The Compactness Paradox at Cosmic Dawn: Empirical Validation of the Continuum Field Entropy (CFE) Framework via UNCOVER DR4

**Preprint | Continuum Field Entropy Empirical Validation Series** The James Webb Space Telescope (JWST) has revealed a population of extreme high-redshift galaxies ($z > 6$) with massive stellar populations packed into extraordinarily tight geometric footprints. Despite their compactness, a significant portion of these early galaxies remain physically larger than the standard hierarchical limits predicted by ΛCDM, which mathematically “over-crushes” early gas clouds due to the Rₑ ∝ (1 + z)⁻¹ geometric scaling relation. We demonstrate that this Compactness Paradox is resolved by the Continuum Field Entropy (CFE) framework. By modeling the universe as a non-Newtonian, shear-thickening Cosserat continuum, we apply a geometric scaling factor anchored to the local critical acceleration limit (a₀ = 1.2 × 10⁻¹⁰ m/s²) to derive an asymptotic vacuum saturation limit. Testing this parameter-free bounding equation against 61 massive targets (M_* > 10⁷ M_) from the UNCOVER DR4 survey (lensing-demagnified via Abell 2744), we find that ΛCDM fails to account for the physical size of 39.3% of the targets. Conversely, the CFE framework empirically bounds 100% of the galaxies without relying on free parameters or ad-hoc feedback mechanisms. The amplified topological gravity of the early universe provides a stable, geometric floor that prevents infinite structural crushing, establishing the continuum field as a stable incubator for primordial structure. **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).