hypothesis5
plain-language theorem explainer
This declaration defines the CKM Wolfenstein parameter λ as sin(π/(4φ)) with φ the golden ratio. Researchers deriving quark mixing angles from Recognition Science would cite it when constructing φ-quantized CKM elements. The definition is a direct one-line assignment of the trigonometric expression in Real.
Claim. Let λ be the Wolfenstein parameter defined by λ = sin(π/(4φ)), where φ denotes the golden ratio.
background
The CKMMatrix module targets derivation of the 3×3 CKM matrix from φ-quantized mixing angles tied to the eight-tick phase structure. The golden ratio φ satisfies the self-similar fixed point condition and enters constants such as ħ = φ^{-5}. Upstream, PrimitiveDistinction.from reduces seven axioms to four structural conditions plus three definitional facts. CPM2D.Hypothesis supplies a bundle containing projection_defect and energy control inequalities for GalerkinState. WZMassRatio.hypothesis5 provides the parallel φ-expression √(1 - 1/(2φ + 1)) for cos(θ_W).
proof idea
The declaration is a one-line definition that directly assigns Real.sin (Real.pi / (4 * phi)) to hypothesis5.
why it matters
This definition supplies one φ-based CKM element in the Recognition Science framework and feeds bestPhiPrediction in WZMassRatio, which compares the resulting numerical value against observation. It fills the paper proposition on CKM Matrix from Golden Ratio Geometry and connects to the eight-tick octave (T7) and D = 3 in the forcing chain. The module doc-comment notes the 4% discrepancy with measured λ ≈ 0.227.
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