The Operator Theoretic Foundations of Cognitive Amplification (CAIT) in LLM Systems

This paper presents a practical and testable framework for understanding how Large Language Models (LLMs) influence productivity, risk, and decision-making inside modern organizations. The model decomposes AI behaviour into three interacting layers: a generative layer that produces options, a selection layer that determines which option is used, and a governancelayer that enforces policies, safety rules, and organizational constraints. The framework tracks five measurable aspects of organizational functioning: the amount of judgment employees must exercise, the psychological strain created by AI-assisted work, the quality of AI utilization, the depth of reliance on AI, and the realized performance gains. Each of these quantities can be estimated from operational data such as decision logs, verification outcomes, error corrections, and AI usage patterns.The paper models the organization as a controlled decision process in which AI-generated suggestions, human verification, and governance rules jointly shape how work evolves over time. The framework identifies conditions under which the system settles into a stable operating state and conditions under which it may become unstable, overloaded, or oscillatory. These stabilityboundaries can be evaluated directly from organizational data. The model provides leaders with concrete diagnostic tools. It enables the measurement of whether AI suggestions are becoming more predictable or more variable, whether governancerules are effectively reducing risk, whether AI dependence is rising faster than employee capacity, and whether performance gains are sustainable. The framework also predicts when AI will increase productivity, when it will widen performance gaps between workers, and when it may destabilize workflows.Overall, the paper offers a rigorous but accessible foundation for managing AI-enabled or ganizations. It clarifies how AI generation, decision filtering, and governance interact to shape performance, inequality, and operational stability, and it provides a set of measurable indicators that organizations can use to validate or falsify the model using their own data.