This work presents a unified structural analysis of galaxies and galaxy clusters within the framework of Elastic Spacetime with Scale-Dependent Coupling (ESSC). We introduce normalized structural coordinates (uX, uₚi) that capture the relative placement of characteristic radii associated with slope transitions and pi-related boundary features. Using rotation curve data for galaxies and X-ray profile data for clusters, we construct a common representation that enables direct comparison across scales. The analysis reveals a clear structural separation: Galaxies occupy an internal regime where uₚi uₚi, indicating internally resolved structural ordering. Clusters collapse toward uₚi approximately equal to 1, showing compression of the boundary scale toward a terminal limit rather than a shared internal configuration. This distinction emerges without introducing new dynamical laws, particles, or modifications to gravity. Instead, it reflects a structural constraint on how observational regimes map onto each other. The results support the ESSC perspective that pi appears not as a fixed constant in dynamics, but as a boundary manifestation associated with structural termination and observational closure. This work does not propose new physical interactions or predictive models. It provides a structural filter for interpreting cross-scale gravitational systems and highlights a fundamental asymmetry between internally structured systems and boundary-compressed regimes.
umimoto (2026) studied this question.