The Continuum Field Entropy (CFE) Framework: Radial Acceleration Relation via Non-Linear Field Elasticity and Tension Gradients Without Dark Matter

**Preprint | Continuum Field Entropy Empirical Validation Series** This standalone paper presents a rigorous empirical test of the Continuum Field Entropy (CFE) framework against the SPARC (Spitzer Photometry and Accurate Rotation Curves) database of 175 disk galaxies. Instead of invoking unobserved cold dark matter halos or phenomenological modifications to Newtonian inertia, we derive galactic gravitational fields as an exact solution to the CFE Modified Poisson equation (G₄₅₅ (T) ) = 4. Using a 355-dimensional Hierarchical MCMC Bayesian inference, the model successfully reproduces the observed Radial Acceleration Relation (RAR) with an exceptionally tight intrinsic scatter of 0. 0965 dex across all measured galactic radii. The inference isolates a local optical retardation factor of ₎₏ₓ 0. 185 and a field power-law parameter of 2. 33, providing strong scale-invariant empirical proof of a non-linear, shear-thickening primordial continuum field. **Project Integration: **This document is a standalone validation report. The underlying universal field equations, foundational axioms, and the complete multi-disciplinary validation framework can be found in the primary master manuscript (DOI: 10. 5281/zenodo. 20631794).