[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84269-en":3,"doc-seo-84269-105":29,"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":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},84269,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Limits of Uniform Certification in the Standard Turing Model: Semantic Invariants and Admissible Methods","The paper establishes a structural limitation of uniform proof-generation methods in the standard Turing model, without resolving the mathematical truth of P versus NP. The key claim is model-theoretic: interaction between semantic invariants and syntactic verification, rather than provability of complexity statements. It formalises admissible methods as generator–verifier pairs that yield finite certificates for semantic program properties, forcing uniform behaviour that implicitly induces a decision procedure. Rice’s theorem then blocks non-trivial semantic invariants; two natural invariants tied to P-versus-NP certification and cryptographic hardness (e.g., one-way functions) cannot be uniformly certified. A complete Coq formalisation captures the semantic–syntactic interaction.","arXiv :2607 .07723v 1 [ cs .LO] 4 Jul 2026  \nLimits of Uniform Certification in the Standard  \nTuring Model  \nSemantic Invariants and Admissible Methods  \nFabio F.G. Buono  \nIndependent Researcher  \nORCID: 0009-0004-9199-2793  \nPreprint – Friday 10th July, 2026  \nAbstract  \nThis paper does not address the mathematical truth of P versus NP.  \nInstead, it identifies a structural limitation of uniform proof-generation methods in the standard Turing model. The observation is model-theoretic:  \nit concerns the interaction between semantic invariants and syntactic verification, not the provability of complexity statements.  \nWe formalise an admissible method as a generator–verifier pair that produces, for each program, a finite certificate establishing a semantic property. Admissibility forces the generator–verifier composition to behave uniformly with respect to the invariant being certified. In the standard model, such uniform semantic certification implicitly induces a decision procedure for the property. Rice’s theorem shows that this implicit behaviour cannot be realised for non-trivial semantic invariants, revealing a structural constraint on formal certification. Understanding this requires a meta-computational perspective: the obstruction arises from the computational behaviour induced by certification, not from the complexity-theoretic status of the property.  \nWe apply this framework to two semantic invariants naturally associated with formal certification of P vs. NP and with cryptographic hardness assumptions (in particular, one-way functions) . Both fall under the same limitation: no uniform admissible method can certify them in the standard model. A complete Coq formalisation is provided, capturing the extensional structure of admissible methods and the semantic–syntactic interaction underlying the result.  \n1 Introduction  \nThis paper does not address the mathematical truth of P versus NP. Its focus is different: we study a structural limitation of uniform proof-generation methods in the standard Turing model, a limitation that has conceptual implications  \nfor formal certification in complexity theory and cryptography. Cryptography provides natural examples of semantic invariants that require uniform certification: hardness assumptions such as one-way functions are semantic properties of programs, and any formal certification of such assumptions must establish anon-trivial semantic invariant.  \nModern cryptography derives its security guarantees from assumptions whose formal certification remains out of reach. The security of RSA, Diffie–Hellman, and many post-quantum proposals ultimately relies on complexity-theoretic separation assumptions. Understanding the scope and limits of what the standard Turing model can certify is therefore a foundational concern for cryptographic security, independent of the mathematical status of P vs. NP.  \nUnderstanding this limitation requires a meta-computational perspective. The argument concerns the behaviour induced by uniform certification within the standard Turing model, rather than the complexity-theoretic status of the statements being certified. This viewpoint is not standard in complexity theory and is conceptual rather than technical: it focuses on what the model can express about semantic invariants, not on what those invariants assert about complexity classes.  \nThe perspective shift. The question we investigate is not whether P = NPas a mathematical fact. Instead, we analyse whether the standard Turing model can produce and verify admissible certificates for two semantic properties Φα and Φβ naturally associated with formal certification of this separation. The analysis shows that the model faces a structural obstruction: admissible methods cannot uniformly certify these properties.  \nThe key is a precise reading of what “settling” means. We work on concrete proof objects: syntactic certificates π that a verification machine accepts as establishing a semantic property o","cbCaikThDFEBWjPc","https://ap.wps.com/l/cbCaikThDFEBWjPc","pdf",403630,1,34,"English","en",105,"# Abstract\n# Introduction\n# Semantic Properties and Rice’s Theorem\n## Structural obstruction and meta-computational perspective","[{\"question\":\"Does the paper prove whether P equals NP?\",\"answer\":\"No. The paper explicitly does not address the mathematical truth of P versus NP, focusing instead on limits of uniform certification in the standard Turing model.\"},{\"question\":\"How does the paper formalise an admissible method?\",\"answer\":\"It defines an admissible method as a generator–verifier pair that, for each program, produces a finite certificate establishing a semantic property.\"},{\"question\":\"What prevents uniform certification of non-trivial semantic invariants?\",\"answer\":\"Extended Rice principle reasoning shows that admissible certification implicitly induces a decider for the semantic property, and Rice’s theorem implies this cannot be realised for non-trivial semantic invariants.\"}]",1784194499,86,{"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":86,"head_meta":88,"extra_data":90,"updated_unix":27},"limits-of-uniform-certification-in-the-standard-turing-model-semantic-invariants-and-admissible-methods","",{"@graph":35,"@context":85},[36,53,68],{"@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/limits-of-uniform-certification-in-the-standard-turing-model-semantic-invariants-and-admissible-methods/84269/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","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},"Does the paper prove whether P equals NP?","Question",{"text":75,"@type":76},"No. The paper explicitly does not address the mathematical truth of P versus NP, focusing instead on limits of uniform certification in the standard Turing model.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper formalise an admissible method?",{"text":80,"@type":76},"It defines an admissible method as a generator–verifier pair that, for each program, produces a finite certificate establishing a semantic property.",{"name":82,"@type":73,"acceptedAnswer":83},"What prevents uniform certification of non-trivial semantic invariants?",{"text":84,"@type":76},"Extended Rice principle reasoning shows that admissible certification implicitly induces a decider for the semantic property, and Rice’s theorem implies this cannot be realised for non-trivial semantic 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