The Omega-Engine: A Python Runtime for Variance Debt Computation

The Omega-Engine is a Python-based runtime designed to audit "Variance Debt" in text corpora and sequential data streams. It operationalizes the theoretical framework of Undecidability Evasion by computing the Psi-Coefficient, a metric derived from: 1. Compression Deltas: Deviation from Maximum Entropy (Null Models) via gzip. 2. K-mer Entropy: Local structural complexity analysis. This software serves as the empirical verification tool for the Recursive Regime Compiler framework (v4.1). Included Modules • metrics.py: The core logic for calculating the Psi-Coefficient and Relative Compression. • router.py: The decision logic that toggles between Mode A (Crystalline) and Mode B (Fluid) based on entropy thresholds. • falsification_matrix.csv: The empirically defined failure boundaries for the Riemann and Collatz attractors. Companion Publications This software provides the empirical verification for the following companion papers: • Formal Proofs (The Shield): Thermodynamic Isomorphisms in Arithmetic Geometry (DOI: 10.5281/zenodo.18135875) • Operational Doctrine (The Sword): Generative Proof Synthesis via Hybrid Annealing Engines (DOI: 10.5281/zenodo.18135882) Usage To run the diagnostic router: python router.py License MIT License. Open for audit and replication.