deltaCP_pmns_torsion_correction
plain-language theorem explainer
The definition supplies the explicit torsion correction to the Dirac CP phase in the PMNS neutrino mixing matrix. Neutrino modelers working with φ-quantized angles cite it when confirming the predicted δ_CP lies near 197°. The value follows from direct substitution of the 6/11 ratio (extracted from Δτ23/Δτ12) into the base expression π plus a scaled quarter-pi term.
Claim. The torsion correction to the Dirac CP-violating phase in the PMNS matrix is given by $π + (6/11)·(π/4)$.
background
The PMNS matrix module derives neutrino flavor mixing from Recognition Science, where angles are φ-quantized and the atmospheric angle is near-maximal at 45°. The torsion correction is introduced via the ratio Δτ23/Δτ12 applied to a π/4 base, producing the 6/11 factor that places the phase in the third quadrant after a sign flip from sub-leading terms.
proof idea
This is a one-line definition that performs the arithmetic combination of π with the product of the 6/11 ratio and π/4. No external lemmas are invoked beyond the field operations on real numbers.
why it matters
The definition is called by deltaCP_pmns_in_third_quadrant and deltaCP_pmns_range to establish the interval (π, 2π), which in turn supports the PMNSScoreCardCert structure that certifies predicted mixing parameters against data. It fills the SM-014 derivation of neutrino mixing from golden ratio geometry and connects to the eight-tick octave through the discrete torsion increments.
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