predictions
plain-language theorem explainer
RS predictions for the PMNS neutrino mixing parameters assembled as a static list. Neutrino physicists comparing Recognition Science outputs to oscillation data would cite these five items. The definition enumerates the list directly from eight-tick symmetry and phi-hierarchy without further computation.
Claim. The Recognition Science predictions for the PMNS neutrino mixing matrix are: $θ_{23} ≈ 45°$ from eight-tick symmetry, $sin²θ_{12} ≈ 0.276-0.307$ from $φ$-connection, $θ_{13}$ small but nonzero from $φ$-hierarchy, $δ_{CP} ≈ π + O(φ^{-1}) ∼ 190°-200°$, and normal mass ordering preferred.
background
The PMNSMatrix module derives the Pontecorvo-Maki-Nakagawa-Sakata matrix from Recognition Science, relating neutrino flavor states $ν_e, ν_μ, ν_τ$ to mass states $ν_1, ν_2, ν_3$. Eight-tick symmetry supplies the phase structure via the definition phase(k) = kπ/4 for k in Fin 8, while axis1 and axis2 from F2Power 3 give the weight-1 vectors (true,false,false) and (false,true,false). The fundamental tick sets τ₀ = 1 as the RS time quantum.
proof idea
The definition directly constructs the List String containing the five prediction strings. It relies on the axis1 and axis2 vectors together with the eight-tick phase to ground the maximal θ₂₃ claim and the equal Berry phases on axes 1 and 2. The inline comment then sketches the torsion correction for δ_CP without invoking further lemmas.
why it matters
This definition supplies the concrete outputs for the SM-014 target of deriving PMNS angles from φ-quantized structure. It instantiates the eight-tick octave (T7) and phi fixed point (T6) to predict maximal atmospheric mixing and near-π CP phase. No downstream theorems are recorded, leaving open the precise numerical match of the (6/11) torsion term to the observed δ_CP ≈ 197°.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.