Paper CLI — Measure-rigorous F₂-CFN ↔ SU(N) Wilson dictionary

The companion paper CIII v3 establishes a positive mass gap for the branched 6-point correlator on the F₂-CFN-decomposed SU(2) Wilson measure. The Cho-Faddeev-Niemi (CFN) decomposition splits the SU(N) link variable into a colour-direction field n on the F₂ flag manifold, a transverse field X_μ, and a residual U(1) phase ρ. Its measure-theoretic equivalence to the standard Wilson measure had not previously been established at the constructive-QFT level. This paper closes the bridge. We construct a measurable Jacobian J = Δ_FP · V_Pl (Faddeev-Popov determinant times Plücker volume form on F₂) and prove that dμ_W^gf = J dμ_(F₂-CFN) is a finite-lattice measure equivalence. The continuum OS axioms reduce to a uniform-in-(L,a) Jacobian bound (Eq. 5.1), closed via smooth positivity of V_Pl on F₂ (constant as the invariant density; chart-relative extrema ≈[0.5, 2.0] for SU(3), §5.3.1) and the factorisation Δ_FP = Δ₀ · Δ₁ with Δ₀ cancelling in normalised Schwinger functions and Δ₁ → 1 along the renormalised trajectory. A concluding §8 sketches a strategy — not a completed proof — for upgrading the finite-lattice equivalence to a continuum measure-equivalence μ_W^(SU(N)) = Φ_ μ_(F₂-CFN)^cont, organised as a seven-sub-row programme (continuum Jacobian existence with engineering dimension d_J=0; an NLO anomaly audit; OS1 and OS3 preservation under a fiber-local θ-equivariant push-forward, with OS2/OS4/OS5 inherited from Paper CL; a conjectured Wilson-loop C^-algebra isomorphism with shared area-law √σ ≈ 420 MeV; and a Kotecký–Preiss cluster cross-check). Its load-bearing continuum steps — preservation of reflection positivity under the push-forward and the proposed fixed-β "Bałaban-bypass" — are stated as strategy and conjecture, and rely on intermediate results developed in separate working files rather than proved here. Paper CLI therefore does not close the Yang–Mills mass gap. The rigorous-lower-bound on the continuum SU(3) gap is dimensionless and effectively vacuous; the [24.5, 245] MeV bracket inherited from CLII Branch A and the 1.7 GeV glueball figure quoted in §8 are phenomenological calibration targets (Morningstar–Peardon 1999), not derived results. The four primary risk classes are addressed at the strategy level; the proper-rigour bodies remain multi-year specialist work.