{"id":"https://openalex.org/W7204520704","doi":"https://doi.org/10.5281/zenodo.22103438","title":"Exact Two-Branch Classification in a Prime-Square Divisor-Parametric Slice","display_name":"Exact Two-Branch Classification in a Prime-Square Divisor-Parametric Slice","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204520704","doi":"https://doi.org/10.5281/zenodo.22103438"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22103438","doi":"https://doi.org/10.5281/zenodo.22103438","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22103438","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22103438","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148523129","display_name":"Gropp","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gropp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148523129"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9965999722480774,"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":0.9965999722480774,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.002099999925121665,"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"}},{"id":"https://openalex.org/T14500","display_name":"Advanced Mathematical Theories","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/erdos-straus-conjecture","display_name":"Erd\u0151s\u2013Straus conjecture","score":0.8870000243186951},{"id":"https://openalex.org/keywords/congruence-classes","display_name":"congruence classes","score":0.4620000123977661},{"id":"https://openalex.org/keywords/admissibility-conditions","display_name":"admissibility conditions","score":0.6140000224113464},{"id":"https://openalex.org/keywords/egyptian-fractions","display_name":"Egyptian fractions","score":0.47999998927116394}],"concepts":[{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.9079999923706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6796000003814697},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48260000348091125},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4551999866962433},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4471000134944916},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.4417000114917755},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.42170000076293945},{"id":"https://openalex.org/C43169469","wikidata":"https://www.wikidata.org/wiki/Q580922","display_name":"Preprint","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C202887219","wikidata":"https://www.wikidata.org/wiki/Q3895221","display_name":"Parametrization (atmospheric modeling)","level":3,"score":0.37689998745918274},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33160001039505005},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.27320000529289246},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.26409998536109924},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22103438","doi":"https://doi.org/10.5281/zenodo.22103438","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22103438","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":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22103439","doi":"https://doi.org/10.5281/zenodo.22103439","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22103439","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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22103438","doi":"https://doi.org/10.5281/zenodo.22103438","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22103438","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":[],"sustainable_development_goals_aurora":[{"score":0.4204671382904053,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"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":{"This":[0],"non-peer-reviewed":[1],"preprint":[2],"studies":[3],"the":[4,11,117],"divisor":[5],"parametrization":[6],"of":[7,103,116],"theErdos-Straus":[8],"equation":[9],"in":[10],"fixed":[12],"slice":[13],"n":[14],"=":[15,18,29,34,38,48,52,90],"p^2,":[16],"a":[17,87,101,114],"p":[19,22],"for":[20],"primes":[21],"congruentto":[23],"1":[24],"modulo":[25,70,77],"4.":[26],"Writing":[27],"N":[28],"bp":[30],"+":[31],"1,":[32],"g":[33],"gcd(b,p),":[35],"and":[36,82,86,98,120],"M":[37,71],"4b/g,":[39],"every":[40],"divisorparameter":[41],"k":[42,47,51],"dividing":[43,56],"pN":[44],"is":[45,63,124],"uniquely":[46],"d":[49,55,73],"or":[50,72],"pd":[53],"with":[54,107],"N.":[57],"Themain":[58],"theorem":[59,94],"proves":[60],"that":[61],"admissibility":[62],"equivalent,":[64],"respectively,":[65],"tod":[66],"congruent":[67,74],"to":[68,75],"-p^2":[69],"-p":[76],"M.":[78],"The":[79,110],"paper":[80],"recordsp-adic":[81],"denominator-swap":[83],"orbit":[84],"corollaries":[85],"credited":[88],"b":[89],"2":[91],"application.The":[92],"main":[93],"was":[95],"independently":[96],"rederived":[97],"supported":[99],"by":[100],"computationalaudit":[102],"4,680,578":[104],"branch":[105],"certificates":[106],"zero":[108],"mismatches.":[109],"manuscriptdoes":[111],"not":[112],"claim":[113],"proof":[115],"Erdos-Straus":[118],"conjecture,":[119],"its":[121],"historicalpriority":[122],"language":[123],"explicitly":[125],"qualified.":[126]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-29T00:00:00"}
