The NLO Mixing Correction from First Principles: Why ε = √17/81 is Not a Free Parameter

The NLO correction parameter ε = √17/81 was identified in UFFT Paper 47 as a universal correction to the PMNS mixing matrix. A reviewer correctly noted that this identification was not derived from first principles. This paper provides the missing derivation. We show that ε arises from second-order perturbation theory of the T₁u mass matrix when the diagonal eigenvalue splitting (r₂−r₁) = √17 is treated as a perturbation to the symmetric sector average. The result ε = (r₂−r₁)/(r₁+r₂)² = √17/81 follows from a Z₂ parity argument that requires no new integers, no new identifications, and no free parameters. The same expression, colour-averaged, gives ε_CKM = √17/363 for the quark sector. A single algebraically fixed expression simultaneously resolves three mixing tensions (Cabibbo 3.7σ→0.07σ, atmospheric 2.2σ→0.2σ, reactor 2.3σ→0.2σ) with coupling strengths predicted a priori — not tuned.