The Odero Theory of Captured Inflation: A Persistence Science Explanation for Asymmetric Price Persistence and Market Capture

The Odero Theory of Captured Inflation extends Persistence Science into the domain of macroeconomic inflation dynamics. Building upon the foundational persistence condition of the Odero Axiom, P = C(I)·E > D, this theory proposes that persistent inflation emerges when information-directed market control becomes insufficient to counter systemic economic decay. The framework introduces a Persistence Science interpretation of inflation persistence, defining captured inflation as a persistence-loss condition characterized by Ω = (C(I)·E)/D < 1 for a sustained duration. The theory formalizes the Odero Capture Gap, the Market Capture Coefficient, and the Odero Captured Inflation Equation, providing quantitative tools for measuring persistent price distortions caused by asymmetric transmission efficiency, market concentration, regulatory failure, and control collapse. Extending persistence dynamics into economics, the framework introduces Persistence Velocity (ω) and Persistence Acceleration (α) as early warning indicators of inflation persistence. Empirical calibration across six Sub-Saharan African economies yields an average Rigidity Coefficient of R_C = 3.0, indicating severe downward transmission failure. The theory further derives an Economic Persistence Theorem, a Purchasing-Power Persistence State Classification, Economic Failure Pathways, Energy Allocation Constraints, and a 4-Pillar De-Capture Act for policy intervention. As a domain-specific application of Persistence Science, the framework seeks to explain why prices often fail to fall after initial cost pressures disappear, positioning inflation persistence as a systemic control problem rather than solely a monetary phenomenon.