bestPhiPrediction
plain-language theorem explainer
bestPhiPrediction supplies the Recognition Science estimate for cos(θ_W) via the algebraic form √(1 - 1/(2φ + 1)). A particle physicist comparing electroweak data to φ-derived models would cite the value 0.874 against the measured ratio 0.881. The definition is a direct alias to hypothesis5 with no additional reduction steps.
Claim. Define bestPhiPrediction $:= √(1 - 1/(2φ + 1))$ where φ denotes the golden ratio fixed point satisfying φ = 1 + 1/φ.
background
The module treats the W/Z mass ratio as cos(θ_W) under electroweak symmetry breaking, with the ratio constrained by φ-quantized gauge mixing in RS-native units. Upstream, Constants.RSNativeUnits.U fixes τ₀ = 1 tick and ℓ₀ = 1 voxel with c = 1, while CPM.LawOfExistence.Model supplies the structure holding constants, defectMass, and energyGap maps. The local setting invokes the φ-ladder and J-cost from the foundation to express the Weinberg angle approximation.
proof idea
The definition is a one-line wrapper that aliases hypothesis5 directly to bestPhiPrediction.
why it matters
This supplies the concrete numerical prediction for the electroweak mixing angle inside the Recognition framework, closing the SM-003 target stated in the module documentation. It links to the self-similar fixed point φ (T6) and the J-uniqueness relation (T5). No downstream uses appear in the used_by edges, leaving open the embedding of this form into a full derivation from the Recognition Composition Law.
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