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

Paper #64 established the NLO Wolfenstein ρ̄ at −0. 002σ from PDG via Rb = 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: δNLO = δLO × (2E−1) / (2E) = 66. 360° × 71/72 = 65. 438°, matching δₑxp = arctan (η̄ₑxp/ρ̄ₑxp) = 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 Rb → (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 Rb 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 Rb companion derivation. Independently verifiable from cell integers (V=24, E=36, F=14). Repository: https: //github. com/WebEnvy/UnifiedFoamFieldTheory.