Elastic Spacetime with Scale-Dependent Coupling (ESSC) v17: Structural Origin of Closure from Primordial Difference to Observability

This work presents ESSC v17, a structural formulation of closure in elastic spacetime, extending the statistical framework established in ESSC v16. Starting from the minimal assumption of primordial difference, we derive the emergence of relations, center formation, and circular closure as a natural structural process. Closure is not imposed as a condition, but arises from the organization of relations into loop configurations characterized by a finite loop time. We introduce the closure fraction f ≈ 2π Hr / V as a measure of the competition between closure tendency (gravity) and opening tendency (cosmic expansion). Within this framework, matter, energy, and dark matter are interpreted as different regimes of relational closure, while space and time correspond to unclosed structure and the process toward closure, respectively. Observability is reinterpreted as the matching of closed relations, emerging not at full closure but within intermediate closure regimes. The results of ESSC v16, including the gamma distribution of f and the emergence of a characteristic band around f ≈ 0.15, are naturally explained as statistical manifestations of interacting closure structures. Taken together, ESSC v16 and v17 provide a unified view: - ESSC v16: statistical realization of closure - ESSC v17: structural origin of closure This framework suggests that observable properties of galactic systems arise from the statistical realization of relational closure across scales.