Geometric Origin of the Time Field: Einstein–Cartan Gravity, Torsion Locking, and the Resolution of Infrared Spin Coupling

In a companion phenomenological study, a scalar time-rate field T(x) was shown to effectively replace dark matter in galactic dynamics, while subsequent analysis of binary pulsars placed a stringent upper bound on its direct coupling to intrinsic spin (κ ≲ 10−12). In this work, we provide the fundamental geometric origin of T(x), demonstrating that it is not an ad hoc scalar, but the effective parametrization of the axial torsion sector in Einstein–Cartan (EC) gravity. We construct a unified effective field theory (EFT) master action where T(x) exhibits a remarkable UV/IR duality. In the UV, it behaves as a dynamical stiff fluid (ρT ∝ a−6) coupled to the QCD topological vacuum. Crucially, in the IR, a non-perturbative geometric locking potential dynamically forces T(x) to align with the metric proper time (√ −uµuνgµν). We show that this locking mechanism naturally suppresses the effective spin-gravity coupling by many orders of magnitude, providing a rigorous, fine-tuning-free explanation for the observational bound κ ≲ 10−12 derived from pulsar timing. This completes the theoretical framework, elevating the time field from a phenomenological ansatz to a consistent, geometrically grounded extension of General Relativity.