A Conditional G16-Cavity Boundary Ansatz Reproducing PMNS Mixing Angles from a Cabibbo-Scale Input

This manuscript presents a conditional (G₁₆)-cavity boundary ansatz for reproducing the three PMNS mixing angles from a single Cabibbo-scale continuous input. The construction uses the seam-contraction parameter λₖ = 0.2250922889, together with discrete REDERO–Klein boundary data fixed before comparison with neutrino data. No measured PMNS mixing angle is used as an input. The elementary seam phase defines the closure qₖ = 8 and the first two-block Dirichlet cavity G₁₆. A four-site boundary mouth with one hidden level gives the projection vectors vₐ = (t³⁻ᵃ, t|ᵃ⁻²|, tᵃ), and the structural mode rule gives (mₐₜₘ, mₛₒₗ, mᵦₒᵣd) = (5, 8, 15). The boundary phase is written as a Klein–Cayley reflection, φₖ = 3π/4 − 2 arctan(λₖ). The resulting unitary matrix gives sin²θ₁₃ = 0.02178, sin²θ₁₂ = 0.31910, and sin²θ₂₃ = 0.54931, all inside the NuFIT 6.0 comparison intervals used in the manuscript. The calculation is reproducible by a companion Python script and includes a Cabibbo-scale uncertainty propagation, a CP/Jarlskog consistency audit, and a discrete look-elsewhere check. The result remains conditional: λₖ, the full covariant tower action, the boundary projection law, and the dynamical origin of the mode-selection rule are not derived here from first principles.