{"id":"https://openalex.org/W7225568000","doi":"https://doi.org/10.5281/zenodo.24056588","title":"The Fifth Coordinate \u2014 the \u0398/\u03b8 Dictionary","display_name":"The Fifth Coordinate \u2014 the \u0398/\u03b8 Dictionary","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225568000","doi":"https://doi.org/10.5281/zenodo.24056588"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24056588","doi":"https://doi.org/10.5281/zenodo.24056588","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056588","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.24056588","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":1,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.4733999967575073,"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.4733999967575073,"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":0.3589000105857849,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.05079999938607216,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/circle-bundles","display_name":"circle bundles","score":0.5709999799728394},{"id":"https://openalex.org/keywords/phase-field-model","display_name":"phase-field model","score":0.6129999756813049},{"id":"https://openalex.org/keywords/winding-number","display_name":"winding number","score":0.828000009059906},{"id":"https://openalex.org/keywords/stokes-theorem","display_name":"Stokes' theorem","score":0.8220000267028809}],"concepts":[{"id":"https://openalex.org/C32518243","wikidata":"https://www.wikidata.org/wiki/Q907926","display_name":"Holonomy","level":2,"score":0.5680999755859375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5113999843597412},{"id":"https://openalex.org/C39777019","wikidata":"https://www.wikidata.org/wiki/Q3505263","display_name":"Worldsheet","level":4,"score":0.4406000077724457},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36489999294281006},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.35510000586509705},{"id":"https://openalex.org/C2780317896","wikidata":"https://www.wikidata.org/wiki/Q2703","display_name":"Epoch (astronomy)","level":3,"score":0.349700003862381},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32499998807907104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24056588","doi":"https://doi.org/10.5281/zenodo.24056588","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056588","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.24056589","doi":"https://doi.org/10.5281/zenodo.24056589","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056589","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.24056588","doi":"https://doi.org/10.5281/zenodo.24056588","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24056588","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":5,"referenced_works":["https://openalex.org/W7225450109","https://openalex.org/W7225452767","https://openalex.org/W7225461202","https://openalex.org/W7225465328","https://openalex.org/W7225574106"],"related_works":["https://openalex.org/W7225574106","https://openalex.org/W7225593125","https://openalex.org/W7207863280","https://openalex.org/W7153819998","https://openalex.org/W7117414433","https://openalex.org/W7115021555","https://openalex.org/W4233844687","https://openalex.org/W7161539991","https://openalex.org/W7108223249","https://openalex.org/W7080833697"],"abstract_inverted_index":{"Derivation":[0],"note,":[1],"R&D":[2],"Division,":[3],"November":[4],"8,":[5,17],"2026.":[6],"Successor":[7],"to":[8],"'The":[9],"Fifth":[10],"Coordinate":[11],"\u2014":[12,24,39,147,252],"the":[13,25,42,45,54,58,68,82,107,124,129,132,136,144,151,154,158,162,169,172,180,185,195,200,210,231,237,255,261,280,284,298],"Bundle":[14],"Construction'":[15],"(November":[16],"2026),":[18],"which":[19],"proved":[20],"a":[21,62,80,234,274],"uniqueness":[22],"count":[23],"corpus":[26,83],"owns":[27],"exactly":[28],"one":[29,32,36,206],"phase":[30,55],"field,":[31],"seated":[33],"twist,":[34],"and":[35,40,53,99,112,143,194,202,242,287],"circle":[37],"bundle":[38],"sharpened":[41],"dictionary":[43,289],"between":[44,140,161],"lineage":[46,173],"twist":[47],"\u0398":[48,66,77,93,118,198],"of":[49,57,128,131,135,153,168,205],"Bounce":[50,96],"Theory":[51,97],"II/III":[52],"\u03b8":[56,102],"torsion":[59,137],"sector":[60],"into":[61],"forced":[63],"fork:":[64],"either":[65],"is":[67,123,171,184,209,214,228,257],"bundle's":[69],"axial":[70,133],"holonomy":[71,134,170],"read":[72],"at":[73,119],"slice":[74],"scale,":[75],"or":[76],"lives":[78],"in":[79,95,104,218,297],"structure":[81],"has":[84],"not":[85,220],"yet":[86],"written.":[87],"This":[88],"note":[89,245],"extracts":[90],"every":[91,100],"load-bearing":[92,101],"statement":[94,103],"I\u2013III":[98],"FRONT-A,":[105],"tests":[106],"first":[108],"horn":[109],"against":[110],"each,":[111],"finds":[113],"no":[114],"contradiction.":[115],"The":[116,165,190,212,225,247],"dictionary:":[117],"an":[120,223,271],"epoch":[121,142,146,188],"hypersurface":[122],"signed":[125],"principal":[126],"value":[127,226],"difference":[130],"connection":[138],"S":[139],"that":[141,277],"home":[145],"by":[148],"Stokes'":[149],"theorem,":[150],"flux":[152],"connection's":[155],"curvature":[156],"through":[157],"axis":[159],"worldsheet":[160,238],"two":[163],"epochs.":[164],"integer":[166],"part":[167],"winding":[174],"number":[175],"(constant,":[176],"invisible":[177],"mod":[178],"2\u03c0);":[179],"reported":[181],"small":[182],"angle":[183],"fractional":[186],"part's":[187],"difference.":[189],"craft-scale":[191],"reading":[192,197],"\u03c7":[193],"slice-scale":[196],"are":[199,267,305],"open-path":[201],"closed-loop":[203],"readings":[204],"field;":[207],"neither":[208],"other.":[211],"identification":[213],"graded":[215],"CONSTRAINED":[216,251],"(unique":[217],"form;":[219],"derived":[221],"from":[222,294],"action).":[224],"\u0398(recombination)":[227],"NOT":[229,307],"DERIVED:":[230],"frame":[232],"owes":[233],"law":[235],"for":[236],"flux,":[239],"whose":[240],"integrand":[241],"surface":[243],"this":[244,288],"names.":[246],"fifth":[248],"coordinate":[249],"remains":[250],"charge":[253,259],"(iii),":[254],"dictionary,":[256],"discharged;":[258],"(ii),":[260],"readout,":[262],"stands":[263],"open.":[264],"Three":[265],"falsifiers":[266],"printed":[268],"(F-D1\u2013F-D3),":[269],"including":[270],"empirical":[272],"one:":[273],"measured":[275],"rotation":[276],"accumulates":[278],"along":[279],"trip":[281],"would":[282],"kill":[283],"boundary-difference":[285],"form":[286],"with":[290],"it.":[291],"Quantities":[292],"drawn":[293],"simulation":[295],"budgets":[296],"parent":[299],"notes":[300],"(\u03c3_\u03c7":[301],"\u2264":[302],"0.0667":[303],"rad)":[304],"SIMULATED,":[306],"MEASURED.":[308]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
