**Preprint | Continuum Field Entropy Empirical Validation Series** The accelerating expansion of the universe (Dark Energy) and the discrepancy between early and late-universe measurements of the Hubble constant (H₀) represent the most severe crises in standard cosmology. In this paper, we demonstrate that both anomalies are optical illusions caused by assuming the vacuum is optically and structurally static. Using the Continuum Field Entropy (CFE) framework, we model cosmological expansion as the macroscopic thermodynamic relaxation of the Primordial Field’s background tension. We show that wavefront dispersion through this decaying impedance organically dims distant supernovae, perfectly mimicking. We validate this by employing a Hamiltonian Monte Carlo (HMC) inference pipeline on all 1, 701 Pantheon+ supernovae, utilizing the full 1701 1701 systematic covariance matrix and an exact thermodynamic cosmological integral. The pipeline successfully isolates the base dispersion (₀ 0. 357) and the elastic relaxation exponent (5. 86), while organically anchoring the local expansion rate at H₀ 72. 94 km s^-1 Mpc^-1. Furthermore, by applying continuum acoustic wave-speed scaling to the 20. 1\% stiffer primordial vacuum, we mathematically derive an apparent CMB expansion rate of H₀ 66. 6 km s^-1 Mpc^-1. The CFE framework thus resolves both Dark Energy and the Hubble Tension via continuous thermodynamic field relaxation. **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).
Sureshkumar Rangasamy (Wed,) studied this question.