hypothesis2
plain-language theorem explainer
This definition supplies the second hypothesis for the Weinberg angle in the Recognition Science treatment of electroweak masses, setting cos(θ_W) to (φ + 1)/(φ + 2) with φ the golden ratio. Model builders comparing φ-derived mixing angles to the observed m_W/m_Z ratio of 0.881 would reference it. The declaration is introduced as a direct noncomputable assignment with no reduction steps.
Claim. The second hypothesis asserts that the cosine of the Weinberg angle satisfies $cos(θ_W) = (φ + 1)/(φ + 2)$, where φ denotes the golden ratio.
background
The module derives the W/Z boson 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 hypothesis supplies a trial φ-based value for this cosine under the φ-quantized gauge structure of SU(2) × U(1) mixing.
proof idea
The declaration is a direct definition that assigns the arithmetic expression (phi + 1) divided by (phi + 2) to hypothesis2. No lemmas or tactics are invoked; the body is the literal expression.
why it matters
This hypothesis contributes a trial value for cos(θ_W) inside the φ-quantized electroweak sector. It is referenced by the parallel hypothesis2 definitions in the CosmologicalConstant and CKMMatrix modules, showing a pattern of φ-expressions across sectors. The module targets a derivation of electroweak parameters from the T5 J-uniqueness and T6 phi fixed point of the forcing chain, leaving open the numerical gap to the measured 0.881 value.
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