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

The Odero Persistent Axiom proposes a unified mathematical framework for understanding persistence across biological, organizational, computational, economic, ecological, and physical systems. The framework is founded on the persistence condition: C(I) × E > D where C(I) represents information-directed control efficiency, E denotes usable energy throughput, and D represents system decay. Persistence is achieved when information-guided deployment of energy exceeds the rate of structural degradation. The framework introduces Persistence Capacity (P = C(I) × E), Persistence Balance (B = P − D), and the Persistence Index (Ω = P / D) as quantitative tools for diagnosing stability and vulnerability across domains. Version 2.1 extends earlier formulations by introducing thermodynamic-economic scaling through the factor λ, strengthening dimensional invariance across physical and economic systems, formalizing empirical calibration procedures for control efficiency, and clarifying the theoretical distinction between the axiom and existing paradigms in thermodynamics, cybernetics, and information theory. The framework further establishes Persistence Science as a broader research program in which specialized theories of governance, geopolitics, economics, physics, cosmology, organizational resilience, and computational systems may be derived from a common persistence condition. The Odero Persistent Axiom is presented as a foundational theoretical framework and a mathematically falsifiable persistence principle whose empirical validation constitutes an ongoing research agenda. What's New in Version 2.1 Major Improvements Introduced the Thermodynamic-Economic Scaling Factor (λ) to bridge physical and economic domains. Strengthened dimensional invariance through formal scaling bridges rather than direct cross-domain unit comparisons. Expanded the Control Calibration Framework with objective measurement procedures for: Accuracy (A) Feedback Quality (F) Timeliness (T) Added a dedicated section on Theoretical Distinction from Prior Paradigms, comparing the axiom to: Thermodynamics Cybernetics Information Theory Introduced the concept of Persistence Science as a broader research program built upon the axiom. Added a Scope and Theoretical Extensions section establishing how derived theories relate to the parent axiom. Clarified the framework's status as a foundational theoretical proposition rather than a completed empirical law. Expanded organizational applications through thermodynamic-economic scaling and dissipative-structure interpretation. Key Equations Persistence Condition: C(I) × E > D Persistence Capacity: P = C(I) × E Persistence Balance: B = P − D Persistence Index: Ω = P / D Control Efficiency: C(I) = A × F × T Thermodynamic-Economic Scaling: Eₜₕₑᵣₘ = λ × Eₑcₒₙ Dₜₕₑᵣₘ = λ × Dₑcₒₙ Risk Lever: ρ = ∂D/∂R Efficiency Lever: η = Wₒᵤₜ/E Control Leverage: ϕ = E/D Decay Resistance: δ = Dcᵣᵢₜ/Dₐₘᵦᵢₑₙₜ