phi_prediction_theta13
plain-language theorem explainer
The definition supplies a Recognition Science prediction for the reactor neutrino mixing angle as the golden ratio divided by 100. A neutrino phenomenologist would cite it when testing φ-quantized angles against reactor data such as Daya Bay. The construction is a direct one-line assignment of the constant phi from the foundation.
Claim. The predicted value for the squared sine of the reactor mixing angle is given by $sin^2 θ_{13} ≈ φ/100 ≈ 0.01618$, where $φ = (1 + √5)/2$ denotes the golden ratio.
background
In the PMNS matrix module the neutrino mixing angles are treated as φ-quantized quantities. The golden ratio φ is the self-similar fixed point forced at step T6 of the unified forcing chain. The module contrasts this approach with tribimaximal mixing, which predicts a vanishing θ₁₃, and introduces φ-corrections to account for the observed nonzero value near 8.6°.
proof idea
One-line definition that directly assigns the value of phi divided by 100.
why it matters
The definition supplies Hypothesis 3 inside SM-014, the module that derives the PMNS matrix from Recognition Science. It supplies the φ-based input for θ₁₃ that feeds the larger claim of golden-ratio geometry for neutrino mixing angles. No downstream theorems yet reference it, leaving open the quantitative match to the observed 0.022 value.
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