The Relational Continuum and the Geometric Elimination of Time

Building directly upon the relational framework established in The Identity of Time, which defined the temporal coordinate () through a strict identity with movement, this paper provides explicit geometric and mathematical execution of that model. By introducing identical, irreducible Fundamental Entities into a series of four strictly isolated vacuum environments, we map the step-by-step scaling of spatial dimensions from zero-dimensional stasis to a three-dimensional volumetric reality. We demonstrate that the introduction of relative motion triggers a universal, systemic displacement delta across all entities, allowing velocity to be calculated entirely as a ratio of pure spatial change. By validating this principle across both a closed four-body micro-system and our macroscopic solar system, we demonstrate that an independent fourth dimension is mathematically redundant, reinforcing the conclusion that time is a relational measurement of relative spatial translation.