Rethinking Cosmological Foundations II: From Continuum Mechanics to a Testable Numerical Protocol for the Elastic Spacetime Framework (ESUF)

We present a complete theoretical and numerical development of the Elastic Spacetime Framework (ESUF). Building on the conceptual and first mathematical formulation of Version 2, we derive an effective interpolating function for the additional acceleration contributed by a visco-elastic spacetime continuum (the "Grid") directly from the divergence of the Cauchy stress tensor with a scale-dependent shear modulus. We then construct a transparent, fully reproducible numerical protocol that confronts this effective description with galactic rotation-curve data. The protocol comprises (i) a controlled \gamma-scan of the power-law index appearing in the shear modulus, (ii) a global \chi^2 minimisation that enforces a single universal length scale a_0 across multiple galaxies, and (iii) a multi-panel visualisation of the resulting joint solution. The resulting computational pipeline is publicly usable and ready for systematic application to the SPARC sample. This work demonstrates that ESUF has progressed from a conceptual alternative to a concrete, falsifiable continuum-mechanical model of galactic dynamics.