A Geometric Relaxation Theory of the Dark Sector

We introduce the TIDE (Torsional Inertia of Dynamical Einsteinian geometry) framework as a geometric relaxation approach to dark-sector phenomenology. The central hypothesis is that spacetime does not respond instantaneously to matter sources but instead exhibits a finite relaxation timescale governed by infrared geometric dynamics. Within a minimal effective-field-theory realization based on the vector trace mode of torsion in Riemann-Cartan spacetime, this delayed response leads naturally to a Maxwell-Debye-type constitutive equation linking the effective gravitational field to its baryonic source. This record contains: - Main paper (PDF): Framework-level synthesis connecting three observational regimes - Complete reproducibility package: All scripts, datasets, and processing pipelines used in the analysis - Companion analysis blocks: Cosmicflows-4 environmental flows, SPARC galactic kinematics, and cosmological/lensing fits The framework organizes three observational regimes from a single geometric-response principle: (i) Late-time cosmological behavior with equation of state near w ≈ −1 (ii) Galactic quasi-static dynamics reproducing the radial acceleration relation (RAR) and baryonic Tully-Fisher scaling (iii) Environmental flow statistics showing density-dependent velocity-dispersion patterns All numerical claims are reproducible from the included scripts. See README.md for claim-to-file traceability and execution instructions.