Unifying Cosmological Expansion and Wave Dispersion via Field Elasticity: A Deep-Space Validation of the Continuum Field Entropy (CFE) Framework

**Preprint | Continuum Field Entropy Empirical Validation Series** We present a comprehensive validation of the Continuum Field Entropy (CFE) framework, which models the universe as a non-material, shear-thickening elastic Cosserat continuum rather than an empty metric spacetime. Utilizing macroscopic state equations for background tension (T₁₆) and effective wave speed (c₄₅₅) derived from Cosmic Chronometer and BAO datasets, we subject the CFE framework to two extreme deep-space astrophysical stress tests. First, we prove the existence of a macroscopic structural phase transition in the Cosmic Microwave Background (z = 1100), isolating a universal primordial field impedance of 0. 721 that perfectly converges with Pantheon+ amplitude drag. Second, we resolve the high-redshift (z > 2) Quasar Hubble Plunge by deriving the exact frequency-dependent rheological dispersion of the continuum, yielding a spectral drag index of n 0. 36. Our deep-space MCMC analysis anchored to the Lusso et al. dataset demonstrates that the universe's thermodynamic friction scales cleanly with the cube root of the wave frequency ( () = ₀ 3/₀). Across these deep-space scales, Evolving Dark Energy and particulate Dark Matter are rendered mathematically obsolete, replaced by the thermodynamic non-linear elasticity and dynamic impedance of the 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).