The Odero Axiom: C(I)·E > D — Foundations of Persistence Science

Abstract

Abstract The Odero Axiom proposes a unified persistence framework in which persistence occurs when information-directed control successfully deploys usable energy at a rate exceeding system decay: C(I)⋅E>D The framework introduces Persistence Capacity (P), Persistence Balance (B), and the Persistence Index (Ω) as quantitative measures of system persistence. Version 2.0 expands the framework through mathematical formalization, theorem development, calibration methods, dynamic system analysis, operational levers, empirical hypotheses, and domain-spanning applications across biological, organizational, computational, ecological, economic, and physical systems. What's New in Version 2.0 Major Framework Extensions Generalized Organizational Decay into System Decay. Introduced explicit Scientific Contributions section. Added dimensional consistency analysis. Added Domain Invariance Principle. Developed Control Calibration Framework: Accuracy Feedback Quality Timeliness Added Domain-Specific Decay Mapping Functions. Introduced Persistence Theorem and proof. Added dynamic persistence equations. Added Second-Law boundary condition analysis. Introduced Operational Levers: Risk Lever (ρ) Efficiency Lever (η) Control Leverage (φ) Decay Resistance (δ) Added quantitative human physiology case study. Added empirical validation roadmap. Expanded falsifiability criteria. Added multiple conceptual and mathematical figures. Expanded scholarly literature foundation. Version Classification This release represents a major theoretical and methodological expansion of the original framework and is therefore classified as Version 2.0.