From ambiguous utterances to governed reuse classes: canonicalization, quotient invariance, and conditional decidability

arXiv:2607.10069v1 Announce Type: new Abstract: Semantic caching defines answer reuse on embedding similarity: two utterances share a stored answer when a similarity score clears a threshold, with no notion of authorization, versioning, or of what makes two demands the same. This note changes the object on which reuse is defined: in a governed domain, reuse should operate on a mathematically characterized quotient of resolved conversational demands, not on a similarity heuristic. Three independently defined relations on resolved utterances -- reading identity, resolution identity, and reuse identity -- form a refinement chain, strict under realized nondegeneracy conditions checkable on deployment logs; the pipeline's outputs are invariant along the chain, and reuse identity is exactly…