ESSC v23: Stable Structural Regimes from Closure and Response Fields

Elastic Spacetime with Scale-Dependent Coupling (ESSC) is formulated here as a reproducible structural extraction framework rather than as a new dynamical theory. This version focuses on whether structural features in galaxy data can be extracted by fixed procedures and remain stable under controlled variations of the pipeline. The analysis separates two observational domains: a closure field, from which a stable structural boundary uₚi is extracted, and a response field, from which a response point uₐttr is extracted. Their difference, Delta u = uₚi - uₐttr, is used as the central regime variable. Using fixed smoothing windows and fixed extraction rules, the paper finds that uₚi remains localized near a narrow band around ~0. 63, while uₐttr is not fixed to a single universal value but separates into two response modes. A two-component Gaussian mixture model applied to Delta u identifies two stable structural regimes. Repeating the classification under smoothing windows of 5, 7, and 9 shows that the majority of galaxies retain the same regime label across all tested windows, indicating that the extracted regimes are not artifacts of a single filtering choice. Restricting attention to the stable subsample, the regime split is associated with systematic differences in galaxy properties. In particular, disk scale length, effective radius, H I mass, luminosity, and flat rotation velocity differ significantly between the two regimes, whereas surface-brightness-based quantities do not dominate the separation. A decision map in the Rdisk-log10 (MHI) plane provides an interpretable visualization of the stable ESSC regimes and suggests that disk scale is the primary organizing axis, with gas content acting as a secondary modifier. The main contribution of this work is methodological. ESSC is not introduced here as a new force law, a modified gravity model, or a refutation of dark matter. Instead, it is presented as a reproducible structural classifier in which a stable boundary and a movable response point are extracted from different observational fields and combined into a regime variable with measurable physical correlates. This upload corresponds to ESSC v23.