{"id":"https://openalex.org/W7166320406","doi":"https://doi.org/10.5281/zenodo.20951707","title":"Representational Incompleteness: No Self-Modeling System Can Capture Its Own Diagonal \u2014 A Machine-Checked Barrier with Six Closed Escape Routes","display_name":"Representational Incompleteness: No Self-Modeling System Can Capture Its Own Diagonal \u2014 A Machine-Checked Barrier with Six Closed Escape Routes","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166320406","doi":"https://doi.org/10.5281/zenodo.20951707"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.20951707","doi":"https://doi.org/10.5281/zenodo.20951707","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20951707","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.20951707","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132989407","display_name":"Nova Spivack","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Spivack, Nova","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5132989407"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.513700008392334,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.513700008392334,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.33059999346733093,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.024299999698996544,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal-argument","display_name":"diagonal argument","score":0.6740000247955322},{"id":"https://openalex.org/keywords/self-reference","display_name":"self-reference","score":0.609000027179718},{"id":"https://openalex.org/keywords/surjectivity","display_name":"surjectivity","score":0.6230000257492065},{"id":"https://openalex.org/keywords/machine-checked-proofs","display_name":"machine-checked proofs","score":0.5849999785423279},{"id":"https://openalex.org/keywords/lean-4","display_name":"Lean 4","score":0.968999981880188},{"id":"https://openalex.org/keywords/mobius-strip","display_name":"M\u00f6bius strip","score":0.7419999837875366},{"id":"https://openalex.org/keywords/closed-cylinder","display_name":"closed cylinder","score":0.6990000009536743},{"id":"https://openalex.org/keywords/orientability","display_name":"orientability","score":0.7639999985694885},{"id":"https://openalex.org/keywords/homeomorphism","display_name":"homeomorphism","score":0.7039999961853027}],"concepts":[{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7720999717712402},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.7527999877929688},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.7253999710083008},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7124000191688538},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48919999599456787},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.46869999170303345},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45320001244544983},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38260000944137573},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3578999936580658},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34040001034736633},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3091999888420105},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.30329999327659607},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.2759999930858612},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.2667999863624573}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.20951707","doi":"https://doi.org/10.5281/zenodo.20951707","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20951707","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.20951708","doi":"https://doi.org/10.5281/zenodo.20951708","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20951708","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.20951707","doi":"https://doi.org/10.5281/zenodo.20951707","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20951707","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.5317239165306091,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Any":[0],"system":[1],"that":[2],"models":[3],"itself":[4],"\u2014":[5,15],"any":[6,37],"s":[7,39],":":[8,48],"A":[9,11],"->":[10,12,50],"B":[13,49,51],"whatsoever":[14],"is":[16,33,104],"necessarily":[17],"incomplete":[18],"with":[19],"respect":[20],"to":[21,36,107],"its":[22],"own":[23],"diagonal":[24,91],"behavior:":[25],"the":[26,42,101,108,111,115],"function":[27],"a":[28,31],"|->":[29],"f(s":[30],"a)":[32],"never":[34],"equal":[35],"row":[38],"a0":[40,54],"of":[41,60,114],"self-model,":[43],"for":[44],"every":[45,53],"fixed-point-free":[46],"f":[47],"and":[52,93],"in":[55],"A.":[56],"No":[57],"surjective":[58],"self-model":[59],"this":[61],"kind":[62],"can":[63],"exist.":[64],"This":[65],"paper":[66],"proves":[67,100],"six":[68],"\"no-escape\"":[69],"routes":[70],"are":[71],"formally":[72],"closed":[73,109],"as":[74],"machine-checked":[75],"Lean":[76],"4":[77],"theorems:":[78],"no":[79,81,84,87,90,94],"surjection,":[80],"injective":[82],"tower,":[83],"idempotent":[85],"loop,":[86],"parametric":[88],"evaluator,":[89],"row,":[92],"representational":[95,116],"bypass.":[96],"The":[97],"topological":[98],"complement":[99],"Mobius":[102],"strip":[103],"not":[105],"homeomorphic":[106],"cylinder,":[110],"orientability":[112],"boundary":[113],"incompleteness":[117],"thesis.":[118]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-06-28T00:00:00"}
