Dynamics of Elastic Membranes (DME): A Dynamic Structural Framework with Observational Constraints in Galactic Systems

This work presents an updated version of the Elastic Membrane Dynamics (DME) framework applied to galaxy rotation curves using observational data from the SPARC catalog. A multi-galaxy analysis is performed, comparing Newtonian dynamics with the DME model through residual analysis and χ² statistics. The results show a consistent improvement in the fit, with an average reduction in χ² of approximately 50%. The model performs better in disk-dominated galaxies and shows reduced accuracy in gas-dominated systems, indicating a structural dependence not fully captured in the current formulation. This version (v3) introduces a refined methodological clarification, improved interpretation of results, and a conceptual extension of the model based on collective structural interactions within an elastic medium. A spreadsheet containing the data, calculations, and graphical analysis is included.