Mathematical Stabilization of Human Decision Authority in High-Impact Algorithmic Systems: The AICOS HUMA-LOCK™ Framework

This paper introduces AICOS HUMA-LOCK™ (Human Authority Stabilization & Cognitive Oversight Layer), a mathematically grounded framework for preserving human decision authority in high-impact algorithmic systems. While existing AI governance approaches emphasize transparency, fairness, and explainability, they do not formally model the structural convergence of human decision-making toward algorithmic outputs. This work reframes human authority as a dynamical variable and demonstrates that authority collapse can be characterized as a stochastic convergence phenomenon under bounded influence dynamics. The paper develops a multi-layer theoretical framework including: • Linear and nonlinear stochastic authority dynamics• Lyapunov-based stability analysis• Continuous-time stochastic differential equation (SDE) modeling• Differential game formulation of human–AI interaction• Multi-agent network authority field modeling• Mean-field population dynamics• Incentive-compatible mechanism design for authority preservation Across analytical scales, a unified stability boundary condition is derived, defining sufficient constraints for preventing asymptotic algorithmic absorption of human authority. The framework establishes Human Authority Infrastructure (HAI) as a structural governance layer that complements AI capability growth by stabilizing accountable human decision sovereignty. Potential applications include finance, healthcare, defense, infrastructure governance, and other irreversible high-impact decision environments. Keywords: Human Authority Infrastructure, AI Governance, Authority Stabilization, Algorithmic Influence, Stochastic Control, Differential Games, Mean-Field Dynamics, Institutional Decision Systems.