theta23_degrees
plain-language theorem explainer
The atmospheric neutrino mixing angle θ₂₃ is assigned the numerical value 49 degrees. Neutrino physicists fitting oscillation data in Recognition Science models would cite this constant when assembling the PMNS matrix. The definition is a direct real-number assignment with no computation or derivation steps.
Claim. The atmospheric mixing angle satisfies $θ_{23} = 49^∘$.
background
Recognition Science models neutrino flavor mixing through the PMNS matrix, where large angles arise from φ-quantized structures rather than the small angles of the CKM matrix. The atmospheric angle θ₂₃ controls μ-τ mixing and is observed near maximal (45°), with this definition supplying the 49° anchor used in best-fit constructions. The module SM-014 targets derivation of the full PMNS matrix from RS principles, noting that φ-connections may explain the observed pattern of θ₁₂ ≈ 34°, θ₂₃ ≈ 45°, and θ₁₃ ≈ 8.6°.
proof idea
This is a direct definition that assigns the literal real value 49.0 to the atmospheric angle. No lemmas, tactics, or upstream results are invoked; the declaration functions as a constant for downstream parameter assembly.
why it matters
The definition feeds the bestFitPMNS constructor that converts all three angles and the CP phase into radians for the PMNSParameters record. It supplies the numerical input required by the SM-014 target of expressing neutrino mixing via RS-native quantities, as described in the module documentation aiming at a PRD paper on golden-ratio geometry for the mixing angles. Within the broader framework it provides an empirical bridge to the φ-ladder and self-similar fixed-point structures that predict large mixing angles.
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