The Odero Axiom of AI Persistence: A Persistence Science Framework for Artificial Intelligence Systems

Advanced artificial intelligence systems are scaling rapidly in capability, deployment, and resource use, raising the question of whether governance, corrective control, and infrastructure can develop fast enough to preserve long-term operational viability. Existing work addresses scaling, alignment, robustness, and governance, but rarely integrates effective information, control, resource throughput, and deterioration within one dynamic model. This paper develops the Odero Axiom of AI Persistence as an application of Persistence Science. Effective information is represented by the Information Index (Iₐᵢ = Sₐᵢηᴵ,ₐᵢ), normalized deterioration by the AI Decay Index (Δₐᵢ = Dₐᵢ / Dₐᵢ,ref), and instantaneous persistence by the Persistence Index (Ωₐᵢ = [C(Iₐᵢ) × Eₐᵢ] / Dₐᵢ = P̂ₐᵢ / Δₐᵢ). The framework defines AI-specific decay channels, operational proxies, dynamic state vectors, local warning horizons, and falsification conditions. Its parameters and predictive validity require calibration using longitudinal data from bounded operational AI systems.