{"id":"https://openalex.org/W7225449641","doi":"https://doi.org/10.5281/zenodo.24032040","title":"Momentum helicity separates triad-local cascade operators from Euler\u2013Arnold operators","display_name":"Momentum helicity separates triad-local cascade operators from Euler\u2013Arnold operators","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225449641","doi":"https://doi.org/10.5281/zenodo.24032040"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24032040","doi":"https://doi.org/10.5281/zenodo.24032040","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24032040","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.24032040","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133620074","display_name":"Adilkhan Salkimbayev","orcid":"https://orcid.org/0009-0003-9763-0294","observed_orcids":["https://orcid.org/0009-0003-9763-0294"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Salkimbayev, Adilkhan","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0003-9763-0294","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5133620074"],"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":0.888700008392334,"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":0.888700008392334,"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":0.060600001364946365,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.008899999782443047,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.607200026512146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5206999778747559},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C134440745","wikidata":"https://www.wikidata.org/wiki/Q1186765","display_name":"Ladder operator","level":4,"score":0.48649999499320984},{"id":"https://openalex.org/C73052347","wikidata":"https://www.wikidata.org/wiki/Q5282616","display_name":"Displacement operator","level":5,"score":0.4722999930381775},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4300000071525574},{"id":"https://openalex.org/C19579662","wikidata":"https://www.wikidata.org/wiki/Q461145","display_name":"Energy operator","level":3,"score":0.42969998717308044},{"id":"https://openalex.org/C162475051","wikidata":"https://www.wikidata.org/wiki/Q692457","display_name":"Momentum operator","level":5,"score":0.39660000801086426},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3427000045776367},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3172000050544739},{"id":"https://openalex.org/C68386474","wikidata":"https://www.wikidata.org/wiki/Q980557","display_name":"Operator norm","level":3,"score":0.3091000020503998},{"id":"https://openalex.org/C2775859700","wikidata":"https://www.wikidata.org/wiki/Q568855","display_name":"Helicity","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C158650840","wikidata":"https://www.wikidata.org/wiki/Q907439","display_name":"Dirac operator","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C150454350","wikidata":"https://www.wikidata.org/wiki/Q1190143","display_name":"Angular momentum operator","level":5,"score":0.28110000491142273},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.2809000015258789},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27889999747276306},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2709999978542328},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.27059999108314514},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.26100000739097595},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2535000145435333}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24032040","doi":"https://doi.org/10.5281/zenodo.24032040","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24032040","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.24032041","doi":"https://doi.org/10.5281/zenodo.24032041","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24032041","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.24032040","doi":"https://doi.org/10.5281/zenodo.24032040","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24032040","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":[],"abstract_inverted_index":{"Tao's":[0,44,211],"averaged":[1],"Navier\u2013Stokes":[2],"equation":[3],"replaces":[4],"the":[5,14,32,36,50,62,71,112,121,141,149,184,193,220,226,243,265],"Euler":[6],"nonlinearity":[7],"by":[8,91],"a":[9,39,57,87,127,152,161],"cascade":[10,59,163,205],"operator":[11,42,60,117,164,174],"that":[12,108],"keeps":[13],"energy":[15],"identity":[16],"and":[17,65,159,225,238],"blows":[18],"up.":[19],"We":[20,180],"ask":[21],"whether":[22],"such":[23],"operators":[24,45,199,206],"can":[25],"be":[26],"Euler\u2013Arnold":[27,93,173],"operators:":[28],"geodesic":[29],"nonlinearities":[30],"on":[31,140],"divergence-free":[33],"fields":[34],"of":[35,115,136,156,264],"torus":[37],"for":[38,102,109,175],"translation-invariant":[40,178],"inertia":[41,198],"A.":[43,179],"are":[46,200],"not":[47,171,201],"translation-covariant,":[48],"so":[49],"meaningful":[51],"case":[52],"is":[53,86,118,170,214],"their":[54],"translation":[55],"average,":[56],"triad-local":[58,162],"with":[61,80,165,251],"same":[63],"species":[64,169],"structure":[66,157],"constants.":[67],"Energy":[68],"cannot":[69],"separate":[70],"two":[72],"classes.":[73],"The":[74,187,217,230,246],"momentum":[75],"helicity":[76,113],"\u222b":[77],"m\u00b7curl":[78],"m,":[79],"m":[81],"=":[82,99],"Au,":[83],"can:":[84],"it":[85],"Lie\u2013Poisson":[88],"Casimir,":[89],"conserved":[90],"every":[92],"flow.":[94],"Using":[95],"S":[96,98],"J":[97,101],"det(S)":[100],"symmetric":[103],"2\u00d72":[104],"matrices,":[105],"we":[106],"show":[107],"reflection-even":[110,177],"A":[111,190],"production":[114],"any":[116,176],"linear":[119],"in":[120,210,240,261],"numbers":[122],"sqrt(det":[123],"A_k).":[124],"This":[125],"gives":[126],"rank":[128],"criterion.":[129],"An":[130],"exact":[131,227],"integer":[132],"certificate":[133,228,231],"(rank":[134],"16":[135,137],"over":[138],"Q":[139],"lattice":[142],"0":[143],"<":[144],"|k|\u00b2":[145],"\u2264":[146],"4)":[147],"proves":[148],"following.":[150],"Outside":[151],"proper":[153],"real-algebraic":[154],"set":[155],"constants":[158],"profiles,":[160],"at":[166],"least":[167],"four":[168],"an":[172],"also":[181],"record":[182,218],"where":[183],"method":[185],"stops.":[186],"Casimir":[188],"sees":[189],"only":[191,237],"through":[192],"vector":[194],"(sqrt(det":[195],"A_k)).":[196],"Parity-odd":[197],"covered.":[202],"Whether":[203],"helicity-conserving":[204],"exist,":[207],"as":[208,259],"suggested":[209],"Remark":[212],"4.3,":[213],"left":[215],"open.":[216],"contains":[219],"paper,":[221],"its":[222],"LaTeX":[223],"source,":[224],"(helicity_separator_certificate.zip).":[229],"uses":[232],"Python":[233],"3":[234],"standard":[235],"library":[236],"runs":[239],"seconds;":[241],"see":[242],"README":[244],"inside.":[245],"work":[247],"was":[248],"carried":[249],"out":[250],"substantial":[252],"help":[253],"from":[254],"generative":[255],"AI":[256],"(Anthropic's":[257],"Claude),":[258],"documented":[260],"Section":[262],"1.5":[263],"paper.":[266]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-08T00:00:00"}
