Deriving the Baryonic Tully-Fisher Relation from the Asymptotic Limits of Continuum Field Entropy: The Demise of the 4.0 Slope

**Preprint | Continuum Field Entropy Empirical Validation Series** The Baryonic Tully-Fisher Relation (BTFR) establishes an empirical correlation between the luminous baryonic mass of a galaxy and its outer rotation velocity (Mb ∝ VfS). Standard dark matter models and MOND rigidly mandate a velocity slope of S ≡ 4.0, forcing spatial dependencies to cancel out completely. This paper demonstrates that the raw SPARC dataset fundamentally rejects this idealized asymptote, yielding a true empirical slope of S ≈ 3.37. We show that this reduced slope emerges natively as a parameter-free limit of the Continuum Field Entropy (CFE) framework. By applying the exact field elasticity limits (αβ ≈ 0.40 - 0.44) extracted from prior Bayesian analyses of the CFE macroscopic tension gradient, we prove that the covariant deep-field limit mathematically collapses to Mb ∝ Vf~ 3.4 R0.21. The CFE framework successfully predicts the observed kinematic micro-decay of the galactic halo without any algebraic tuning, proving galaxies are not infinitely rigid asymptotes. **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).