sin2_theta_w_value
plain-language theorem explainer
The declaration proves that sin²(θ_W) lies strictly between 0.22 and 0.23. Electroweak model builders referencing Recognition Science would cite this bound to confirm consistency between the φ-derived W/Z mass ratio and measured boson masses. The proof is a direct term reduction that substitutes the explicit mass ratio and checks the resulting numerical inequalities.
Claim. $0.22 < 1 - (m_W / m_Z)^2 < 0.23$, where the mass ratio $m_W / m_Z = 6 / (3 + φ)$ follows from the φ-quantized gauge structure and $φ$ is the golden ratio.
background
The module derives W and Z boson masses from Recognition Science's φ-structure. The Weinberg angle satisfies $m_W / m_Z = cos θ_W$, so sin²(θ_W) = 1 - (m_W / m_Z)². The mass ratio is supplied by the explicit definition 6 / (3 + φ) from the gauge boson construction in GaugeBosonMassesFromRS.
proof idea
The term proof unfolds sin2ThetaW, massRatio, m_W, and m_Z to expose the concrete numerical expression, splits the conjunction via constructor, and confirms both sides of the inequality with norm_num.
why it matters
This supplies the sin²(θ_W) interval required by the downstream WZ boson ratio scorecard theorem. It completes the SM-003 derivation of electroweak parameters from the φ-structure, consistent with the self-similar fixed point and eight-tick octave in the forcing chain. The result supports the paper proposition on RS-derived electroweak parameters.
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