TBM_theta12
plain-language theorem explainer
The tribimaximal mixing hypothesis fixes the solar neutrino angle parameter at one third. Researchers modeling neutrino oscillations within Recognition Science would reference this value when comparing the base TBM prediction against measured mixing data. The declaration is a direct real-number assignment requiring no further justification.
Claim. The tribimaximal mixing prediction for the solar neutrino mixing angle satisfies $sin^2 theta_{12} = 1/3$.
background
The PMNS matrix encodes neutrino flavor mixing between electron, muon, and tau neutrinos and their mass eigenstates. In Recognition Science the module derives these angles from phi-quantized values, with tribimaximal mixing as the symmetric starting point before corrections. The tribimaximal mixing predicts sin squared theta12 equals one third, sin squared theta23 equals one half, and sin squared theta13 equals zero, though the last deviates from observation and requires phi-corrections.
proof idea
The definition directly assigns the constant value one third to the tribimaximal solar mixing parameter with no lemmas or tactics applied.
why it matters
This definition anchors Hypothesis 4 on tribimaximal mixing plus corrections within the PMNS matrix module. It provides the base value that subsequent phi-predictions for theta12 build upon, connecting to the Recognition Science mechanism where neutrino angles are phi-quantized. The parent structure is the overall PMNS derivation from RS, with the open question being the precise phi-corrections needed to match the observed reactor angle.
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