[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81797-en":3,"doc-seo-81797-105":29,"detail-sidebar-cat-0-en-105":90},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},81797,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Theoria: Rewrite-Acceptability Verification over Informal Reasoning States","Theoria presents a verification architecture for deciding when an AI answer can be trusted, addressing the gap between formal proof assistants and opaque scalar LLM judges. A candidate solution is rewritten as a sequence of typed state transitions, each justified by an explicit citation, computation, or problem-given fact. The completeness-of-change invariant forces every difference between consecutive proof states to be licensed, surfacing hidden premises as unlicensed mutations. Evaluations on HLE-Verified Gold and GPQA Diamond report certified precision and human-readable proof traces.","arXiv :2607 .0 1223v 3 [ cs .AI] 9 Jul 2026  \nTheoria: Rewrite-Acceptability Verification  \nover 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  \n∗ A preliminary white paper describing the framework, architecture, and the primary HLE-Verified Gold evaluation accompanied the project’s June 2026 open-source release: github .com/zaladbar/theoria.  \nnatural-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, this 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 system","cbCaih0pRxODHvL3","https://ap.wps.com/l/cbCaih0pRxODHvL3","pdf",322322,1,20,"English","en",105,"# Introduction\n## Verification as Acceptable Reliance Boundary\n## Formal Methods and Their Semantic Fragility\n## Scalar/Judge Approaches and Missing Certificates\n## Theoria’s Witness-Based Rewrite Architecture","[{\"question\":\"What trust problem does Theoria address in AI reasoning?\",\"answer\":\"Theoria targets the question of when a produced answer should create justified reliance, not just whether the answer is correct on average. It focuses on whether the steps that make the answer usable can be verified and bounded by known failure surfaces.\"},{\"question\":\"How does Theoria represent and verify a candidate solution?\",\"answer\":\"The candidate solution is rewritten into a witness consisting of an initial state and a sequence of typed state-to-state transformations. Each transformation has a single justification type—citation, computation, or problem-given evidence—and the verifier checks whether that justification licenses the observed change.\"},{\"question\":\"What does the completeness-of-change invariant guarantee?\",\"answer\":\"Completeness of change requires accounting for every difference between consecutive proof states. Unlicensed mutations, such as hidden premises or illicit changes, cannot pass silently and must be detectable as violations of the logged justification chain.\"}]",1784176224,50,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"theoria-rewrite-acceptability-verification-over-informal-reasoning-states","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/theoria-rewrite-acceptability-verification-over-informal-reasoning-states/81797/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What trust problem does Theoria address in AI reasoning?","Question",{"text":74,"@type":75},"Theoria targets the question of when a produced answer should create justified reliance, not just whether the answer is correct on average. It focuses on whether the steps that make the answer usable can be verified and bounded by known failure surfaces.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does Theoria represent and verify a candidate solution?",{"text":79,"@type":75},"The candidate solution is rewritten into a witness consisting of an initial state and a sequence of typed state-to-state transformations. Each transformation has a single justification type—citation, computation, or problem-given evidence—and the verifier checks whether that justification licenses the observed change.",{"name":81,"@type":72,"acceptedAnswer":82},"What does the completeness-of-change invariant guarantee?",{"text":83,"@type":75},"Completeness of change requires accounting for every difference between consecutive proof states. Unlicensed mutations, such as hidden premises or illicit changes, cannot pass silently and must be detectable as violations of the logged justification chain.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,113,118,121,125,128,132],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":28,"slug":112},6,"Technology","technology",{"id":114,"doc_module":4,"doc_module_name":45,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":119,"slug":120},30,"research-report",{"id":122,"doc_module":4,"doc_module_name":45,"category_name":123,"show_sort_weight":21,"slug":124},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":126,"show_sort_weight":21,"slug":127},"World Cup","world-cup",{"id":129,"doc_module":4,"doc_module_name":45,"category_name":130,"show_sort_weight":129,"slug":131},10,"Lifestyle","lifestyle",{"id":133,"doc_module":4,"doc_module_name":45,"category_name":134,"show_sort_weight":105,"slug":135},19,"General","general"]