Just-In-Time Ontology: How Embedded Knowledge Graphs Discover Their Own Structure

We show that a knowledge graph built from 83,610 biomedical concepts embedded in 768-dimensional space self-organizes into a geometric ontology without explicit design. Five measurable properties emerge from the angular structure: (1) an angular specificity gradient where concept generality decreases monotonically with distance from the distributional centroid (rho = -0.976); (2) domain-specific perpendicular signatures whose pairwise angles predict shared biology (rho = -0.936, p = 5e-17); (3) hub non-centrality; (4) a universal organizational centroid shared by all domains; and (5) a seed scaffold that predicts 90% of the centroid direction while contributing negligibly to the self-organization. Cross-graph validation on six graphs spanning five construction types confirms hub non-centrality is universal (95-100%) and the angular specificity gradient holds on all graphs with learned embeddings. Hetionet v1.0 (47K nodes, 11 types, 2.25M edges) scores 6/6 on all tested properties. These properties constitute a Just-In-Time Ontology (JiTO): an ontological hierarchy that is never explicitly constructed but emerges from embedding geometry and is always readable. Traditional ontologies are the input to knowledge systems. This one is the output. Code: github.com/mjgodat/cosine-drainage-theorem