Formal Koide Structure: Mass Bounds, Generation Counting, and Neutrino Predictions from the Z_N Ansatz

The Z₃ Ansatz \sqrt{m_r} = a(1 + b\cos(\theta_0 + 2\pi r/3)) with b^2 = 2 is a parametrization — not a dynamical model — that encodes the Koide mass relation Q = 2/3. Maturity: Short Draft. Includes formal verification (Lean 4 / Platonic kernel). Part of The Latent research program. Related papers in this program: Neutrino Mass.