Defining Novelty in the Conceptual Space of the Functional Model of Intelligence Defined Through Human-Centric Functional Modeling

This paper develops a formal definition of novelty inside the Functional Model of Intelligence (FMI) and its related first-principles account of conceptual navigation, reach, contraction, and topology. The motivating problem is simple: the FMI papers provide a rich account of cognition as motion in conceptual space, but they do not yet isolate novelty as a primitive quantity. They provide the ingredients—conceptual distance, density, reach, bridge operators, topological coherence, and human-comprehensible visualization—without yet turning those ingredients into a unified novelty functional. Building on those ingredients, I define novelty as the emergence of a concept in a region of conceptual space that was previously empty relative to a specified observer and scale, with novelty magnitude increasing as the concept lies farther from previously occupied concepts, sits in a lower-density neighborhood, requires more bridge work for coherent integration, and changes the topology or navigability of the space in a more substantial way. The paper is intentionally organized in a human-readable way. The main body explains why such a definition is needed, how it differs from existing novelty definitions in creativity theory, design research, novelty search, curiosity/compression accounts, and innovation studies, and why a human-centric indexing of conceptual space is not optional but methodologically necessary. The mathematical statements are theorem-driven but are kept conceptually interpretable in the main body. Full proofs, estimation procedures, and implementation detail are relegated to the appendices. The central methodological claim is stronger than a mere modeling preference: if novelty is meant to be about cognition, communication, science, or design as humans understand them, then novelty cannot be defined only in arbitrary latent machine coordinates. It must be defined on a human-indexed conceptual field or on a quotient of machine representations by human-equivalence classes. Otherwise, novelty scores can be changed by representational refinements that leave humanly accessible conceptual content unchanged. The resulting theory yields a layered account of novelty: metric novelty, field novelty, operator novelty, and topological novelty. This layered account clarifies how novelty differs from surprise, rarity, creativity, usefulness, and prediction error; explains why some apparently "new" outputs are only local recombinations inside already dense regions; and provides a practical estimation pipeline for empirical work on novelty in human and hybrid human-machine systems.