[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-327253-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-327253-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","theoria-acceptability-verification-over-informal-reasoning-states","Theoria - Acceptability Verification over Informal Reasoning States","","When should an AI answer be trusted beyond average correctness? The paper presents Theoria, a verification architecture that rewrites a candidate solution into typed state transitions, each authorized by an explicit justification such as citations, computations, or problem facts. Using completeness of change, any difference between consecutive proof states must be explained, preventing hidden premise mutations. Experiments show high certified precision on multiple benchmarks and reduced errors from hidden premises and fabricated citations.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/theoria-acceptability-verification-over-informal-reasoning-states/327253/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/theoria-acceptability-verification-over-informal-reasoning-states/327253.png","ImageObject",300,407,{"name":42,"@type":43},"Lucas Martin","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-13","2026-09-21",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",8,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What problem does Theoria address in AI reasoning verification?","Question",{"text":63,"@type":64},"It focuses on deciding when an AI-produced answer should create justified reliance, not just increasing average correctness. The work emphasizes verifying the steps that make an output usable in safety-critical settings.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does Theoria verify acceptability of a solution?",{"text":68,"@type":64},"It rewrites the solver’s answer into a witness consisting of an initial state plus a sequence of typed state-to-state transformations. Each transformation must be licensed by an explicit justification type, and the verifier checks that the justification authorizes the entire change.",{"name":70,"@type":61,"acceptedAnswer":71},"What evidence shows Theoria improves over holistic LLM judging?",{"text":72,"@type":64},"On HLE-Verified Gold, Theoria certifies higher strict precision than holistic judging at matched coverage, and on adversarial poisoned proofs across multiple domains it catches a larger fraction of structured judge violations. The paper attributes gains mainly to hidden premises and fabricated citations.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},327253,1790920919,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":55,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":117,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":104,"preview_page_count":4},8796095360427,"https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d","arXiv :2607 .0 1223v2 [ cs .AI] 2 Jul 2026  \nTheoria: Rewrite-Acceptability Verification over Informal Reasoning States  \nMichael Saldivar Ben Slivinski  \nIndependent Researchers  \n[github. com/zaladbar/theoria](github. com/zaladbar/theoria)  \nAbstract  \nWhen should an AI system’s answer be trusted? Formal proof assistants offer certainty but cannot reach most of the problem distribution; scalar LLM judges offer coverage but produce opaque scores that cannot be audited after the fact and are subject to the same coherence issues as any LLM. We present Theoria, a verification architecture that closes this gap. A candidate solution is rewritten into a sequence of typed state transitions, each licensed by an explicit justification, whether that be a citation, computation, or problem-given fact, and every transition is independently auditable. The foundational invariant is completeness of change:  \nevery difference between consecutive proof states must be accounted for, so hidden premises surface as unlicensed mutations rather than passing silently.  \nOn HLE-Verified Gold (185 text-only expert problems), Theoria certifies 105 at 91.4% strict precision (Wilson 95% CI [84.5%, 95.4%]) . Every certification produces a human-readable proof trace in which each step can be independently challenged. Holistic LLM judges achieve comparable precision at matched coverage but fail on different problems (Jaccard 0.14–0.36), making the approaches complementary. On 95 adversarial poisoned proofs across 15 domains, structured judges catch 94.7% versus 83.2% for holistic judging (p = 0 .0017) . The overall 11.5 pp gap concentrates in hidden premises (90.6% vs. 62.5%, a 28 pp difference) and fabricated citations (100% vs. 90%), the error classes where the formal analysis predicts an advantage; performance is identical on arithmetic and theorem-misapplication errors, where no advantage is predicted. On GPQA Diamond (n = 65), certified precision is 97.1%(Wilson CI [85.1%, 99.5%]) .  \n1 Introduction  \nReasoning verification is not the problem of making an AI system produce more correct answers on average. It is the problem of deciding when a produced answer should create justified reliance. For casual use, a plausible answer suffices. For scientific discovery, legal analysis, financial modeling, medical decision support, engineering verification, or any other ”safety critical field”, the relevant object is not the answer alone but the steps by which the system proposes to make that answer usable. A verifier that merely improves average accuracy has not solved the trust problem. A verifier must draw a boundary: these outputs have survived a procedure with a known failure surface, those outputs have not.  \nToday, two approaches exist. At one end, formal methods make correctness a kernel property. Proof assistants like Lean [Lean project], Coq/Rocq [The Rocq Prover project], and Isabelle [Nipkowet al. , 2002] accept or reject proof terms, and modern AI systems exploit this by translating natural-language problems into formal targets and searching for formal proofs [Xin et al. , 2024 , Google DeepMind, 2024 , Hubert et al. , 2025 , Tsoukalas et al. , 2026 , Achim et al. , 2025 , Chen et al. , 2026] . Formal verification yields strong results once the specification is fully formalized. However,  \nthis approach becomes fragile at the point where informal, natural-language requirements must be interpreted. When the primary challenge lies in determining which formal specification accurately reflects the real-world problem, the verification kernel may flawlessly prove an incorrect theorem. Hence, the barrier to autoformalization is not just a limitation of current tooling, but a fundamental semantic boundary.  \nAt the other end, scalar reward and judge systems operate over ordinary reasoning traces and cover far more of the problem distribution. Process reward models [Lightman et al. , 2023 , Wanget al. , 2023 , Yuan et al. , 2024] provide dense training signal ","cbCaiswaw6sfHF4Y","https://ap.wps.com/l/cbCaiswaw6sfHF4Y","pdf",347178,"English","# Abstract\n# Introduction","[{\"question\":\"What problem does Theoria address in AI reasoning verification?\",\"answer\":\"It focuses on deciding when an AI-produced answer should create justified reliance, not just increasing average correctness. The work emphasizes verifying the steps that make an output usable in safety-critical settings.\"},{\"question\":\"How does Theoria verify acceptability of a solution?\",\"answer\":\"It rewrites the solver’s answer into a witness consisting of an initial state plus a sequence of typed state-to-state transformations. Each transformation must be licensed by an explicit justification type, and the verifier checks that the justification authorizes the entire change.\"},{\"question\":\"What evidence shows Theoria improves over holistic LLM judging?\",\"answer\":\"On HLE-Verified Gold, Theoria certifies higher strict precision than holistic judging at matched coverage, and on adversarial poisoned proofs across multiple domains it catches a larger fraction of structured judge violations. The paper attributes gains mainly to hidden premises and fabricated citations.\"}]","Theoria - Acceptability Verification over Informal Reasoning States | PDF",1789976822]