Paper CCLII: Neutrino Δm² Ratio from Class III Gudermannian Saturation with Negative G₂ Tilt — Zero-Free-Parameter Closure of JUNO at 0.01%

Zero-free-parameter derivation of the neutrino mass-squared ratio Δm²₃₁/Δm²₂₁ = 33.7957 (vs JUNO+atmospheric 33.8, deviation 0.013%) from three previously-locked One-Octonion Brane-Bulk framework constants: (i) the G₂ holonomy ratio cos(Θ_G₂) = 2389/2413; (ii) the Class III Gudermannian saturation fraction f_III = 1 − 4/π² = 0.59471 (from the brane-bulk transit formula at the bulk self-coupling point and the GRB 250702B burst-to-encounter energy hierarchy in Paper CCXLIV); (iii) the CXXI brane-touch factor (1 + 2α√7) from the electron mass formula. The three Fano edges through e₇ sit at angles (−4.044°, 40.956°, 85.956°), the tilt magnitude locked by 2389/2413 to better than 10⁻⁴ degree. Neutrino mass eigenstates follow the Gudermannian blend m_i = f_III·sinh²(φ_i) + (1−f_III)·sin²(φ_i). Independently solving for the blend fraction that hits 33.8 yields f_req = 0.594793, matching f_III to 77 ppm. The negative sign of the genesis tilt sources leptonic CP violation with δ_CP < 0. The CKM-Wolfenstein analog applied to the (1,3) channel — squared brane-touch because it mediates non-adjacent generations 1↔3 through the second generation — closes sin²θ₁₃ to 0.52σ (predicted 0.0216 vs reactor 0.0220) and sin²θ₁₂ to 0.29σ (predicted 0.3117 vs JUNO 0.3092) via the conservation rule sin²θ₁₂ + sinh²θ₁₃ = 1/3. The predicted PMNS small parameter √(sin²θ₁₃/sin²θ₁₂) = 0.263 sits next to CKM Cabibbo λ = 0.225, indicating shared hierarchical origin in brane-touch geometry. Static-saturation interpretation forbids cosmological Δm² ratio drift — a falsifiable CMB-S4+DESI prediction. Normal hierarchy is structurally mandatory. Supersedes Paper CCLI (deprecated, which conflated absolute-scale and ratio-only sectors). CCLII addresses Problem B (the Δm² ratio and PMNS mixing) only; absolute mass scale (Problem A) remains open pending derivation of R_K(7) in physical units from charged-fermion data. Zero free parameters. Verification script reproducible from framework constants only. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.