bestPrediction
The declaration supplies the best RS-derived value for sin²θ_W as (3 - φ)/6 ≈ 0.230. Electroweak unification researchers comparing φ-based models to the observed 0.2229 would cite it for its 3% match. It is realized as a direct alias to the prediction3 definition.
claimThe best RS prediction for the weak mixing parameter is $sin^2 θ_W = (3 - φ)/6 ≈ 0.230$, where φ denotes the golden ratio.
background
The StandardModel.WeinbergAngle module derives the Weinberg angle θ_W from RS φ-structure via 8-tick phase geometry. The upstream prediction3 supplies the explicit formula (3 - phi)/6, which evaluates to approximately 0.230. Module documentation states that electroweak mixing corresponds to an embedding of gauge groups constrained by φ optimization.
proof idea
The definition is a one-line alias that directly references prediction3, which expands to the arithmetic expression (3 - phi)/6.
why it matters in Recognition Science
It supplies the value used by WeinbergAngleScoreCardCert and row_best_prediction_match for the 1% match test, and by weak_mixing_phi_based and coupling_formulas_distinct in GaugeCouplingsComplete to establish distinct geometric origins for the couplings. The result realizes the C-014.3 claim and connects to the eight-tick octave (T7) in the forcing chain.
scope and limits
- Does not derive the formula from the full forcing chain T0-T8.
- Does not include renormalization-group running or scale dependence.
- Does not claim exact equality to the experimental central value.
- Does not address higher-order electroweak corrections.
Lean usage
theorem use_best : |bestPrediction - 0.2229| < 0.01 := best_prediction_close_to_observedformal statement (Lean)
94noncomputable def bestPrediction : ℝ := prediction3
proof body
Definition body.
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