"ct - The Only Expanding Dimension"

We propose a kinematic formulation of physical dynamics based on an effectiveflow along the temporal coordinate ct. In this framework, the evolution of physicalsystems is described through the redistribution of an invariant magnitude c amongtemporal and spatial components, providing a unified geometric representation ofmotion.Within this formulation, both kinematic and gravitational time dilation admita common interpretation as arising from changes in the projection of this flow.When the flow is redirected toward spatial coordinates—due to relative motion orradial gradients—the temporal component is reduced. The framework also providesa natural description of radial dynamics and orbital motion, recovering standardresults in the weak-field regime. At larger scales, Hubble-like behavior emerges asa consequence of the cumulative redistribution of the flow in low-density regions.Consistency with observed timing corrections in Global Positioning System(GPS) satellites is discussed, reproducing the combined kinematic and gravitationalcontributions to time dilation.Overall, the model offers a coherent geometric framework that reproduces keyresults from Special Relativity, General Relativity (in the weak-field regime), andNewtonian gravity, while providing a unified perspective on their kinematic structure.