Solving the Pantheon+ Host Galaxy Mass Anomaly: A Continuous Thermodynamic Saturation Limit via Continuum Field Entropy (CFE)

**Preprint | Continuum Field Entropy Empirical Validation Series** Type Ia Supernovae (SNe Ia) are utilized as standard cosmological candles under the assumption of baseline intrinsic luminosity. However, the Pantheon+ dataset reveals a persistent empirical anomaly: SNe Ia residing in massive host galaxies (> 10^10 M⊙) systematically appear brighter than those in low-mass galaxies. Standard cosmology corrects this using a phenomenological “Mass Step” nuisance parameter, offering no physical mechanism for the discrete jump. In this paper, we resolve the anomaly mathematically using the Continuum Field Entropy (CFE) framework. By defining the vacuum as a tension-bearing Cosserat continuum, we derive a closed-form optical retardation equation dictating the dynamic impedance of the local environment. We prove that the empirical Mass Step is not a discrete jump, but an optical illusion caused by the fundamental saturation limit of the vacuum’s tension gradient (Δ m = -γₒₚₜ MM+Mcrit). When combined with the known morphological phase transition from dense spiral galaxies (R ∝ M0.28 → Tₛₚᵢᵣₐₗ ∝ M0.44) to diffuse elliptical galaxies (R ∝ M1.0 → Telliptical ∝ M-1.0), we derive the exact effective tension scalars (Teff) driving this phenomenon. The resulting bifurcated CFE formulation organically reproduces the exact step and pressure-release "hook" morphology extracted from 1,698 raw un-patched Pantheon+ supernovae without algebraic tuning, maintaining extreme parameter stability when subjected to the full 1701 × 1701 systematic covariance matrix. **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).