{"id":"https://openalex.org/W7225203318","doi":"https://doi.org/10.5281/zenodo.23909828","title":"Lawvere's Fixed-Point Theorem Unifies Diagonal Arguments Categorically \u2014 E8 Intelligence Research","display_name":"Lawvere's Fixed-Point Theorem Unifies Diagonal Arguments Categorically \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-03","ids":{"openalex":"https://openalex.org/W7225203318","doi":"https://doi.org/10.5281/zenodo.23909828"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23909828","doi":"https://doi.org/10.5281/zenodo.23909828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23909828","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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.23909828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152673107","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152673107"],"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":0.6064000129699707,"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":0.6064000129699707,"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":0.2551000118255615,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.07180000096559525,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/diagonal-argument","display_name":"diagonal argument","score":0.5590000152587891},{"id":"https://openalex.org/keywords/self-reference","display_name":"self-reference","score":0.9760000109672546},{"id":"https://openalex.org/keywords/cartesian-closed-categories","display_name":"cartesian closed categories","score":0.9860000014305115},{"id":"https://openalex.org/keywords/godel-s-incompleteness-theorems","display_name":"G\u00f6del's incompleteness theorems","score":0.8220000267028809},{"id":"https://openalex.org/keywords/cantor-s-diagonal-argument","display_name":"Cantor's diagonal argument","score":0.8799999952316284},{"id":"https://openalex.org/keywords/russell-s-paradox","display_name":"Russell's paradox","score":0.9860000014305115},{"id":"https://openalex.org/keywords/y-combinator","display_name":"Y Combinator","score":0.828000009059906},{"id":"https://openalex.org/keywords/fixed-points","display_name":"fixed points","score":0.6740000247955322},{"id":"https://openalex.org/keywords/categorical-logic","display_name":"categorical logic","score":0.3880000114440918}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7087000012397766},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.6018000245094299},{"id":"https://openalex.org/C2185349","wikidata":"https://www.wikidata.org/wiki/Q190558","display_name":"Negation","level":2,"score":0.5853999853134155},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.511900007724762},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.46779999136924744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40369999408721924},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.38530001044273376},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37549999356269836},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.3450999855995178},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.3091999888420105},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.2824000120162964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28139999508857727},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26489999890327454},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.26440000534057617}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23909828","doi":"https://doi.org/10.5281/zenodo.23909828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23909828","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.23909829","doi":"https://doi.org/10.5281/zenodo.23909829","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23909829","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.23909828","doi":"https://doi.org/10.5281/zenodo.23909828","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23909828","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7214306279","https://openalex.org/W7225171031","https://openalex.org/W7225083547","https://openalex.org/W7214158127","https://openalex.org/W7218863850","https://openalex.org/W7225006467","https://openalex.org/W7225050140","https://openalex.org/W7224792231","https://openalex.org/W7224603522","https://openalex.org/W7225196537"],"abstract_inverted_index":{"FINDING:":[0],"Lawvere's":[1],"fixed-point":[2,133],"theorem":[3],"unifies":[4],"all":[5],"diagonal/self-reference":[6],"arguments":[7],"(G\u00f6del,":[8],"Cantor,":[9],"Tarski,":[10],"Turing,":[11],"Russell)":[12],"as":[13,63,122],"a":[14,19,25,47,106,110,148],"single":[15],"categorical":[16,100],"statement":[17],"about":[18],"\"point-surjective\"":[20],"morphism.":[21],"|":[22,85,154],"MATH:":[23],"In":[24],"Cartesian":[26],"closed":[27],"category,":[28],"if":[29],"f:":[30],"A":[31,91],"\u2192":[32,44,92],"B^A":[33],"is":[34,98,105,130,144],"point-surjective":[35,58],"(\u2200g:B^A":[36],"\u2203a\u2208A:":[37],"f(a)=g),":[38],"then":[39],"every":[40],"endomorphism":[41],"\u03b1:":[42],"B":[43,45],"has":[46],"fixed":[48,54,72,149],"point.":[49],"Contrapositive:":[50],"no":[51,57],"\u03b1":[52,68,80],"without":[53],"point":[55,73],"\u27f9":[56],"f.":[59],"G\u00f6del":[60],"sentence":[61],"arises":[62],"g":[64],"=":[65,69,81],"\u03b1\u2218f":[66],"where":[67],"negation":[70],"(no":[71],"in":[74,127],"{T,F}).":[75],"Cantor:":[76],"B={0,1},":[77],"\u03b1=\u00ac.":[78],"Turing:":[79],"\"flip":[82],"halting":[83],"bit.\"":[84],"CONNECTION:":[86],"The":[87],"diagonal":[88],"morphism":[89],"\u0394:":[90],"A\u00d7A":[93],"and":[94],"its":[95,152],"transpose/evaluation":[96],"structure":[97],"the":[99,118,123,131,141,145,165],"skeleton":[101],"of":[102,147,164],"self-reference.":[103],"This":[104],"*universal*":[107],"construction,":[108],"not":[109,151],"numerical":[111],"ratio":[112],"\u2014":[113],"but":[114],"it":[115],"sits":[116],"at":[117],"same":[119],"structural":[120],"level":[121],"Y-combinator":[124],"(fix:":[125],"(A\u2192A)\u2192A)":[126],"\u03bb-calculus,":[128],"which":[129],"typed/untyped":[132],"combinator.":[134],"No":[135],"direct":[136],"link":[137],"to":[138],"0.618/1.618":[139],"ratios;":[140],"relevant":[142],"\"constant\"":[143],"*existence*":[146],"point,":[150],"value.":[153],"DEPT":[155],"Author:":[156],"Andrew":[157],"Stewart":[158],"Caldin,":[159],"Independent":[160],"Researcher,":[161],"UK.":[162],"Part":[163],"E8":[166],"Intelligence":[167],"Research":[168],"series.":[169],"Platform:":[170],"e8intelligence.com":[171]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-04T00:00:00"}