)_EM and corresponding to a J-cost minimum. The weak coupling g emerges from the gauge structure, with the mass ratio m_W / m_Z = cos θ_W and sin²θ_W ≈ 0.231. The vacuum expectation value is fixed at 246.22 GeV and the W mass at approximately 80.37 GeV, placing the electroweak scale on the phi-ladder.
proof idea
This is a one-line wrapper that applies simplification to the definitions of the weak coupling, W boson mass, and vacuum expectation value, then performs numerical normalization to confirm the bound.
why it matters
The result supplies a numerical consistency check inside the electroweak boson mass derivations (P-015, P-016). It supports the framework predictions m_W ≈ 80.38 GeV and v ≈ 246 GeV that follow from the J-uniqueness fixed point and the eight-tick octave. No downstream theorems depend on it, yet it closes a verification step for the gauge coupling at the electroweak scale.
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