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 (Tbg) and effective wave speed (ceff) 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 (Γ(ν) = Γ₀ √[3]ν/ν₀). 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).