predictions
plain-language theorem explainer
RS predictions for the PMNS neutrino mixing parameters collected as a list of five qualitative statements. Neutrino phenomenologists would cite the list when testing Recognition Science against oscillation data. The definition is a direct enumeration drawing on eight-tick phase symmetry and axis vectors from the F2Power algebra.
Claim. The Recognition Science predictions for the PMNS parameters are: $\theta_{23} \approx 45^\circ$ from eight-tick symmetry, $\sin^2\theta_{12} \in [0.276,0.307]$ from the golden-ratio connection, $\theta_{13}$ small but nonzero from $\phi$-hierarchy, $\delta_{CP} \approx \pi + O(\phi^{-1})$, and normal mass ordering preferred.
background
The module derives the PMNS matrix from Recognition Science by treating neutrino mixing angles as $\phi$-quantized quantities. Neutrinos occupy the axes-1 and axes-2 subspace of the three-dimensional F2 vector space, where axis1 and axis2 are the weight-1 vectors (true,false,false) and (false,true,false). The tick supplies the fundamental time quantum equal to 1, while the phase function from the eight-tick construction returns $k\pi/4$ for $k=0\dots7$. The local setting states that the PMNS matrix relates flavor to mass eigenstates and that large mixing angles arise from eight-tick symmetry and $\phi$-scaling, in contrast to the small angles of the CKM sector.
proof idea
Direct definition that enumerates the five strings given in the doc-comment. The surrounding comment invokes the Berry-phase calculation on axis1 and axis2 (both with flipCount 2) to obtain the leading-order $\delta_{CP}$ correction from generation torsion, using the phase values $k\pi/4$ and the Gray-code structure already established for the eight-tick octave.
why it matters
The definition assembles the concrete RS predictions that follow from the eight-tick octave (T7) and the $\phi$-ladder mass formula. It supplies the target statements for the module's goal of deriving PMNS angles from golden-ratio geometry, as stated in the module doc-comment. No downstream theorems are recorded, leaving the list available for direct comparison with oscillation data.
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