Rey-TIDE Cosmological Framework: A Unified Solution to the H0 Tension and Dark Matter via Dynamic Torsion

We introduce the Rey-TIDE (Torsion-Induced Dynamic Effects) cosmological framework, a geometric extension of Einstein–Cartan–Sciama–Kibble (ECSK) gravity in which a redshift-dependent torsional coupling modifies the effective gravitational response of baryonic matter. Using an expanded observational sample of 30 massive galaxy clusters (0.018 < z < 1.13), combining Sunyaev–Zel'dovich measurements from the South Pole Telescope and the Planck PSZ2 catalog, we show that a single universal coupling parameter (ξ_H0 ≈ 0.083 ± 0.003) provides a statistically robust improvement over ΛCDM. The model naturally reconciles local and global determinations of the H₀ parameter and predicts a suppressed growth of structure consistent with weak lensing constraints on S₈. An independent geometric validation is provided through the double Einstein ring system SDSS J0946+1006, where Rey-TIDE reproduces both observed Einstein radii without requiring ad hoc adjustments to the dark matter fraction. Within its intended regime of validity—post-recombination cosmology and virialized large-scale structures—the framework offers a falsifiable, particle-agnostic geometric interpretation of phenomena commonly attributed to dark matter. ---Version 1.3 (January 2026) • Fixed typographical encoding artifacts and notation inconsistencies.• Corrected likelihood metric labeling for internal consistency.• Minor editorial refinements for clarity and tone.• No changes to the theoretical framework, equations, datasets, or numerical results.