{"id":"https://openalex.org/W7225346266","doi":"https://doi.org/10.5281/zenodo.23985056","title":"The Level That Was Never Returned: Kolmogorov's Similarity Hypotheses, Priced","display_name":"The Level That Was Never Returned: Kolmogorov's Similarity Hypotheses, Priced","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225346266","doi":"https://doi.org/10.5281/zenodo.23985056"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23985056","doi":"https://doi.org/10.5281/zenodo.23985056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23985056","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.23985056","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159396451","display_name":"William Alexander Aldred","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aldred, William Alexander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1215-577X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159396451"],"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9980000257492065,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.00039999998989515007,"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/T10251","display_name":"Solar and Space Plasma Dynamics","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/turbulence","display_name":"turbulent flow","score":0.42399999499320984},{"id":"https://openalex.org/keywords/inertial-range-scaling","display_name":"inertial range scaling","score":0.6809999942779541},{"id":"https://openalex.org/keywords/energy-spectrum","display_name":"energy spectrum","score":0.7900000214576721},{"id":"https://openalex.org/keywords/dissipation-rate","display_name":"dissipation rate","score":0.6669999957084656},{"id":"https://openalex.org/keywords/viscosity","display_name":"viscosity","score":0.5},{"id":"https://openalex.org/keywords/local-isotropy","display_name":"local isotropy","score":0.6740000247955322},{"id":"https://openalex.org/keywords/scaling-exponents","display_name":"scaling exponents","score":0.7519999742507935},{"id":"https://openalex.org/keywords/karman-howarth-equation","display_name":"Karman-Howarth equation","score":0.8320000171661377},{"id":"https://openalex.org/keywords/direct-numerical-simulation-of-turbulence","display_name":"direct numerical simulation of turbulence","score":0.7129999995231628},{"id":"https://openalex.org/keywords/high-reynolds-number-turbulence","display_name":"high Reynolds number turbulence","score":0.5879999995231628},{"id":"https://openalex.org/keywords/microscale","display_name":"microscale","score":0.5270000100135803}],"concepts":[{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.7110999822616577},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5800999999046326},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5644000172615051},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.5573999881744385},{"id":"https://openalex.org/C52130261","wikidata":"https://www.wikidata.org/wiki/Q39825","display_name":"Census","level":3,"score":0.5570999979972839},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.462799996137619},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4336000084877014},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4334000051021576},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.41019999980926514},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.40380001068115234},{"id":"https://openalex.org/C165743212","wikidata":"https://www.wikidata.org/wiki/Q104555","display_name":"Ruler","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C2777146004","wikidata":"https://www.wikidata.org/wiki/Q14949826","display_name":"CLARITY","level":2,"score":0.31119999289512634},{"id":"https://openalex.org/C143271835","wikidata":"https://www.wikidata.org/wiki/Q254515","display_name":"Similitude","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2815000116825104},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2687000036239624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2515000104904175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25060001015663147}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.23985056","doi":"https://doi.org/10.5281/zenodo.23985056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23985056","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.23985057","doi":"https://doi.org/10.5281/zenodo.23985057","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23985057","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.24034984","doi":"https://doi.org/10.5281/zenodo.24034984","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24034984","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.23985056","doi":"https://doi.org/10.5281/zenodo.23985056","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23985056","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/W7225227826","https://openalex.org/W2001160701","https://openalex.org/W2138522572","https://openalex.org/W2010393018","https://openalex.org/W2129264076","https://openalex.org/W3211911917","https://openalex.org/W1978936892","https://openalex.org/W1966745894","https://openalex.org/W1991405960","https://openalex.org/W2912585617"],"abstract_inverted_index":{"A":[0],"ruler":[1],"can":[2],"be":[3],"true":[4],"in":[5,36,45,133,142,149],"every":[6,124,185],"ratio":[7,92,161],"and":[8,25,55,115,126,258],"still":[9],"never":[10],"tell":[11],"you":[12],"how":[13],"long":[14],"anything":[15],"is.":[16],"Kolmogorov's":[17],"1941":[18],"theory":[19,44],"of":[20,67,233],"turbulence":[21],"is":[22,27,101,139],"that":[23,163],"ruler,":[24],"it":[26],"also":[28],"\u2014":[29,39,112,121,156,216,253],"I":[30,99],"credit":[31],"this":[32,37,241],"at":[33,91,184,191,196,201,206,245],"full":[34,246],"strength":[35],"paper":[38],"the":[40,52,56,63,70,72,79,103,143,150,167,173,182,211,217,226,230],"most":[41],"successful":[42],"scaling":[43],"classical":[46],"physics.":[47],"From":[48],"two":[49],"declared":[50,213],"inputs,":[51],"viscosity":[53],"\u03bd":[54],"mean":[57],"dissipation":[58],"\u03b5,":[59],"its":[60],"hypotheses":[61,104,111,168,227],"organise":[62],"entire":[64],"small-scale":[65],"structure":[66],"high-Reynolds-number":[68],"turbulence:":[69],"microscales,":[71],"inertial-range":[73],"spectrum":[74],"E(k)":[75,134],"\u221d":[76],"\u03b5^(2/3)":[77,137],"k^(\u22125/3),":[78,138],"scale":[80],"separation":[81],"(L/\u03b7)":[82],"=":[83,96,135,178,193,198,203,208,221],"Re^(3/4),":[84],"which":[85,122],"my":[86,153],"bench":[87],"verifies":[88],"reads":[89],"back":[90],"1.000000":[93],"across":[94],"Re":[95],"10\u2074\u201310\u2078.":[97],"What":[98],"evaluate":[100],"what":[102],"are:":[105],"premises":[106],"their":[107],"author":[108],"named":[109],"as":[110],"local":[113],"isotropy,":[114],"unique":[116],"determination":[117],"by":[118],"(\u03bd,":[119],"\u03b5)":[120],"return":[123],"exponent":[125,174],"no":[127,164],"level.":[128],"The":[129,262],"spectrum's":[130],"constant,":[131],"C":[132,136],"fitted:":[140],"\u22481.5":[141],"standard":[144],"record,":[145],"1.68":[146],"\u00b1":[147],"0.15":[148],"direct-simulation":[151],"record":[152,183,214],"census":[154,242],"carries":[155],"a":[157,256,260],"12%":[158],"band":[159],"(bench":[160],"1.120000)":[162],"argument":[165],"from":[166],"has":[169],"ever":[170],"computed.":[171],"And":[172],"family":[175],"itself,":[176],"\u03b6_p":[177],"p/3,":[179],"fails":[180],"against":[181],"order":[186],"except":[187],"one:":[188],"deviations":[189],"+0.029333":[190],"p":[192,197,202,207,220],"2,":[194],"\u22120.053333":[195],"4,":[199],"\u22120.220000":[200],"6,":[204],"\u22120.466667":[205],"8":[209],"on":[210],"bench's":[212],"inputs":[215],"sole":[218],"agreement,":[219],"3,":[222],"belonging":[223],"not":[224,255,259],"to":[225,229],"but":[228],"K\u00e1rm\u00e1n\u2013Howarth":[231],"derivation":[232],"1938,":[234],"three":[235],"years":[236],"before":[237],"them.":[238],"Grade":[239],"for":[240],"entry,":[243],"printed":[244],"size:":[247],"REASON":[248],"FOUND":[249],"/":[250,271],"STILL":[251],"TURNING":[252],"explicitly":[254],"kill":[257],"falsification.":[261],"program":[263],"headline":[264],"stands":[265],"unmoved:":[266],"vacuum":[267],"catastrophe":[268],"NOT":[269],"SOLVED":[270],"PARTIAL,":[272],"producing-count":[273],"0.":[274]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-06T00:00:00"}
