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

Abstract

The Odero Axiom proposes a general framework for understanding the persistence of systems across biological, organizational, computational, economic, ecological, and physical domains. The foundational persistence condition is expressed as: C(I)·E > D where C(I) denotes Information-Directed Control Efficiency, E denotes usable energy throughput, and D denotes System Decay. The framework introduces two foundational operational equations of Persistence Science: the Information Index, I = S × ηᵢ and the Persistence Index, Ω = P/D which respectively quantify effective information availability and persistence margin. By linking information, control, energy, and decay into a unified, mathematically falsifiable framework, the Odero Axiom provides a domain-invariant approach for analyzing persistence, resilience, adaptation, and systemic failure across diverse classes of systems.