ICC XVI: Geometric Phases and the Limits of Quantitative CP Prediction

We investigate whether geometric phases in the Information-Copying Cosmology framework can yield quantitative predictions for the CP-violating phase δCP in the PMNS matrix. Building on the topological structure π1(M) ∼ = Z established in ICC XIII, we test the minimal ansatz θi = θ0 +γgeom i +εi with γi ∝ mi/mτ. Monte Carlo simulations yield a broad distribution δCP = 1.04π ±0.63π, with only 11% of realizations within the current T2K/NOvA 1σ range. We trace this to the extreme mass hierarchy mν/mτ ∼ 10−11, which suppresses geometric phases for neutrinos to γν ∼ 10−6π, leaving phase differences dominated by the charged lepton sector. This constitutes a structural constraint: sharp predictions for δCP require either (i) a geometric phase functional form that remains O(1) for m → 0, (ii) sector-dependent reference scales, or (iii) additional dynamical correlations. The predicted broad distribution is falsifiable: future measurements constraining σδ ≲ 0.2π would require extensions beyond the minimal geometric ansatz. This work establishes the geometric foundation for leptonic CP violation and defines the minimal conditions for quantitative precision.