Dynamic Gravitational Time Matrix (DGTM): An Operational Framework for Vector-Based Representation of Local Proper Time This working paper introduces the Dynamic Gravitational Time Matrix (DGTM) as a heuristic-operational framework for the structured representation of spacetime event states within explicitly defined relativistic reference systems. The framework does not propose new physics or modifications to general relativity. Instead, it aims to improve transparency, interoperability, reproducibility, and comparability in spacetime-related calculations by explicitly linking reference frame, coordinate time, worldline, position vector, velocity vector, gravitational potential structure, and accumulated proper time within a unified event-state representation. The DGTM addresses a practical systems-engineering problem frequently encountered in astronomy, astrometry, geodesy, satellite navigation, spacecraft operations, and simulation environments: relativistic quantities are often distributed across different models, time scales, coordinate systems, and computational interfaces. This fragmentation can produce ambiguities, silent inconsistencies, and interoperability problems even when the underlying physical theory is correct. The proposed framework formalizes spacetime event states as structured tuples containing: reference frame or reference anchor, coordinate time, position vector, velocity vector, gravitational potential structure, and accumulated proper time along a defined worldline. Methodologically, the paper combines conceptual analysis, weak-field relativistic approximations, operational modelling principles, and reproducibility requirements. The DGTM is designed to remain forward-integrable, backward-verifiable, and falsifiable against known relativistic reference cases such as GNSS satellite clock corrections and planetary proper-time comparisons. Illustrative applications include Earth surface clocks, geocentric and barycentric reference cases, GNSS satellites, Jupiter-related worldlines, and Voyager-type spacecraft trajectories. These examples demonstrate that different worldlines associated with the same astronomical object may accumulate different proper times depending on gravitational environment and kinematic state. The framework introduces a staged precision taxonomy (DGTM-0 to DGTM-4), ranging from conceptual representation to higher-order relativistic implementations, and proposes a machine-readable metadata structure intended to support future interoperability between simulations, ephemeris systems, mission calculations, and educational models. The DGTM is therefore positioned not as a competing physical theory, but as a structured documentation and comparison framework for relativistic spacetime calculations. Its primary contribution lies in operational clarification, explicit assumption tracking, and reduction of ambiguity in complex calculation chains.
Rudolf Schäfer (Wed,) studied this question.