{"id":"https://openalex.org/W7225804850","doi":"https://doi.org/10.5281/zenodo.24125609","title":"Petals, Tubes and Rings: The Structure of the Four-Direction Orbit","display_name":"Petals, Tubes and Rings: The Structure of the Four-Direction Orbit","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225804850","doi":"https://doi.org/10.5281/zenodo.24125609"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24125609","doi":"https://doi.org/10.5281/zenodo.24125609","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24125609","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.24125609","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134618493","display_name":"Fedge No","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"No, Fedge","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5134618493"],"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.4717000126838684,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.4717000126838684,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11960","display_name":"Relativity and Gravitational Theory","score":0.20430000126361847,"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/T10523","display_name":"Atomic and Molecular Physics","score":0.13609999418258667,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.7378000020980835},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5932999849319458},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.43459999561309814},{"id":"https://openalex.org/C59108619","wikidata":"https://www.wikidata.org/wiki/Q2261398","display_name":"Circular orbit","level":2,"score":0.43380001187324524},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C90296322","wikidata":"https://www.wikidata.org/wiki/Q619776","display_name":"Concentric","level":2,"score":0.39340001344680786},{"id":"https://openalex.org/C136336744","wikidata":"https://www.wikidata.org/wiki/Q1133479","display_name":"Halo orbit","level":4,"score":0.38179999589920044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3781999945640564},{"id":"https://openalex.org/C190694206","wikidata":"https://www.wikidata.org/wiki/Q3276654","display_name":"Polygon (computer graphics)","level":3,"score":0.37720000743865967},{"id":"https://openalex.org/C74261601","wikidata":"https://www.wikidata.org/wiki/Q40112","display_name":"Ellipse","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C184481792","wikidata":"https://www.wikidata.org/wiki/Q1992087","display_name":"Heteroclinic orbit","level":5,"score":0.32179999351501465},{"id":"https://openalex.org/C44074806","wikidata":"https://www.wikidata.org/wiki/Q1066790","display_name":"Inscribed figure","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C148189969","wikidata":"https://www.wikidata.org/wiki/Q146657","display_name":"Great circle","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C173990265","wikidata":"https://www.wikidata.org/wiki/Q2268240","display_name":"Elliptic orbit","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25699999928474426}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24125609","doi":"https://doi.org/10.5281/zenodo.24125609","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24125609","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.24125610","doi":"https://doi.org/10.5281/zenodo.24125610","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24125610","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.24132763","doi":"https://doi.org/10.5281/zenodo.24132763","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24132763","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.24125609","doi":"https://doi.org/10.5281/zenodo.24125609","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24125609","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":{"The":[0,186],"electron's":[1],"orbit":[2,76,168,198],"runs":[3],"through":[4,180],"four":[5],"spatial":[6],"directions.":[7],"Its":[8,79],"path":[9,36],"has":[10,128,172],"an":[11,153,197],"exact":[12,154],"closed":[13],"form:":[14],"the":[15,25,75,83,97,100,106,113,118,122,126,144,150,158,167,181,206],"product":[16],"of":[17,33,40,48,62,85,96,108,169],"two":[18],"turning":[19,22],"directions,":[20],"one":[21,31,164],"once":[23],"while":[24],"other":[26],"turns":[27],"L":[28,70,146,173],"times.":[29],"In":[30],"plane":[32],"view":[34,102],"that":[35,131,160,170,192],"is":[37,45,56,77,112,147],"a":[38,46,53,57,63,86,91,133,202],"rose":[39],"petals,":[41],"in":[42,90,99],"another":[43],"it":[44,55],"set":[47,148],"nested":[49],"rings,":[50],"and":[51,93,136,156],"along":[52],"third":[54],"tube.":[58],"These":[59],"are":[60,82],"views":[61],"single":[64],"object.":[65],"For":[66],"every":[67],"whole":[68],"number":[69],"from":[71],"2":[72],"to":[73,205],"8":[74],"stable.":[78],"petal":[80,207],"tips":[81],"vertices":[84],"regular":[87],"polygon":[88],"inscribed":[89],"circle,":[92],"its":[94],"crossings":[95],"axis":[98],"end-on":[101],"lie":[103],"exactly":[104],"at":[105,157,163,201],"heights":[107],"those":[109],"vertices,":[110],"which":[111],"construction":[114],"chemists":[115],"know":[116],"as":[117],"Frost":[119],"circle.":[120],"Under":[121],"proton's":[123,187,193],"own":[124],"force":[125],"electron":[127],"stable":[129],"orbits":[130],"fill":[132],"hollow":[134],"tube":[135],"show":[137],"concentric":[138],"rings":[139],"when":[140],"time":[141],"averaged.":[142],"There":[143],"ratio":[145],"by":[149,152],"radius,":[151,166],"formula,":[155],"width":[159],"places":[161],"Lyman-\u03b3":[162],"Bohr":[165],"radius":[171],"=":[174],"2.998,":[175],"very":[176],"nearly":[177],"three":[178],"cycles":[179],"fourth":[182,194],"direction":[183],"per":[184],"revolution.":[185],"down":[188],"quark":[189],"singles":[190],"out":[191],"direction,":[195],"so":[196],"can":[199],"stand":[200],"right":[203],"angle":[204],"orbit.":[208]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}