Temporal Gravitational Interweaving (TGI): Relational Decomposition of Observer Frame Transport in General Relativity

Temporal Gravitational Interweaving (TGI) is presented as a candidate relational geometric representation of temporal–gravitational structure within General Relativity, rather than as a new theory of gravity or an additional dynamical field. The framework organizes the kinematical decomposition of observer congruences, causal accessibility, and Lorentz holonomy into the relational structure TGI[u,g] = {∇u, C(g), H(g,e)}. The observer-congruence sector includes acceleration, expansion, shear, and vorticity, while frame dragging is treated separately through the shift vector, its derivatives, extrinsic curvature, or appropriate non-Eulerian twist structures. The formulation explicitly distinguishes ZAMO/Eulerian observers from spatially fixed Killing observers, incorporates cosmological expansion through the FLRW limit, and separates gravitational clock-rate effects, local proper time, and causal escape at horizons. Lorentz holonomy is used as the preferred geometric foundation for interpreting the original interweaving intuition without introducing a new temporal connection or new dynamical degrees of freedom. In the minimal realization, TGI is observationally equivalent to General Relativity (ΔO = 0). Its proposed contribution is therefore representational and interpretive: a unified relational language for temporal depth, expansion, shear, rotational dragging, causal accessibility, path dependence, and observer-frame transport within standard relativistic geometry.