sin2_theta23_observed
plain-language theorem explainer
The definition supplies the experimental central value sin²θ₂₃ = 0.545 for the atmospheric neutrino mixing angle. Neutrino physicists fitting PMNS parameters inside Recognition Science reference it when comparing φ-quantized predictions to atmospheric and reactor data. The declaration is a direct numerical assignment of the observed quantity with no further computation or derivation.
Claim. $sin^2 θ_{23} = 0.545$, where θ_{23} denotes the atmospheric neutrino mixing angle in the PMNS matrix.
background
The module derives the PMNS neutrino mixing matrix from Recognition Science by treating the three mixing angles as φ-quantized quantities. Large mixing is expected: θ_{12} ≈ 34°, θ_{23} ≈ 45° (maximal), and θ_{13} ≈ 8.6°. The sibling definitions theta23_degrees and maximal_theta23 supply the corresponding angle in degrees and the symmetry argument that θ_{23} should saturate at 45°.
proof idea
Direct definition that assigns the numerical constant 0.545 to the real number representing the observed sin²θ_{23}.
why it matters
It supplies the experimental anchor for the PMNS parameters inside the StandardModel module, allowing direct comparison of Recognition Science predictions (maximal_theta23, phi_prediction_theta13) against data. The module doc states that the near-maximal θ_{23} suggests an underlying symmetry tied to the φ-ladder and the eight-tick octave. No downstream theorems yet consume it, leaving open the question of whether the 0.045 offset from 0.5 is itself a higher-order φ correction.
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