Topological Geometry of Neutrino Mass and Mixing

This Letter transitions neutrino mixing from an empirical fit to a geometric law by analytically deriving the PMNS mixing angles and mass spectrum from an $A_5$ topological manifold. Solving the Quantum Yang-Baxter Equation forces a geometric fracture at $M_0\approx 3.88\times {10}^{16}$ GeV. Projecting this to the Electroweak scale yields parameter-free targets: maximal CP violation ${\delta }_{CP}=\pm \pi \mathrm{/}2$, a mass sum $\sum m_i\approx 72.48$ meV, with $m_1<m_3$, and effective masses $m_{\beta }\approx 12.47$ meV and $m_{\beta \beta }\approx 8.20$ meV, setting definitive experimental thresholds.