Resolving the Wide Binary Anomaly via Continuum Field Entropy (CFE): A 1D Kinematic Analysis

**Preprint | Continuum Field Entropy Empirical Validation Series** Recent studies of wide binary stars using Gaia DR3 telemetry have revealed a kinematic anomaly at low accelerations, often cited as evidence for Modified Newtonian Dynamics (MOND) or particulate dark matter. We analyze this anomaly through the framework of Continuum Field Entropy (CFE), which models the vacuum as an asymmetric, shear-thickening Cosserat field. By systematically eliminating unresolved hierarchical triples (via SB9 spectroscopic veto and strict RUWE < 1.05 astrometric filtering) and chance optical alignments, we isolate a pristine sample of wide binaries in the deep vacuum (7,000$-$20,000 AU). Using an unbinned Bayesian Markov Chain Monte Carlo (MCMC) pipeline, we demonstrate that the Continuum Field organically stiffens at a universal threshold of ∇ Tbg ≈ 9.2 × 10⁻¹¹ m/s². The data traces the CFE tensor mechanics precisely until ~ 15,000 AU, where 2D projected kinematics succumb to the asymptotic noise floor of unbound background stars. The results establish scale invariance across both galactic and stellar structures without modifying Newtonian inertia or invoking unseen dark matter mass. **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).