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 (ΘG₂) = 2389/2413; (ii) the Class III Gudermannian saturation fraction fIII = 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 mᵢ = fIII·sinh² (φᵢ) + (1−fIII) ·sin² (φᵢ). Independently solving for the blend fraction that hits 33. 8 yields fᵣeq = 0. 594793, matching fIII to 77 ppm. The negative sign of the genesis tilt sources leptonic CP violation with δCP < 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 RK (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.