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 $\mathbf{3} \otimes \mathbf{6}$ lead to two cyclic qutrit channels with fixed relative strength $1 : 1/\sqrt{2}$. 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 $\vert{}J_{\mathrm{CP}}\vert{}$ are reconstructed algebraically up to discrete $\mu$–$\tau$ and $\mathrm{CP}$ choices. Comparison with the published NuFIT 6.1 IC24+SK one-dimensional marginals leaves a nonempty $3\sigma$ branch but no common solar-reactor $1\sigma$ 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.