The Continuum Field Entropy (CFE) Framework: Triangulating the Macroscopic Kinematic Drag from the Early Universe to Modern SPARC Galaxies

**Preprint | Continuum Field Entropy Empirical Validation Series** The discrepancy between visible baryonic mass and galactic rotation curves is traditionally attributed to Dark Matter halos. This paper presents a complete mathematical triangulation of the Continuum Field Entropy (CFE) framework, modeling the universe as a non-Newtonian, tension-bearing Cosserat continuum. By subjecting 175 modern SPARC galaxies (z ≈ 0) to a rigorous 355-dimensional Hierarchical Markov Chain Monte Carlo (MCMC) inference, we prove that the structural elasticity of the vacuum is an invariant property (α ≈ 2.30, β ≈ 0.19, log₁₀(∇ Tbg) ≈ 3.85). Furthermore, by replacing a linear optical retardation proxy with the exact thermodynamic wave-speed equation (ceff) derived from the early universe, the MCMC seamlessly maintained an ultra-tight intrinsic scatter of σᵢₙₜ = 0.0749 dex. This mathematical integration proves that the Kinematic Drag exponent (ΓKin) responsible for the optical illusion of Dark Matter is the exact same mechanism responsible for the illusion of Dark Energy. We successfully map the decay of this exponent from its stiff primordial state (ΓKin = 0.275 at $z = 2.33$) to its relaxed modern state (ΓKin = 0.0463 at z ≈ 0), finalizing the epoch-spanning validation of the CFE framework. **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).