AICOS: Mathematical Foundations of Decision Safety Infrastructure for Reliable Artificial Intelligence Systems

Artificial Intelligence (AI) systems have achieved significant progress in prediction, generation, and automated analysis. However, the transition of AI from experimental environments into high-impact institutional domains such as finance, governance, and critical decision processes introduces a fundamental challenge: ensuring reliability, explainability, controllability, and operational trust. This research presents AICOS (Artificial Intelligence Constitutional Operating System), a decision safety architecture designed to address the gap between artificial intelligence capability and institutional-grade reliability. The study proposes that intelligence alone is insufficient for trustworthy AI deployment. Reliable AI requires an integrated framework combining mathematical uncertainty modeling, distribution shift analysis, reality drift monitoring, data integrity evaluation, risk propagation modeling, governance constraints, deterministic auditability, and human decision authority. The paper introduces mathematical foundations for AI reliability, including formal representations of model error, environmental drift, uncertainty boundaries, verification mechanisms, and constrained decision optimization. The central contribution of this work is the concept of Decision Safety Infrastructure: an architectural layer that transforms AI systems from prediction engines into controlled, explainable, and auditable decision-support systems. The proposed AICOS framework is particularly relevant for financial technology environments where AI-driven decisions require transparency, accountability, and institutional trust. This work establishes a theoretical foundation for future research and implementation of reliable artificial intelligence systems. Keywords: Artificial Intelligence, AI Governance, Decision Safety, Reliable AI, AI Risk Management, Explainable AI, Financial AI, System Engineering, Uncertainty Modeling, Human-AI Collaboration