Temporal Synchrony Gradient Gravity: Foundations, Newtonian Recovery, and Low-Acceleration Structure

This paper presents the current foundational formulation of Temporal Synchrony Gradient Gravity (TSGG), a gravitational framework in which observed gravitational phenomena arise from spatial gradients in accumulated proper-time desynchronization rather than from spacetime curvature alone. The work develops TSGG from first principles in the weak-field, quasi-static regime, demonstrating exact recovery of Newtonian gravity and consistency with general relativity in high-acceleration, fast-response environments. Deviations from Newtonian behavior emerge only when local temporal synchrony cannot be maintained, leading to an effective modification of gravitational response without the introduction of dark matter or ad hoc force laws. A key advance in this version is the explicit identification of a two-condition activation structure governing the onset of non-local gravitational response. In TSGG, low acceleration is shown to be a necessary but not sufficient condition for modification. A second criterion—comparison between the local dynamical timescale and a finite synchrony response timescale—determines whether accumulated temporal desynchronization can develop. This structure naturally permits the existence of characteristic, dimensionless activation radii in extended virialized systems, a feature absent in purely acceleration-based modified gravity frameworks. Within this framework, familiar MOND-like scaling relations arise as emergent consequences of delayed synchrony response rather than as fundamental postulates. The theory remains predictive while retaining a conservative scope, explicitly separating foundational structure from empirical application. This paper is intended as a theoretical foundations document, providing the conceptual and mathematical groundwork for subsequent empirical tests on galactic and cluster scales, which are addressed separately. Version update: Clarified the physical interpretation of the deep low-acceleration regime by explicitly distinguishing stiff temporal synchrony as the default state from the conditions under which that synchrony breaks down. Introduced a formal two-condition criterion—combining local acceleration and dynamical response timescale ordering—that governs the onset of non-local gravitational response. Added a new subsection in the deep low-acceleration regime to formalize this structure and to show how it naturally permits the emergence of characteristic, dimensionless activation radii in extended systems. No changes were made to the core field equations or to the previously established Newtonian and relativistic limits.