{"id":"https://openalex.org/W7225835298","doi":"https://doi.org/10.5281/zenodo.24141443","title":"Lemoine's Conjecture in Quaternionic Eulerian Calculus: Odd Numbers, Prime Corners and the Line of Reflection","display_name":"Lemoine's Conjecture in Quaternionic Eulerian Calculus: Odd Numbers, Prime Corners and the Line of Reflection","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225835298","doi":"https://doi.org/10.5281/zenodo.24141443"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24141443","doi":"https://doi.org/10.5281/zenodo.24141443","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141443","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":null,"license_id":null,"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.24141443","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048615546","display_name":"Willie Johnson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Willie Johnson Jr.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048615546"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.00019999999494757503,"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"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.824999988079071},{"id":"https://openalex.org/C143732363","wikidata":"https://www.wikidata.org/wiki/Q485520","display_name":"Goldbach's conjecture","level":3,"score":0.7455000281333923},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6841999888420105},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6258999705314636},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.54830002784729},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5027999877929688},{"id":"https://openalex.org/C143352335","wikidata":"https://www.wikidata.org/wiki/Q110863","display_name":"Twin prime","level":3,"score":0.4575999975204468},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C11067248","wikidata":"https://www.wikidata.org/wiki/Q7243373","display_name":"Prime k-tuple","level":4,"score":0.4406999945640564},{"id":"https://openalex.org/C125605598","wikidata":"https://www.wikidata.org/wiki/Q306393","display_name":"abc conjecture","level":4,"score":0.39500001072883606},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.3849000036716461},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.3781000077724457},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.3449999988079071},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34119999408721924},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3165000081062317},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C2992444157","wikidata":"https://www.wikidata.org/wiki/Q775079","display_name":"Single point","level":3,"score":0.2944999933242798},{"id":"https://openalex.org/C128814272","wikidata":"https://www.wikidata.org/wiki/Q837314","display_name":"Collatz conjecture","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C9973445","wikidata":"https://www.wikidata.org/wiki/Q8349849","display_name":"Congruence relation","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.2590999901294708},{"id":"https://openalex.org/C163540240","wikidata":"https://www.wikidata.org/wiki/Q936614","display_name":"Almost prime","level":4,"score":0.2574999928474426}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24141443","doi":"https://doi.org/10.5281/zenodo.24141443","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141443","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.24141444","doi":"https://doi.org/10.5281/zenodo.24141444","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141444","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24141443","doi":"https://doi.org/10.5281/zenodo.24141443","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24141443","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":null,"license_id":null,"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":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Lemoine's":[0,109,168],"conjecture":[1,110,169,226],"states":[2],"that":[3,62,118,136],"every":[4,119,137,181,215],"odd":[5,74,120,182,216],"number":[6,44,75,97,121,183,217],"greater":[7],"than":[8],"5":[9,123],"is":[10,84,90,111,124,158,184,227],"\ud835\udc5d":[11,15],"+":[12,54,101,141],"2\ud835\udc5e":[13,98],"with":[14,164],"and":[16,40,72,175,203,224],"\ud835\udc5e":[17,83,100],"prime.":[18,154],"In":[19],"Quaternionic":[20],"Eulerian":[21],"Calculus":[22],"(QEC)":[23],"the":[24,28,36,47,57,64,69,77,86,95,116,134,171,177,193,196,198,201,204,212,225,230,236],"integers":[25],"stand":[26],"on":[27,133],"line":[29,139],"of":[30,60,66,68,106,161,188,195,200,214,233,235],"reflection":[31],"\ud835\udc66":[32],"=":[33,99,143],"\ud835\udc65":[34,140],"between":[35,79],"dual":[37],"curves":[38],"\ud835\udc52\u02e3":[39],"\ud835\udc52\u02b8:":[41],"each":[42,73],"even":[43,96,178],"2\ud835\udc5b":[45],"at":[46,76],"corner":[48,87],"(\ud835\udc5b,":[49],"\ud835\udc5b),":[50],"formed":[51],"as":[52],"\ud835\udc5b":[53,55],"under":[56],"inherent":[58],"slope":[59],"2":[61],"accompanies":[63],"area":[65],"two":[67,150,165],"1/\ud835\udc65":[70],"curve,":[71],"midpoint":[78],"consecutive":[80],"corners.":[81],"When":[82],"prime":[85,92,127,130],"(\ud835\udc5e,":[88],"\ud835\udc5e)":[89],"a":[91,129,147,159,186],"corner,":[93,131],"carrying":[94],"\ud835\udc5e,":[102],"an":[103,125],"equal":[104],"pair":[105],"FTOA":[107,126],"primes.":[108,190],"shown":[112],"to":[113,206,220],"be":[114],"exactly":[115],"statement":[117,180],"beyond":[122],"plus":[128],"and,":[132],"lattice,":[135],"Lemoine":[138],"2\ud835\udc66":[142],"\ud835\udc41":[144],"passes":[145],"through":[146],"point":[148],"whose":[149],"coordinates":[151],"are":[152,208,222,240],"both":[153],"Every":[155],"such":[156],"split":[157],"sum":[160,187],"three":[162,189],"primes":[163],"equal,":[166],"so":[167],"strengthens":[170],"ternary":[172],"Goldbach":[173,179,207],"theorem;":[174],"by":[176,229],"already":[185],"The":[191],"reduction,":[192],"parity":[194],"summands,":[197],"range":[199],"corners":[202],"relation":[205],"proved":[209],"in":[210],"full,":[211],"representations":[213],"from":[218],"7":[219],"43":[221],"tabulated,":[223],"completed":[228],"QEC":[231],"principle":[232],"inheritance":[234],"rule.":[237],"All":[238],"quantities":[239],"pure":[241],"numbers.":[242]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}
