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.

This preprint presents the full theoretical formulation of AICOS HUMA-LOCK™ as a mathematical authority stabilization framework within high-impact algorithmic systems. The manuscript integrates stochastic process modeling, Lyapunov stability theory, nonlinear influence dynamics, differential game analysis, multi-agent network modeling, and mean-field population theory into a unified governance architecture. The framework does not modify algorithmic predictions. Instead, it conditions the structural formation of human decision authority prior to execution in irreversible contexts. Authority stability is operationalized through bounded influence constraints, variance floor preservation, and incentive-compatible mechanism design. All mathematical derivations are provided in continuous-time and discrete-time formulations. Simulation methodology for empirical validation is included conceptually; computational code and parameterization layers remain implementation-dependent. This version constitutes Version 1.0 of the theoretical foundation manuscript and is intended for journal submission and academic review. Future versions may include extended empirical validation datasets and domain-specific deployment case studies.