Temporal Gradient Cosmology (TGC): A Unified Framework for Time as a Physical Field (v2)

Temporal Gradient Cosmology (TGC) introduces a physical time field τ(t, x) whose gradients and curvature govern gravitational dynamics, cosmological evolution, and large-scale structure. In this framework, redshift arises from temporal curvature rather than spatial expansion, giving observational equivalence to FRW cosmology under the mapping a(t) ↔ 1/τ(t). This revised 2025 edition presents a unified treatment of the τ-metric, τ-geodesics, and the Principle of Temporal Co-Flatness, clarifying why early epochs embedded in extreme τ-depth remain locally normal for their observers. The model reproduces Newtonian gravity, post-Newtonian corrections, gravitational lensing, and CMB acoustic structure, while offering alternatives to dark matter, dark energy, and cosmic expansion. TGC provides a single-field mechanism for redshift, structure formation, CMB anisotropies, and black-hole temporal wells, with predictions that diverge from ΛCDM at high redshift and in gravitational-wave phase evolution. Originally completed October 30, 2025. This v2 Zenodo release reflects the expanded and refined November 2025 edition.