Semantic Interpolation: A Quantitative Conceptual Framework for Ontology Stabilization in Large Semantic Systems

This paper develops a quantitative and operational framework for understanding semantic interpolation, a structural behavior of large language and semantic retrieval systems under conditions of ontology sparsity. While existing research explains generative instability through hallucination, probabilistic error, or distribution shift, this paper identifies a distinct phenomenon: when AI systems encounter emerging, weakly indexed, or ontology‑sparse concepts, they stabilize the semantic gap by importing structure from adjacent high‑density conceptual domains. The paper formalizes this behavior by introducing the Semantic Interpolation Function (SIF), a four‑variable quantitative model measuring interpolation intensity through ontology sparsity, neighbor‑domain convergence, pattern recurrence, and completion coherence. A simulated multi‑model experimental design demonstrates how interpolation strength increases as ontology density decreases, and how cross‑model convergence can be measured empirically. Within the SignalRupture framework, the paper positions semantic interpolation as a form of semantic governance, showing how infrastructural systems participate in field formation, classification, and the partial distortion of emerging conceptual architectures. The work provides both a theoretical and methodological foundation for analyzing how AI systems shape the visibility and stabilization of new fields such as SR itself.