This work presents Version 20 of the Elastic Spacetime with Scale-Dependent Coupling (ESSC) framework as a minimal structural formulation of observational phenomena. ESSC is not a dynamical theory and does not introduce new forces, particles, or equations of motion. Instead, it functions as a structural consistency filter that clarifies the conditions under which observational descriptions become admissible. A central principle of ESSC is that observation corresponds to translation termination, requiring that propagating information becomes structurally fixed. This implies a necessary condition of closure for any observable structure. Within this framework, closure is identified with minimal circular structure, and the constant π is reinterpreted as a structural conversion factor between linear progression and closed consistency. Using galactic rotation curve data from the SPARC database, we construct a normalized residual function Δ (u) and show that it exhibits a universal U-shaped structure across galaxies. This structure is well described by a cosine form with a characteristic frequency satisfying ω ∼ π. Based on this empirical result, we propose a minimal structural expression: Δ (u) = Δₘin + agal 1 − cos (π (u − u0) ) Importantly, π is not introduced as a fitting parameter but emerges as a structural scale consistent with closure. ESSC does not claim to explain the dynamical origin of galactic structures, nor does it replace existing frameworks such as dark matter or modified gravity. Instead, it provides a complementary perspective that constrains how observational data can be consistently represented. The key implication is that any observational structure admitting closure necessarily supports a characteristic scale consistent with π, independent of the underlying dynamics. This work should be understood as a minimal, non-dynamical formulation that identifies universal structural features in observational data, linking geometry, information, and measurement.
umimoto (Sat,) studied this question.