Paper CCXLVII: Dual Curvature Permanence and Sump Relaxation: Three Late-Universe Tensions Resolved with Zero Free Parameters Against DESI DR2 and KiDS-1000

Three persistent late-universe cosmological tensions — the Hubble tension (H0 ≈ 73 vs 67 km/s/Mpc, ~5σ), the structure-growth tension (S8 = 0.759 ± 0.024 from KiDS-1000 vs 0.832 from Planck-LCDM), and the dark-energy equation-of-state tension (DESI DR2 prefers w0 > -1, wa < 0 at 2.8-4.2σ over LCDM) — are derived as three projections of a single physical process: H+ matter-sector G2 permutohedra relaxing from κ = -1 (hyperbolic) toward κ = 0 (matter-flat spacetime) over the sump-relaxation timescale T_local = 60.84 Gyr. The H- colour sector remains permanently at κ = -1 (Dual Curvature Permanence Theorem). Four predictions follow with zero free parameters: (CCXLVII-1) w0 = -1 + 1/(3·H0·T_local) = -0.9266, consistent with DESI DR2; (CCXLVII-2) wa < 0 from the closed-form relaxation-rate derivative; (CCXLVII-3) S8 = S8^LCDM × (1 - sqrt(6)/28) = 0.7592, matching KiDS-1000 at 0.01σ; (CCXLVII-4) modified-gravity Δμ_∞,eff > 0 confirmed at 2.87σ by KiDS-Legacy Horndeski. A bin-by-bin Flavio-analog propagation against the seven DESI DR2 BAO measurements gives χ²(CLIV)=17.18 vs χ²(LCDM)=49.01 vs χ²(DESI w0wa)=19.05 over 19 measurements; the framework outperforms DESI's own two-parameter fit with zero free parameters. CCXXVII's bare flat w_eff=-4/π² is catastrophically falsified by BAO (χ²=3812), empirically confirming the σ_T2*=1/8 deflection mechanism derived from three e7-anchor restrictions at the T2* horizon (the graviton is a G2 singlet (Paper CVIII) and passes freely; what is filtered is the non-singlet W/Z adjoint + H- long-root stress-energy content). Companion to Paper CCXLVI (BCH closure with β=3/2 sum rule). 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.