Paper CLIV of the One-Octonion Brane-Bulk Series Three Cosmological Tensions as Projections of G2 Permutohedron Relaxation:

The three persistent late-universe cosmological tensions — the Hubble tension (H0), the structure growth tension (S8), and the dark energy equation of state (w0, wa) — are not independent anomalies. They are three projections of a single physical pro- cess: the H+ matter-sector G2 permutohedra relaxing from κ = −1 (hyperbolic) toward κ = 0 (matter-flat spacetime) over the sump relaxation timescale Tsump = 60.84 Gyr (lo- cal). The H−colour-sector permutohedra remain permanently at κ = −1 because QCD confinement algebraically fixes the colour geometry. Thus the universe can never be truly flat: matter can relax, colour cannot. Four predictions follow with zero free parameters. CLIV-1: w0 > −1 and specifically w0 = −1 + 1/(3H0Tlocal) = −0.93, confirmed by DESI DR2 (Abdul Karim et al. 2025, arXiv:2503.14738) at 2.8–4.2σ. CLIV-2: wa < 0 (the permutohedron relaxation rate decreases with time), confirmed by combined KiDS + DESI. CLIV-3: S8 = SΛCDM 8 (1 − √ 6/28) = 0.832 × 0.9125 = 0.7592, where √ 6/28 is the fractional permutohedron asymmetry imprint (Paper CXXXVIII). This matches KiDS–1000 (0.759 ± 0.024) to 0.01σ and is bracketed by KiDS-Legacy fiducial (Reischke et al. 2025, A&A, DOI: 10.1051/0004-6361/202557993; 0.815–0.837 across probe combi- nations). CLIV-4: A residual modified-gravity signal ∆µ∞,eff > 0, detected at 2.87σ by KiDS-Legacy Horndeski analysis (St¨olzner et al. 2025, arXiv:2512.11039). Zero free parameters. 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.