Semantic Caching Redefined for Governed AI Domains

Traditional semantic caching typically relies on embedding similarity to determine if two user utterances can share a stored answer, often without considering authorization, versioning, or a precise definition of equivalence. This research proposes a fundamental shift, defining reuse based on a mathematically rigorous "quotient" of resolved conversational demands within a governed domain. This approach ensures that answer reuse is tied to a precise identity rather than a heuristic similarity score. The framework introduces three distinct relations on resolved utterances—reading identity, resolution identity, and reuse identity—which form a strict refinement chain. Reuse identity is established as the kernel of the resolution map, directly linking it to a governed answer partition. This allows for a certified answer space and a governed query key, ensuring that answer reuse is both authorized and version-controlled. The paper details supporting layers, including exact-denotation normal forms and total computability, providing a robust foundation for building reliable and auditable AI systems.