TBM_theta23
plain-language theorem explainer
TBM_theta23 assigns the exact value one half to the sine squared of the atmospheric neutrino mixing angle in the tri-bimaximal approximation. Neutrino modelers working inside Recognition Science cite this constant when assembling the PMNS matrix from phi-quantized angles and comparing it to oscillation data. The definition is a direct constant assignment with no lemmas or computation steps.
Claim. In the tri-bimaximal mixing ansatz the atmospheric neutrino mixing parameter satisfies $sin^2 theta_{23} = 1/2$.
background
The PMNS matrix encodes the transformation between neutrino flavor states (electron, muon, tau) and mass eigenstates through three angles and one CP phase. Recognition Science treats these angles as phi-quantized quantities rather than free parameters, with the atmospheric angle theta_23 singled out for its near-maximal value of 45 degrees. The module develops this picture under the heading SM-014, emphasizing that large mixing angles arise from golden-ratio geometry while the CKM matrix remains small.
proof idea
The declaration is a direct definition that sets the real number to exactly 1/2 with no lemmas applied and no tactics invoked.
why it matters
The constant supplies the exact maximal value for theta_23 inside the Recognition Science derivation of the PMNS matrix from phi-angles. It anchors the comparison between the tri-bimaximal pattern and the observed atmospheric sector, feeding the broader claim that neutrino mixing follows from the self-similar fixed point and eight-tick octave of the forcing chain. The definition therefore serves as a benchmark for the paper proposition on neutrino mixing angles from golden-ratio geometry.
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