From Quadratic Flag-Manifold Cohomology to Exact Sum Rules for a One-Phase Flavor Transducer

We develop a one-phase flavor-frame construction on the full flag manifold SU(3)/U(1)². A Borel–Weil–Bott chiral ladder, normalized quadratic cohomology, and the multiplicity-one adjoint component of 3 ⊗ 6 lead to two cyclic qutrit channels with fixed relative strength 1 : 1/√2. Their nontrivial Fourier component yields a Hermitian selector unitarily equivalent to a standard three-site finite Harper-type Hamiltonian. On the physical middle-eigenvalue sheet, an exact nonlinear electron-row invariant determines a unique reactor-solar curve; the remaining PMNS modulus rows and JCP are reconstructed algebraically up to discrete μ–τ and CP choices. Comparison with the published NuFIT 6.1 IC24+SK one-dimensional marginals leaves a nonempty 3σ branch but no common solar-reactor 1σ solution. The construction is deliberately presented as a falsifiable one-phase model: it does not derive the remaining continuous phase, a microscopic selector action, or a neutrino mass-generation mechanism.