[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85801-en":3,"doc-seo-85801-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},85801,8796095462418,"Noah","https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780",8,"Research & Report","From Ambiguous Utterances to Governed Reuse Classes","Semantic caching reuses answers for embedding-similar utterances via a threshold, but ignores authorization, versioning, and—crucially—what makes two demands the same governed question. This work defines reuse over a mathematically characterized quotient of resolved conversational demands in a governed domain. Three relations (reading identity, resolution identity, reuse identity) form a refinement chain; pipeline outputs are invariant along it, and reuse identity yields the exact kernel of the resolution map into the governed answer partition.","arXiv :2607 . 10069v 1 [ cs .AI] 11 Jul 2026  \nFrom ambiguous utterances to governed reuse classes: canonicalization, quotient invariance, and conditional  \ndecidability⋆  \nCosimo Spera∗, Ray Garcia  \nMinerva CQ (Bourbaki Intelligent Systems, Inc.), Los Gatos, CA, USA  \nAbstract  \nSemantic 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 the kernel of the resolution map into the governed answer partition, so the reuse quotient is the utterance-side object that partition induces, not a relabeling of it. Reuse identity licenses the governed query key and its certified answer space; reuse of a particular answer requires resolution identity or an applicability certificate. The supporting layer is stated at exactly the strength proved: exact-denotation normal forms; join aggregation as a design operator, with closure-stable cells characterizing no-escape; total computability of the full pipeline relative to an untrusted proposal layer; policy admissibility for arbi-  \n⋆ This note extracts and hardens the canonicalization layer of the working paper Certified Resolution: A Formal Theory of Governed Answer Spaces for Enterprise AI (Minerva CQ, 2026) .  \n∗ Corresponding author.  \nEmail addresses: [cosimo@minervacq.com](cosimo@minervacq.com) (Cosimo Spera), [ray@minervacq.com](ray@minervacq.com)  \n(Ray Garcia)  \ntrary proposers—and provably not factual grounding or intent fidelity; and elicitation terminating after finitely many informative replies, sound under target consistency.  \nKeywords: formal semantics of questions, closure systems, canonical forms, Datalog, decidability, AI governance  \n1. Problem  \nA governed conversational system—one whose answers must be licensed by a corpus of policies, regulations, and standard operating procedures—receives utterances, not questions.“Tell me about Paris,”“can you do something about this fee?,”“what about last month?” are ambiguous along at least three axes: which question is being asked, whether the domain is competent to answer it at all, and whether enough material facts have been disclosed to single out one answer. Retrieval pipelines dissolve the problem by ranking documents against the raw utterance; the cost is that the system has no representation of the question it is answering, hence no principled notion of when two utterances ask the same governed question—the property on which certified answer reuse depends. Semantic caching substitutes a similarity threshold for that notion [7]; this note replaces the threshold with a quotient: the central object is the surjection Ures ↠ Rc , where Rc := Ures / ≡reuse is the realized governed reuse space—the quotient of resolved utterances by governed reuse identity (abstentions are terminal outcomes, held outside the quotient)—and the theorems below say when that map is well-defined, what it is invariant under, and what it does and does not guarantee. Figure 1 is the whole paper in one picture: reading identity, resolution identity, andreuse identity form a chain of coarsening surjections, and certified reuse is defined on the rightmost quotient.  \nOne clarification prevents the objection that this is a relabeling. The governed answer partition P (c) lives on worlds; the reuse quotient lives on utterances. The content of the construction is not the codomain but the factoriz","cbCaigb7knv3zJP4","https://ap.wps.com/l/cbCaigb7knv3zJP4","pdf",525882,3,1,20,"English","en",105,"# Problem\n## Quotient-based governed reuse vs similarity threshold\n# Governed-answer-space framework\n## Context, admissibility closure, and partitions","[{\"question\":\"Why does semantic caching based on embedding similarity fail for governed answer reuse?\",\"answer\":\"It uses a similarity threshold without representing which governed question is being answered. That prevents a principled notion of when two utterances should reuse the same licensed, certified answer.\"},{\"question\":\"What replaces the similarity threshold in this approach?\",\"answer\":\"A quotient object of resolved utterances: the map Ures ↠ Rc, where Rc is the realized governed reuse space formed by the governed reuse identity as a kernel of the resolution map.\"},{\"question\":\"How do reading identity, resolution identity, and reuse identity relate?\",\"answer\":\"They form a refinement chain of coarsening surjections. Under realizable nondegeneracy conditions checkable on deployment logs, the pipeline outputs stay invariant along the chain, and reuse identity is exactly the kernel of the resolution map.\"}]",1784206352,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"from-ambiguous-utterances-to-governed-reuse-classes","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/from-ambiguous-utterances-to-governed-reuse-classes/85801/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-26","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does semantic caching based on embedding similarity fail for governed answer reuse?","Question",{"text":75,"@type":76},"It uses a similarity threshold without representing which governed question is being answered. That prevents a principled notion of when two utterances should reuse the same licensed, certified answer.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What replaces the similarity threshold in this approach?",{"text":80,"@type":76},"A quotient object of resolved utterances: the map Ures ↠ Rc, where Rc is the realized governed reuse space formed by the governed reuse identity as a kernel of the resolution map.",{"name":82,"@type":73,"acceptedAnswer":83},"How do reading identity, resolution identity, and reuse identity relate?",{"text":84,"@type":76},"They form a refinement chain of coarsening surjections. Under realizable nondegeneracy conditions checkable on deployment logs, the pipeline outputs stay invariant along the chain, and reuse identity is exactly the kernel of the resolution map.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,114,119,122,126,129,133],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":29,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":22,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":22,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]