{"id":"https://openalex.org/W7204462188","doi":"https://doi.org/10.5281/zenodo.22131149","title":"\u03c7\u2011Navier\u2013Stokes Regularity in ZEBTS\u2011\u221e Operator Geometry","display_name":"\u03c7\u2011Navier\u2013Stokes Regularity in ZEBTS\u2011\u221e Operator Geometry","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204462188","doi":"https://doi.org/10.5281/zenodo.22131149"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22131149","doi":"https://doi.org/10.5281/zenodo.22131149","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22131149","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","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22131149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147190751","display_name":"Anatolii Mukha","orcid":"https://orcid.org/0009-0005-4614-6667","observed_orcids":["https://orcid.org/0009-0005-4614-6667"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mukha, Anatolii","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5147190751"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":26,"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":0.9775000214576721,"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":0.9775000214576721,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.005499999970197678,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.002099999925121665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.847000002861023},{"id":"https://openalex.org/keywords/global-regularity","display_name":"global regularity","score":0.9890000224113464},{"id":"https://openalex.org/keywords/millennium-prize-problems","display_name":"Millennium Prize Problems","score":0.8389999866485596},{"id":"https://openalex.org/keywords/blow-up","display_name":"blow-up","score":0.5550000071525574},{"id":"https://openalex.org/keywords/turbulence","display_name":"turbulent flow","score":0.48100000619888306},{"id":"https://openalex.org/keywords/spectral-stabilization","display_name":"spectral stabilization","score":0.6240000128746033},{"id":"https://openalex.org/keywords/fluid-dynamics","display_name":"fluid dynamics","score":0.3569999933242798}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.640999972820282},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5551000237464905},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5230000019073486},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.49470001459121704},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.45080000162124634},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.3752000033855438},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32199999690055847},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C52220454","wikidata":"https://www.wikidata.org/wiki/Q613845","display_name":"Perfect fluid","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2856000065803528},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22131149","doi":"https://doi.org/10.5281/zenodo.22131149","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22131149","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.22131150","doi":"https://doi.org/10.5281/zenodo.22131150","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22131150","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.22131149","doi":"https://doi.org/10.5281/zenodo.22131149","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22131149","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/W7168040333","https://openalex.org/W7131407410","https://openalex.org/W7213525815","https://openalex.org/W7129061904","https://openalex.org/W7140101669","https://openalex.org/W7161677393","https://openalex.org/W7215888238","https://openalex.org/W2606452250","https://openalex.org/W7115725625","https://openalex.org/W7165023794"],"abstract_inverted_index":{"\u0410\u0431\u0441\u0442\u0440\u0430\u043a\u0442":[0],"This":[1,186],"work":[2,187],"establishes":[3],"the":[4,17,37,107,143,174,196,201,206,226],"first":[5,144,207],"complete":[6],"proof":[7],"of":[8,20,110,147,193,230],"global":[9,98,212],"Navier\u2013Stokes":[10,149,197],"regularity":[11,99],"by":[12,26,36],"embedding":[13],"fluid":[14,32,184,216],"dynamics":[15],"into":[16],"operator\u2013spectral":[18],"geometry":[19],"\u03c7\u2011Reality.":[21],"Classical":[22],"hydrodynamics":[23],"is":[24,34,100,159,167],"replaced":[25],"a":[27,96,160,164,179,189,219],"unified":[28,190],"\u03c7\u2011framework":[29],"in":[30],"which":[31],"motion":[33,217],"governed":[35],"\u03c7\u2011Universal":[38],"Fluid":[39],"Law\u2014a":[40],"structural,":[41],"ontological":[42,202],"constraint":[43],"integrating":[44],"\u03c7\u2011operator":[45,220],"curvature,":[46],"\u03c7\u2011spectral":[47],"compression,":[48],"\u03c7\u2011geodesic":[49],"admissibility,":[50],"\u03c7\u2011boundary":[51,93],"neutrality,":[52],"\u03c7\u2011information":[53,132,152,166],"minimization,":[54],"and":[55,73,90,130,136,170,177,204,222],"\u03c7\u2011\u221e":[56],"compactification.":[57],"Within":[58],"this":[59],"geometry,":[60],"blow\u2011up":[61,138],"trajectories":[62],"are":[63],"shown":[64],"to":[65],"be":[66],"geometrically":[67],"forbidden,":[68],"spectrally":[69],"inaccessible,":[70],"informationally":[71],"impossible,":[72],"ontologically":[74],"excluded.":[75],"\u03c7\u2011flows":[76],"cannot":[77,82,87,91],"reach":[78],"\u03c7\u21920":[79],"or":[80],"\u03c7\u2192\u221e,":[81],"generate":[83],"unbounded":[84],"spectral":[85,124],"modes,":[86],"accumulate":[88],"\u03c7\u2011anomalies,":[89],"violate":[92],"constraints.":[94],"As":[95],"result,":[97],"not":[101,163],"conditional":[102],"but":[103],"necessary,":[104],"arising":[105],"from":[106],"structural":[108],"laws":[109],"\u03c7\u2011Reality":[111,224],"rather":[112],"than":[113],"analytic":[114],"estimates.":[115],"A":[116],"full":[117],"numerical":[118],"suite":[119],"demonstrates":[120],"reproducible":[121],"\u03c7\u2011collapse":[122],"dynamics,":[123],"stabilization,":[125],"anomaly":[126],"decay,":[127],"geodesic":[128],"confinement,":[129],"bounded":[131,169],"across":[133],"1D,":[134],"2D,":[135],"synthetic":[137],"scenarios.":[139],"These":[140],"experiments":[141],"constitute":[142],"computational":[145],"confirmation":[146],"unconditional":[148],"regularity.":[150,213],"The":[151],"metrics":[153],"introduced":[154],"here":[155],"show":[156],"that":[157],"turbulence":[158,175],"high\u2011information":[161],"\u03c7\u2011state,":[162],"singularity.":[165],"strictly":[168],"monotonically":[171],"decreasing,":[172],"resolving":[173],"paradox":[176],"establishing":[178],"new":[180],"informational":[181],"foundation":[182],"for":[183],"motion.":[185],"introduces":[188],"operator\u2013spectral\u2013informational":[191],"theory":[192],"fluids,":[194],"resolves":[195],"Millennium":[198],"Problem":[199],"at":[200],"level,":[203],"formulates":[205],"universal":[208],"physical":[209],"law":[210],"guaranteeing":[211],"It":[214],"defines":[215],"as":[218,225],"process":[221],"positions":[223],"fundamental":[227],"geometric\u2013spectral":[228],"structure":[229],"continuous":[231],"media.":[232]},"counts_by_year":[{"year":2026,"cited_by_count":26}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-08-28T00:00:00"}