{"id":"https://openalex.org/W7225709366","doi":"https://doi.org/10.5281/zenodo.24107686","title":"UDCT v7.14-TN01: Phase-Space Admissibility Audit (p=1.5, r_a/a\u22480.4665)","display_name":"UDCT v7.14-TN01: Phase-Space Admissibility Audit (p=1.5, r_a/a\u22480.4665)","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225709366","doi":"https://doi.org/10.5281/zenodo.24107686"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24107686","doi":"https://doi.org/10.5281/zenodo.24107686","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24107686","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":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24107686","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137602421","display_name":"Won Shik Paik","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paik, Won Shik","raw_affiliation_strings":["Independent Researcher, Auckland, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, Auckland, New Zealand","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5137602421"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.6273999810218811,"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"}},"topics":[{"id":"https://openalex.org/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.6273999810218811,"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"}},{"id":"https://openalex.org/T10095","display_name":"Cosmology and Gravitation Theories","score":0.14970000088214874,"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"}},{"id":"https://openalex.org/T10039","display_name":"Stellar, planetary, and galactic studies","score":0.12389999628067017,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.625},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.5347999930381775},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.4772000014781952},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.45399999618530273},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.44369998574256897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41850000619888306},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3806999921798706},{"id":"https://openalex.org/C150172559","wikidata":"https://www.wikidata.org/wiki/Q6126499","display_name":"Principal value","level":2,"score":0.3804999887943268},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37290000915527344},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.33649998903274536},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.2653999924659729},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24107686","doi":"https://doi.org/10.5281/zenodo.24107686","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24107686","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":"article-journal"},{"id":"doi:10.5281/zenodo.24107687","doi":"https://doi.org/10.5281/zenodo.24107687","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24107687","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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24107686","doi":"https://doi.org/10.5281/zenodo.24107686","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24107686","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":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W7223662914","https://openalex.org/W7225716874"],"related_works":[],"abstract_inverted_index":{"Overview":[0],"UDCT":[1,22,571],"v7.14-TN01:":[2],"Phase-Space":[3],"Admissibility":[4],"Audit":[5],"(p=1.5,":[6],"r_a/a\u22480.4665)":[7],"This":[8,93,176,224,413],"independent":[9,407],"technical":[10,320,423],"note":[11,39,321,414],"provides":[12,376],"a":[13,71,81,95,153,212,232,264,270,308,389,420,427,546,583,588,591],"retrospective,":[14],"source-grounded":[15],"examination":[16],"of":[17,34,83,101,181,189,303,409,490,590],"exploratory":[18,55,77,422,580],"results":[19],"developed":[20],"during":[21],"v7.14,":[23],"focusing":[24],"on":[25],"phase-space":[26,238,492],"consistency,":[27,327],"gravitational-field":[28],"diagnostics,":[29,325],"and":[30,48,57,115,119,228,241,316,330,358,365,379,447,459,477,502,524,534,563],"the":[31,52,76,84,102,107,123,130,141,146,168,178,182,187,190,203,208,249,255,260,275,300,304,340,384,394,439,466,488],"physical":[32,301,457],"admissibility":[33,315,493],"specified":[35,72,124,204,341],"equilibrium":[36,342,529],"models.":[37,462],"The":[38,99,244,280,319,360,527],"consolidates":[40],"mathematical":[41,97,120,179,242,440],"interpretations,":[42],"numerical":[43,209,278,561],"boundary":[44,197],"conditions,":[45],"reproducibility":[46,402],"considerations,":[47],"limitations":[49],"arising":[50],"from":[51],"earlier":[53],"50-step":[54],"program":[56],"subsequent":[58],"audits.":[59],"Principal":[60],"Findings":[61],"1.":[62],"Central":[63],"asymptotic":[64,78,556],"cancellation":[65,82,184],"at":[66,89,106],"p":[67,90,161,221,444,531],"=":[68,91,158,162,165,200,218,222,445,532],"1.5":[69,446,533],"Within":[70,122],"isolated":[73,125],"spherical":[74,126,367,528],"model,":[75,129],"analysis":[79,114,210,386,467],"identifies":[80,211],"leading":[85,169],"distribution-function":[86,171,267,328,368,559],"inversion":[87,172],"coefficient":[88,173],"1.5.":[92,223],"is":[94,134,226,284,295,387],"conditional":[96],"result.":[98],"sign":[100,188],"complete":[103,191,395],"distribution":[104,192,335],"function":[105,336],"equality":[108],"case":[109],"remains":[110],"unresolved":[111],"without":[112,185],"higher-order":[113,555],"full-domain":[116],"verification.":[117],"Physical":[118,240,314],"interpretation:":[121,243],"QUMOND-inspired":[127],"Plummer":[128],"generalized":[131],"tracer-density":[132,154],"family":[133],"\u03c1\u209a(r)":[135],"\u221d":[136],"[1":[137],"+":[138],"(r/a)\u1d56]\u207b\u2075/\u1d56.":[139],"Under":[140,202],"adopted":[142],"central":[143],"deep-MOND":[144],"asymptotics,":[145],"potential":[147],"difference":[148],"scales":[149],"as":[150,287,419],"r\u00b3\u141f\u00b2,":[151],"giving":[152],"expansion":[155],"exponent":[156],"s":[157,164],"2p/3.":[159],"At":[160,259],"1.5,":[163],"1,":[166],"causing":[167],"singular":[170],"to":[174,254,393,495,542,545],"vanish.":[175],"explains":[177],"origin":[180],"identified":[183],"establishing":[186],"function.":[193],"2.":[194],"Local":[195],"anisotropy":[196,206,234,251,473],"near":[198,216],"r_a/a":[199,217,247,292,448,535],"0.4665":[201,294,450,537],"Osipkov\u2013Merritt":[205,250],"prescription,":[207],"local":[213,271],"finite-window":[214],"tangency":[215,282,305],"0.466466787396":[219],"for":[220],"value":[225],"model-dependent":[227],"does":[229,345],"not":[230,299,346,388,405,539,582],"establish":[231],"universal":[233,593],"threshold":[235],"or":[236,307,352,453,587],"global":[237],"positivity.":[239],"dimensionless":[245],"quantity":[246],"represents":[248],"radius":[252,302],"relative":[253],"model":[256,317,381],"scale":[257],"radius.":[258],"reported":[261,286],"critical":[262],"value,":[263],"sampled":[265],"negative":[266,334],"region":[268],"reaches":[269],"zero-contact":[272],"condition":[273],"within":[274],"prescribed":[276],"finite":[277],"window.":[279],"corresponding":[281,491],"coordinate":[283],"separately":[285],"r/a":[288],"\u2248":[289,293,449,536],"0.47409755.":[290],"Thus,":[291],"an":[296],"anisotropy-parameter":[297],"boundary,":[298],"point":[306],"globally":[309],"established":[310],"positivity":[311],"threshold.":[312],"3.":[313],"consistency":[318,510],"distinguishes":[322],"gravitational":[323,500,594],"Hessian":[324,363],"Jeans-equation":[326],"non-negativity,":[329],"dynamical":[331],"stability.":[332],"A":[333],"indicates":[337],"inconsistency":[338],"under":[339,455],"assumptions;":[343],"it":[344],"independently":[347,564],"falsify":[348],"MOND,":[349],"QUMOND,":[350],"GQUMOND,":[351],"modified":[353],"gravity":[354],"generally.":[355],"Scientific":[356],"Scope":[357],"Limitations":[359],"early":[361],"three-dimensional":[362],"investigations":[364],"later":[366],"calculations":[369],"are":[370],"separate":[371],"computational":[372,411],"branches.":[373],"Hydrus":[374,463],"I":[375],"observational":[377,429],"motivation":[378],"selected":[380],"inputs,":[382],"but":[383],"present":[385],"direct":[390,478],"likelihood":[391],"fit":[392],"individual-star":[396],"line-of-sight":[397],"velocity":[398],"dataset.":[399],"Previously":[400],"archived":[401],"checks":[403],"do":[404],"constitute":[406],"verification":[408],"every":[410],"step.":[412],"should":[415],"therefore":[416],"be":[417,513,540],"interpreted":[418],"retrospective":[421],"audit":[424],"rather":[425],"than":[426],"peer-reviewed":[428],"validation.":[430],"Future":[431,434],"Research":[432,568],"Directions":[433],"work":[435,551],"will":[436,538,552],"investigate":[437],"whether":[438,508],"mechanisms":[441],"associated":[442],"with":[443,480],"persist,":[451],"shift,":[452],"disappear":[454],"alternative":[456],"assumptions":[458],"observationally":[460,469],"constrained":[461,470],"I:":[464],"Extend":[465],"toward":[468],"stellar-density":[471],"profiles,":[472,499],"models,":[474],"external-field":[475],"effects,":[476],"comparisons":[479],"individual":[481],"stellar":[482],"velocities.":[483],"Other":[484],"dwarf":[485],"galaxies:":[486],"Test":[487],"sensitivity":[489],"boundaries":[494],"galaxy":[496,548],"structure,":[497],"tracer":[498],"potentials,":[501],"environmental":[503],"conditions.":[504],"Bullet":[505],"Cluster:":[506],"Investigate":[507],"analogous":[509],"constraints":[511],"can":[512],"formulated":[514],"in":[515],"three-dimensional,":[516],"non-equilibrium":[517],"cluster":[518],"dynamics,":[519],"including":[520],"evolving":[521],"mass":[522],"distributions":[523],"gravitational-lensing":[525],"comparisons.":[526],"values":[530],"assumed":[541],"transfer":[543],"directly":[544],"colliding":[547],"cluster.":[549],"Further":[550],"also":[553],"address":[554],"terms,":[557],"full-energy-domain":[558],"positivity,":[560],"convergence,":[562],"reproducible":[565],"confirmatory":[566,585],"tests.":[567],"Status":[569],"Version:":[570],"v7.14-TN01":[572],"Document":[573],"type:":[574],"Independent":[575,601],"Technical":[576],"Note":[577],"Status:":[578],"Retrospective":[579],"audit;":[581],"preregistered":[584],"result":[586],"claim":[589],"new":[592],"theory.":[595],"Author:":[596],"Won":[597],"Shik":[598],"Paik":[599],"\u2014":[600],"Researcher,":[602],"Auckland,":[603],"New":[604],"Zealand":[605],"Zenodo":[606],"DOI:":[607],"https://doi.org/10.5281/zenodo.24107687":[608],"GitHub":[609],"repository:":[610],"https://github.com/wspaik5/UDCT_v7.14_TN01_Phase_Space_Admissibility_Audit":[611]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-11T00:00:00"}
