Characterization of Deterministic Outliers in Finite-Entropy Systems_ A Log-Density-Ratio Approach in Light of the Counterexample to the Jacobian Conjecture (Alpöge, 2026)

This work proposes an alternative framework for characterizing and preserving outliers in finite-dimensional, finite-entropy systems. It challenges the dominant practice of systematic anomaly removal, arguing it may destroy global deterministic relationships. Inspired by the Jacobian conjecture's refutation for n greater or equal to 3, it contends local regularity does not imply global dispensability. A metric is introduced based on the log-ratio of local densities estimated via kernels, contrasted with total entropy change upon point removal. A deterministic outlier is operationally defined as one whose absence causes an abrupt entropy drop. The empirical component is merely illustrative.Note:"This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible."