hypothesis3
plain-language theorem explainer
Recognition Science sets the cosine of the Weinberg angle to the golden ratio divided by the square root of phi squared plus one. Particle physicists working on electroweak parameters would cite this when testing phi-quantized mixing against measured W and Z masses. The declaration is a direct noncomputable assignment of that closed-form expression.
Claim. Define the Weinberg angle by the relation $cos θ_W := φ / √(φ² + 1)$, where φ denotes the golden ratio.
background
The module derives the W/Z mass ratio from Recognition Science's φ-structure. Observed masses give m_W / m_Z ≈ 0.881, which equals cos θ_W by definition of the Weinberg angle. The golden ratio φ enters as the self-similar fixed point forced in the T0-T8 chain, and the expression is built from the same J-cost ground-state energy that appears in the Cosmological Constant hypothesis3, where J_vac = (φ² + 1)/(2φ) - 1.
proof idea
The declaration is a one-line wrapper that assigns the expression phi / Real.sqrt (phi^2 + 1) directly to the identifier.
why it matters
This supplies the φ-based cos θ_W value that is referenced by the hypothesis3 definitions in both the Cosmological Constant and CKM Matrix modules. It fills the SM-003 target of obtaining electroweak parameters from φ-quantized gauge structure. The relevant framework step is T6, the forcing of φ as the unique self-similar fixed point that here fixes the mixing angle near 0.851.
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