sin2_theta12_observed
plain-language theorem explainer
sin2_theta12_observed records the experimental central value sin²θ₁₂ = 0.307 for the solar neutrino mixing angle. RS model builders cite it when testing φ-quantized predictions against PMNS data and when computing deviations from tribimaximal mixing. The entry is a bare numerical definition with no computation or lemmas.
Claim. The observed central value of the solar neutrino mixing parameter satisfies $sin^2 θ_{12} = 0.307$.
background
The PMNSMatrix module derives the neutrino mixing matrix from Recognition Science by treating angles as φ-quantized quantities arising from the eight-tick octave and the Recognition Composition Law. Large mixing angles appear naturally: θ₁₂ ≈ 34° (solar), θ₂₃ ≈ 45° (atmospheric), θ₁₃ ≈ 8.6° (reactor). The supplied definition supplies the measured central value of sin²θ₁₂ that serves as the empirical anchor for all subsequent corrections.
proof idea
The declaration is a one-line definition that directly assigns the literal real number 0.307. No lemmas, tactics, or upstream results are applied.
why it matters
This constant is referenced by the downstream definition TBM_correction_theta12, which forms 1/3 - sin2_theta12_observed and compares the result to powers of (φ - 1). It supplies the experimental input required by the module's target proposition on neutrino mixing angles from golden-ratio geometry. The placement closes the interface between the φ-ladder and observed PMNS parameters while leaving open the precise size of higher-order corrections.
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