ICC XVIII: Dynamical Phase Correlations and Structural Constraints on Quantitative CP Prediction

Building on the refined structural constraint identified in ICC XVII, we investigate whether dynamical phase correlations can suppress unitarization-induced scrambling and restore quantitative predictivity for the CP-violating phase δCP in the PMNS matrix. We in troduce a simple effective potential V ({θi}) ∝ i< 2%; (ii) generic phase correlations do not target the specific linear combinations amplified by the nonlinear unitary projection V = polar(M). This constitutes a further refined structural constraint: sharp predictions for δCP require targeted correlations aligned with the eigenvectors of the unitarization map’s Hessian. We provide a schematic expression for the targeted potential: Vtargeted = λ 2 α 1 Λα +ϵ vα·(θ−θ(0) −∆γ) 2 , (1) where vα andΛα areeigenvectors and eigenvalues of the Hessian Hij = ∂2 logdet(M†M)/∂θi∂θj evaluated at the ensemble-averaged ⟨M⟩. This potential directly suppresses modes with small Λα that are amplified during polar decomposition. The predicted broad distribution is falsifiable: DUNE (projected σ(δCP) ≈ 15◦ by 2035) and Hyper-Kamiokande (σ(δCP) ≈ 10◦ by 2030) will test the hypothesis σδ ≲ 0.2π at > 3σ significance. This work identifies the minimal conditions for quantitative precision and establishes targeted dynamical correlations as the next necessary ingredient.