hypothesis1
plain-language theorem explainer
Particle physicists testing Recognition Science predictions for electroweak parameters would cite this definition of a candidate Weinberg angle. It sets cos(θ_W) to the square root of one minus phi to the minus two. The assignment follows directly from the module's algebraic setup without invoking upstream lemmas.
Claim. The first hypothesis asserts that the cosine of the Weinberg angle satisfies $cos(θ_W) = √(1 - φ^{-2})$, where φ denotes the golden ratio fixed point.
background
The module derives the W/Z boson mass ratio from φ-structure in Recognition Science. By Standard Model convention the ratio equals cos(θ_W), and the definition supplies one φ-constrained candidate for that cosine. Parallel hypothesis definitions appear in the CosmologicalConstant module (Λ ∝ τ₀^{-2}) and the CKMMatrix module (λ = 1/(2φ)).
proof idea
The declaration is a one-line definition that directly assigns the real number obtained by taking the square root of one minus the reciprocal of phi squared.
why it matters
This populates the hypothesis interface for the WZ mass ratio derivation and is referenced by the hypothesis1 definitions in CosmologicalConstant and CKMMatrix. The module targets a PRL paper on electroweak parameters from RS, linking to the φ fixed point at T6 in the forcing chain.
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