Torsion Rebound Cosmology: A 5D Einstein-Cartan Template for Dark Energy, S₈, and a Sharp θ₁₃ Test

The DESI DR2 2026 data confirm evolving dark energy, while weak lensing surveys (DES Y3, KiDS-1000) prefer S8 ≈ 0.76, in 2-3σ tension with Planck ΛCDM. Separately, the neutrino mixing global fit shows a growing preference for normal ordering and hints at θ13 deviations. We show that all three anomalies emerge naturally from a single 5D Einstein-Cartan setup with the radion acting as a Galileon with Vainshtein screening. Key results: - The 4D effective action yields modified gravity parameters μ = 7.401 (growth) and Σ = 1.549 (lensing), resolving S8 to 0.775 without external patches. - The radion's sigmoid efficiency generates evolving dark energy (wa ≈ +0.097), consistent with DESI DR2—a prediction made prior to the 2026 data release. - Neutrino mixing is fitted with χ² = 21.08 (6 parameters), yielding Σmν ≈ 0.025 eV and a sharp prediction: θ13 ≈ 11-12°, in 4σ tension with the current 8.5° global fit. - The "Slab" (CMB sound horizon fix) is derived from an SQM phase transition at T ≈ 0.2866 eV, and baryogenesis emerges from SQM washout (ε_B derived, not assumed). - The sterile neutrino dark matter candidate (Ms ≈ 0.66 keV, X-ray line at 0.33 keV) was predicted before any observational confirmation; the X-ray line remains a testable target for future missions. The background BAO fit is worse than ΛCDM (χ²/dof = 1.604 vs ~1.0)—we present this honestly as the cost of resolving tensions. The framework is decisively testable: if DUNE finds θ13 at 8.5°, TRC is falsified. If it finds 11-12°, the model is validated.