{"id":"https://openalex.org/W7224600649","doi":"https://doi.org/10.5281/zenodo.23764886","title":"No Verified Solution to Clay Millennium Problems; Navier\u2013Stokes Claim Unconfirmed \u2014 E8 Intelligence Research","display_name":"No Verified Solution to Clay Millennium Problems; Navier\u2013Stokes Claim Unconfirmed \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224600649","doi":"https://doi.org/10.5281/zenodo.23764886"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23764886","doi":"https://doi.org/10.5281/zenodo.23764886","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23764886","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.23764886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","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/A5153285007"],"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.6021000146865845,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.6021000146865845,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.09380000084638596,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13806","display_name":"Mathematical and Computational Methods","score":0.01979999989271164,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/clay-millennium-prize-problem","display_name":"Clay Millennium Prize Problem","score":0.7950000166893005},{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.890999972820282},{"id":"https://openalex.org/keywords/existence-and-smoothness","display_name":"existence and smoothness","score":0.7710000276565552},{"id":"https://openalex.org/keywords/global-smooth-solutions","display_name":"global smooth solutions","score":0.5820000171661377},{"id":"https://openalex.org/keywords/finite-time-blow-up","display_name":"finite-time blow-up","score":0.9589999914169312},{"id":"https://openalex.org/keywords/p-versus-np","display_name":"P versus NP","score":0.7760000228881836},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.33799999952316284},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.6880000233650208},{"id":"https://openalex.org/keywords/base-60","display_name":"base-60","score":0.6510000228881836},{"id":"https://openalex.org/keywords/crystal-symmetry","display_name":"crystal symmetry","score":0.7540000081062317},{"id":"https://openalex.org/keywords/root-systems","display_name":"root systems","score":0.6460000276565552},{"id":"https://openalex.org/keywords/lattice-structures","display_name":"lattice structures","score":0.4650000035762787}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47859999537467957},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.4377000033855438},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.4221999943256378},{"id":"https://openalex.org/C2779010991","wikidata":"https://www.wikidata.org/wiki/Q2720909","display_name":"Artifact (error)","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.36149999499320984},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.3418999910354614},{"id":"https://openalex.org/C66783780","wikidata":"https://www.wikidata.org/wiki/Q1166625","display_name":"Mathematical problem","level":2,"score":0.33799999952316284},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.33309999108314514},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2924000024795532},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2709999978542328},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.262800008058548}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23764886","doi":"https://doi.org/10.5281/zenodo.23764886","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23764886","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.23764887","doi":"https://doi.org/10.5281/zenodo.23764887","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23764887","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.23764886","doi":"https://doi.org/10.5281/zenodo.23764886","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23764886","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223685004","https://openalex.org/W7204555599","https://openalex.org/W7223071309","https://openalex.org/W7203534676","https://openalex.org/W7204682250","https://openalex.org/W7204653287","https://openalex.org/W7203662990","https://openalex.org/W7204232692","https://openalex.org/W7222926671","https://openalex.org/W7222920049"],"abstract_inverted_index":{"FINDING:":[0,122],"No":[1,73,97],"verified":[2],"solution":[3],"to":[4,25,138],"any":[5,116],"Clay":[6,139],"Millennium":[7],"Problem":[8],"exists":[9],"as":[10],"of":[11,156],"the":[12,15,57,79,89,129,157],"search":[13],"results;":[14],"\"OpenAI":[16],"solved":[17],"Navier\u2013Stokes\"":[18],"claim":[19],"is":[20,60,82,86,131],"unconfirmed,":[21],"contested,":[22],"and":[23,145],"appears":[24,114],"originate":[26],"from":[27,78],"YouTube":[28],"commentary":[29],"rather":[30],"than":[31],"peer-reviewed":[32],"literature.":[33],"|":[34,91,119],"MATH:":[35],"Navier\u2013Stokes":[36],"existence/smoothness":[37],"in":[38,88,115,128],"\u211d\u00b3:":[39],"\u2202\u209cu":[40],"+":[41,45],"(u\u00b7\u2207)u":[42],"=":[43,48],"\u2212\u2207p":[44],"\u03bd\u0394u,":[46],"\u2207\u00b7u":[47],"0,":[49],"with":[50],"finite-energy":[51],"initial":[52],"data":[53],"u\u2080":[54],"\u2208":[55],"L\u00b2(\u211d\u00b3);":[56],"open":[58],"question":[59],"whether":[61],"smooth":[62],"global":[63],"solutions":[64,137],"exist":[65],"for":[66],"all":[67],"t>0":[68],"or":[69,76,111],"finite-time":[70],"blow-up":[71],"occurs.":[72],"equation,":[74],"constant,":[75],"ratio":[77],"claimed":[80],"\"solution\"":[81],"extractable":[83],"\u2014":[84],"none":[85],"provided":[87],"sources.":[90],"CONNECTION:":[92],"None":[93],"supported":[94],"by":[95],"evidence.":[96],"geometric-harmony":[98],"constants":[99],"(0.382,":[100],"0.618,":[101],"0.786,":[102],"1.618,":[103],"2.618),":[104],"base-60":[105],"structure,":[106],"crystallographic":[107],"symmetry,":[108],"root":[109],"system,":[110],"lattice":[112],"structure":[113],"cited":[117],"source.":[118],"DEPTH:":[120],"1":[121],"The":[123],"only":[124],"concrete":[125],"mathematical":[126],"artifact":[127],"results":[130],"arXiv:1902.07265v23,":[132],"a":[133],"self-published":[134],"preprint":[135],"claiming":[136],"Problems":[140],"#3":[141],"(P":[142],"vs":[143],"NP)":[144],"#4":[146],"(Navier\u2013S":[147],"Author:":[148],"Andrew":[149],"Stewart":[150],"Caldin,":[151],"Independent":[152],"Researcher,":[153],"UK.":[154],"Part":[155],"E8":[158],"Intelligence":[159],"Research":[160],"series.":[161],"Platform:":[162],"e8intelligence.com":[163]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-30T00:00:00"}