CID: Measuring Cognitive Work Through Semantic State Change

Ron Fulbright

Traditional information theory provides powerful tools for analyzing statistical properties of information but offers limited insight into meaning and semantic transformation. It has never been possible to quantify the meaning of an arbitrary piece of information. Large language models represent information as vectors embedded within high-dimensional semantic spaces, enabling meaning to be analyzed geometrically. This paper defines semantic state as the vector representation of information within a model's semantic space and defines cognitive work as the transformation between semantic states, movement through semantic space. To quantify this transformation, we introduce the Contextual Information Differential (CID), a covariance-aware metric based on Mahalanobis distance measuring semantic displacement relative to the structure of the embedding manifold. By treating meaning as a geometric property of semantic space, CID provides a practical method for measuring semantic change, cognitive transformation, and information processing. This framework establishes a foundation for analyzing cognitive processing, learning, reasoning, knowledge generation, synthetic expertise, and…