{"id":"https://openalex.org/W7225794891","doi":"https://doi.org/10.5281/zenodo.24124197","title":"Multipole Vectors and the Area Statistic: How Often Random Skies Produce Octopole Planarity and Quadrupole-Octopole Vector Alignments","display_name":"Multipole Vectors and the Area Statistic: How Often Random Skies Produce Octopole Planarity and Quadrupole-Octopole Vector Alignments","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225794891","doi":"https://doi.org/10.5281/zenodo.24124197"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24124197","doi":"https://doi.org/10.5281/zenodo.24124197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24124197","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":"JournalArticle"},"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.24124197","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161362375","display_name":"William Alexander Aldred","orcid":"https://orcid.org/0009-0000-1215-577X","observed_orcids":["https://orcid.org/0009-0000-1215-577X"]},"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/A5161362375"],"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9932000041007996,"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/T10095","display_name":"Cosmology and Gravitation Theories","score":0.9932000041007996,"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/T11090","display_name":"Dark Matter and Cosmic Phenomena","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/T10026","display_name":"Galaxies: Formation, Evolution, Phenomena","score":0.00039999998989515007,"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/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.7132999897003174},{"id":"https://openalex.org/C52765159","wikidata":"https://www.wikidata.org/wiki/Q1027847","display_name":"Multipole expansion","level":2,"score":0.5123000144958496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49230000376701355},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.4465999901294708},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.41929998993873596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.41359999775886536},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.40459999442100525},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4016000032424927},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39590001106262207},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36820000410079956},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.3668999969959259},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C122048520","wikidata":"https://www.wikidata.org/wiki/Q2913954","display_name":"Percentile","level":2,"score":0.34850001335144043},{"id":"https://openalex.org/C138405894","wikidata":"https://www.wikidata.org/wiki/Q3179949","display_name":"Multivariate random variable","level":3,"score":0.3467999994754791},{"id":"https://openalex.org/C55769033","wikidata":"https://www.wikidata.org/wiki/Q7049018","display_name":"Non-sampling error","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C2776481522","wikidata":"https://www.wikidata.org/wiki/Q40218","display_name":"Orbiter","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.298799991607666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2766000032424927},{"id":"https://openalex.org/C141042865","wikidata":"https://www.wikidata.org/wiki/Q200125","display_name":"Expected value","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C73782692","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Random error","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C39984356","wikidata":"https://www.wikidata.org/wiki/Q2121987","display_name":"Quadrupole","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26269999146461487},{"id":"https://openalex.org/C2986587452","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical analysis","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24124197","doi":"https://doi.org/10.5281/zenodo.24124197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24124197","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":"JournalArticle"},{"id":"doi:10.5281/zenodo.24124198","doi":"https://doi.org/10.5281/zenodo.24124198","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24124198","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":"JournalArticle"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24124197","doi":"https://doi.org/10.5281/zenodo.24124197","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24124197","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":"JournalArticle"},"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":{"The":[0,97,165],"octopole":[1,60,163],"of":[2,73,88,115,133,155,159],"the":[3,27,30,46,50,59,76,80,105,122,131,139,146,149,160],"microwave":[4],"sky":[5],"is":[6,24,167],"described":[7],"as":[8,43,45],"planar,":[9],"its":[10,22],"multipole":[11],"vectors":[12,18],"clustered":[13],"so":[14],"that":[15],"their":[16,136],"area":[17,61,107],"nearly":[19],"coincide,":[20],"and":[21,67,91,104,118,135],"orientation":[23],"tied":[25],"to":[26],"quadrupole's":[28],"in":[29,75,84,93,111,151],"alignment":[31,62,120,141],"discussions.":[32],"This":[33],"paper":[34],"computes":[35],"how":[36],"often":[37],"isotropic":[38],"skies":[39,58],"produce":[40],"area-vector":[41],"statistics":[42,150],"extreme":[44],"values":[47],"quoted":[48],"for":[49,79],"real":[51,81],"sky.":[52],"In":[53],"two":[54],"hundred":[55],"thousand":[56],"random":[57,89,101],"statistic":[63],"has":[64],"mean":[65],"0.5":[66],"95th":[68],"percentile":[69],"0.821;":[70],"a":[71,100],"value":[72],"0.80,":[74],"range":[77],"reported":[78,123],"octopole,":[82],"occurs":[83],"6.18":[85],"per":[86,95,113],"cent":[87,114],"skies,":[90],"0.90":[92],"1.56":[94],"cent.":[96],"cross-alignment":[98],"between":[99,148],"quadrupole":[102],"axis":[103,140],"octopole's":[106],"directions":[108],"reaches":[109],"0.80":[110],"3.58":[112],"skies.":[116],"Planarity":[117],"vector":[119],"at":[121],"levels":[124],"are":[125,157],"therefore":[126],"uncommon":[127],"but":[128],"well":[129],"within":[130],"repertoire":[132],"chance,":[134],"conjunction":[137],"with":[138,145],"should":[142],"be":[143],"counted":[144],"dependence":[147],"view,":[152],"since":[153],"all":[154],"them":[156],"functions":[158],"same":[161],"seven":[162],"numbers.":[164],"study":[166],"simulated,":[168],"not":[169],"measured.":[170]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
