The R_b NLO Denominator 2V − F = 34 from Fermion-Walk Operator Perturbation Theory

Paper #67 closed the η̄ lever-arm of the Wolfenstein unitarity triangle by identifying the NLO CKM phase δ_NLO = δ_LO × (2E − 1)/(2E) = 65.44°, then paired this with a candidate radial coordinate R_b = (F − 1)/(2V − F) = 13/34 = 0.38235. The numerator F − 1 was identified as β₁(edge skeleton) — the first Betti number of the 1-skeleton of the Kelvin cell — which is a Tier 1 topological invariant. The denominator 2V − F = 34 was listed with three candidate decompositions (|G| − F, V + (V − F), 2E − 2N_gauge − F) but without an operator-theoretic anchor. Paper #67 therefore assigned the R_b companion Tier 3. This paper closes that gap. We prove that 2V − F = dim(H_fermion^eff), where H_fermion^eff is the effective fermion walk Hilbert space on the truncated-octahedron cell, after (i) vertex-doubling the 24 cell vertices by T₁u chirality projection (r₁ ↔ left, r₂ ↔ right) and (ii) decoupling the F = 14 face-scalar modes that live orthogonally to the vertex sector under the block-diagonal decomposition of the master operator H = L + ηV. The decoupling is proven as a corollary of the A₂u/T₁u parity theorem (Paper #45) combined with the face-Laplacian irrep decomposition (Paper #5). Combined with δ_NLO, this gives (ρ̄, η̄) = (0.1589, 0.3478), joint tension 0.02σ against PDG 2023, with R_b = 0.3824 vs PDG 0.3826 ± 0.011 (−0.02σ). The unitarity-triangle apex is therefore closed at Tier 2 with zero free parameters.