Elastic Spacetime with Scale-Dependent Coupling (ESSC) v6. 1 refines the structural admissibility framework introduced in ESSC v6 by clarifying the role of the geometric factor π and separating two previously conflated structural objects: a localized transition entrance and an extended post-transition persistence band. ESSC does not modify gravitational dynamics and introduces no new forces, fields, or particles. Instead, it compares local and global gravitational probes across radial scales using logarithmic structural derivatives. The framework evaluates whether their mismatch remains bounded in a scale-dependent manner. The minimal consistency condition | Gᵥ (R) - GL (R) | (R) R is reinterpreted in v6. 1 as governing admissible structural mismatch within a persistence band rather than identifying a critical inversion threshold. Empirical analysis of disk galaxy rotation-curve datasets indicates that: Structural exchange between baryonic and halo components is localized. Structural compatibility persists across a finite radial annulus beyond that transition. The π-factor parameterizes the width of this admissible persistence region. The radial position of the persistence band shifts with galaxy morphology, while the bound form remains invariant. ESSC v6. 1 strengthens falsifiability by specifying operational criteria for identifying transition entrances and persistence bands, and by clearly distinguishing structural admissibility from dynamical stability diagnostics such as the Toomre Q parameter or halo dominance fraction. This version maintains structural continuity with ESSC v6 while narrowing interpretation and strengthening empirical grounding. The framework remains a structural diagnostic tool rather than a dynamical theory.
umimoto (2026) studied this question.