Square-Root Mass Mixing and a Split-and-Recombined Tribimaximal Ansatz for the Pontecorvo--Maki--Nakagawa--Sakata matrix

We propose a deterministic phenomenological ansatz for the Pontecorvo--Maki--Nakagawa--Sakata (PMNS) matrix that combines Koide--Brannen square-root mass ratios with a phase-dressed, split-and-recombined tribimaximal product. The principal branch is specified by four fixed inputs, not by fitted continuous PMNS parameters: the Brannen-sector sine input \(sinϑ₃₁\), the two TBM-sector sine entries \(sinθν12\) and \(sinθν23\), and the fixed third-generation rephasing angle \(1/2π\). The 3–1 sector is one-sided because Uₑ₃₁ = I; the 1–2 and 2–3 sectors use balanced A-type matrix-element splittings. Candidate 1, the \(B31+A12+A23\) branch, gives realistic solar and reactor angles, an upper-octant atmospheric angle, and CP conservation. Its reactor-angle pull is about \(-1.9σ\) in the NuFIT one-dimensional reactor profile and about \(-0.6σ\) in the direct Daya Bay diagnostic. We also provide the charged-lepton-basis Majorana mass matrix, a CP-real representative, residual Klein generators, and reproduction scripts. The ansatz is phenomenological, not a derived flavor theory; its falsifiable features are CP conservation and an upper-octant atmospheric prediction.