ICC XVII: Non-Vanishing Geometric Phases and the Refined Limits of Quantitative CP Prediction

Building on the structural constraint identified in ICC XVI, we investigate whether a non-vanishing geometric phase ansatz can restore quantitative predictivity for the CP violating phase δCP in the PMNS matrix. We propose a modified functional form γi ∝ arctan( mi/m0) with m0 ∼ 10−2 eV, which remains O(1) for m → 0 while preserving the √mscaling for heavy states. Monte Carlo simulations yield δCP = 1.00π±0.56π, with the central value shifted closer to the T2K/NOvA best fit compared to ICC XVI (1.04π → 1.00π). However, the distribu tion remains broad due to the nonlinear unitary projection V = polar(M), which amplifies residual stochastic fluctuations even when geometric phase differences are O(0.1–0.4π). This constitutes a refined structural constraint: sharp predictions for δCP require not only non-vanishing geometric phases but also additional dynamical correlations that sup press the sensitivity of the unitarization map to stochastic noise. The predicted distribution is falsifiable: future measurements constraining σδ ≲ 0.2π would require physics beyond geo metric phases alone. This work establishes the minimal conditions for quantitative precision and identifies dynamical correlations as the next necessary ingredient.