The Odero Axiom: C(I) · E > D - A Unified Persistence Framework for Control, Information, Energy, and Decay

We propose the Odero Axiom: a first-principles mathematical law governing the persistence of all organized systems. The Axiom states: C(I) · E > D Where C(I) is Control informed by Information [0,1], E is Usable Energy Throughput, and D is Organizational Decay. v1.1 KEY HIGHLIGHTS:1. Formalized 3 core metrics: Persistence Capacity P = C(I) · E, Persistence Balance B = P - D, Persistence Index Ω = P/D2. Introduced the Odero Triad Framework {C(I), E, D} for cross-domain diagnosis 3. Defined 3 Failure Modes: Energy Collapse, Control Collapse, Decay Overtake4. Established 6 falsifiable predictions for empirical testing5. Explicitly named Control as a core pillar in title and framework Persistence requires P > D, or equivalently Ω > 1. Failure occurs when Ω ≤ 1. The framework is domain-invariant in structure while domain-specific in measurement. Applications span biology, organizations, economics, computation, ecology, and physics. This version includes Harvard-style formatting, improved readability, and expanded operationalization tables.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-07-30
DOI
https://doi.org/10.5281/zenodo.21708303
Primary Topic
Topological and Geometric Data Analysis
Type
preprint
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preprint

The Odero Axiom: C(I) · E > D - A Unified Persistence Framework for Control, Information, Energy, and Decay

John Otieno Odero
Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
preprint

The Odero Axiom: C(I) · E > D - A Unified Persistence Framework for Control, Information, Energy, and Decay

John Otieno Odero
preprint en

Abstract

We propose the Odero Axiom: a first-principles mathematical law governing the persistence of all organized systems. The Axiom states: C(I) · E > D Where C(I) is Control informed by Information [0,1], E is Usable Energy Throughput, and D is Organizational Decay. v1.1 KEY HIGHLIGHTS:1. Formalized 3 core metrics: Persistence Capacity P = C(I) · E, Persistence Balance B = P - D, Persistence Index Ω = P/D2. Introduced the Odero Triad Framework {C(I), E, D} for cross-domain diagnosis 3. Defined 3 Failure Modes: Energy Collapse, Control Collapse, Decay Overtake4. Established 6 falsifiable predictions for empirical testing5. Explicitly named Control as a core pillar in title and framework Persistence requires P > D, or equivalently Ω > 1. Failure occurs when Ω ≤ 1. The framework is domain-invariant in structure while domain-specific in measurement. Applications span biology, organizations, economics, computation, ecology, and physics. This version includes Harvard-style formatting, improved readability, and expanded operationalization tables.

Zenodo (CERN European Organization for Nuclear Research)
Affordable and clean energy
Topological and Geometric Data Analysis
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