NLO Correction to δ_CKM: Closing the η Lever-Arm of the Unitarity Triangle

Paper #64 established the NLO Wolfenstein ρ̄ at −0.002σ from PDG via R_b = r₁²/(r₁r₂−1) = (49−9√17)/30, leaving a residual η̄ tension of +1.5σ attributable to a 0.91° offset in the CKM phase δ. That offset was identified in Paper #64 as a lever-arm effect, not a formula failure, and an NLO correction to δ was flagged as the natural closure mechanism. This paper proposes and tests that correction. The central result is a single-integer NLO factor: δ_NLO = δ_LO × (2E−1)/(2E) = 66.360° × 71/72 = 65.438°, matching δ_exp = arctan(η̄_exp/ρ̄_exp) = 65.44° to within 0.002°. The factor (2E−1)/(2E) has a clean interpretation: at next order in the face-graph walk expansion, the vertex self-energy subtracts one edge from the full edge-incidence count 2E = 72. A companion candidate R_b → (F−1)/(2V−F) = 13/34 gives (ρ̄, η̄) = (0.1589, 0.3478) at (−0.01σ, −0.02σ), closing the combined unitarity-triangle tension to 0.02σ. Paper #67 therefore closes the δ lever-arm at Tier 2 and raises the combined unitarity-triangle closure to Tier 3, pending derivation of the R_b companion NLO from operator perturbation theory.Part of the Unified Foam Field Theory series. Priority date: 20 February 2026. Completes the NLO Wolfenstein programme: combined with Papers #51, #64, #66, all four parameters (λ, A, ρ̄, η̄) are now derived from cell integers with the unitarity-triangle apex closed to 0.02σ pending R_b companion derivation. Independently verifiable from cell integers (V=24, E=36, F=14). Repository: https://github.com/WebEnvy/UnifiedFoamFieldTheory.