Square-root mass-space 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 a Koide–Brannen square-root mass-space input with a discrete split-and-recombined deformation of tribimaximal mixing (TBM). The square-root input defines an auxiliary rotation between signed-root and positive-root mass coordinates and fixes the 3–1 seed angle. After the structural prescriptions are chosen, the principal branch is fixed by two TBM-sector sine inputs and one geometric Brannen seed, together with one third-generation basis-phase assignment, rather than by continuously fitted PMNS parameters. Before comparison with data, the TBM-like sectors use the A-type matrix-element split: the off-diagonal rotation-matrix element is split, not the angle. The selected branch improves the solar-angle agreement relative to the TBM-limit baseline, predicts an upper-octant atmospheric angle, conserves CP by construction as a falsifiable structural feature, and gives a reactor angle below the global-fit central value. We also provide the charged-lepton-basis Majorana mass matrix, a CP-real representative, residual Klein generators, and reproduction scripts.