hypothesis4
plain-language theorem explainer
Definition hypothesis4 supplies the Recognition Science expression for cos(θ_W) as sqrt(1 - 1/(phi^2 + 1)). Electroweak model builders would cite it when linking the observed W/Z mass ratio 0.881 to the golden ratio constraint. It is introduced as a direct noncomputable definition.
Claim. $cos(θ_W) = √(1 - 1/(φ² + 1))$
background
Module SM-003 derives the W/Z mass ratio from Recognition Science φ-structure. The masses satisfy m_W/m_Z = cos(θ_W) with observed ratio 0.8815, and the angle is constrained by φ-quantized SU(2)×U(1) mixing. Upstream CPM2D.Hypothesis supplies a bundle of projection-defect and energy-control axioms for GalerkinState models. CKMMatrix.hypothesis4 defines the related parameter λ = (3 - φ)/3.
proof idea
One-line definition that directly assigns Real.sqrt(1 - 1/(phi^2 + 1)) to hypothesis4.
why it matters
It supplies the φ-derived cos(θ_W) used by CKMMatrix.hypothesis4 to constrain λ. The declaration fills the electroweak-parameter step in the SM-003 paper proposition, connecting to the φ-ladder and T6 self-similar fixed point.
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