{"id":"https://openalex.org/W7225562148","doi":"https://doi.org/10.5281/zenodo.24055105","title":"The JNL Framework: An Upgraded Map of the Syracuse Problem","display_name":"The JNL Framework: An Upgraded Map of the Syracuse Problem","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225562148","doi":"https://doi.org/10.5281/zenodo.24055105"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24055105","doi":"https://doi.org/10.5281/zenodo.24055105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055105","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.24055105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112835771","display_name":"Kevin White","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"White, Kevin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5112835771"],"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.413100004196167,"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"}},"topics":[{"id":"https://openalex.org/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.413100004196167,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.3582000136375427,"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/T11166","display_name":"Analytic Number Theory Research","score":0.17710000276565552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/collatz-conjecture","display_name":"Collatz conjecture","score":0.9929999709129333},{"id":"https://openalex.org/keywords/integer-sequences","display_name":"integer sequences","score":0.6650000214576721}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6021000146865845},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5378999710083008},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5218999981880188},{"id":"https://openalex.org/C65045869","wikidata":"https://www.wikidata.org/wiki/Q81365","display_name":"Decimal","level":2,"score":0.4982999861240387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4390999972820282},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39070001244544983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3896999955177307},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3831000030040741},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3580999970436096},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25279998779296875},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24055105","doi":"https://doi.org/10.5281/zenodo.24055105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055105","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.24055106","doi":"https://doi.org/10.5281/zenodo.24055106","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055106","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.24055105","doi":"https://doi.org/10.5281/zenodo.24055105","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055105","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":["https://openalex.org/W7167421165","https://openalex.org/W3203052559","https://openalex.org/W6912135955","https://openalex.org/W6893318791","https://openalex.org/W7105766800","https://openalex.org/W1901474581","https://openalex.org/W2762286780","https://openalex.org/W2341276918","https://openalex.org/W654119202","https://openalex.org/W6968618614"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,36,73,80,87,91,97],"unique":[4],"method":[5],"for":[6,100],"the":[7,13,23,28,42],"statistical":[8],"and":[9],"structural":[10],"analysis":[11],"of":[12],"3x":[14],"+":[15],"1":[16],"problem.":[17],"By":[18],"transforming":[19],"odd":[20],"integers":[21],"with":[22],"function":[24],"f(x)":[25],"=":[26],"(x+1)/4,":[27],"framework":[29],"organizes":[30],"all":[31],"positive":[32,68],"integer":[33,69],"sequences":[34,57,65,105],"into":[35,49],"single":[37],"linear":[38],"number":[39,104],"line":[40],"called":[41],"JNL":[43],"line.":[44],"The":[45],"system":[46],"sorts":[47],"values":[48],"distinct":[50],"groups":[51],"to":[52],"track":[53],"their":[54],"movement.":[55],"Group1":[56],"create":[58],"half-integer":[59],"decimal":[60],"drops,":[61],"while":[62],"Group":[63],"2":[64],"result":[66],"in":[67],"increases.":[70],"Rather":[71],"than":[72],"traditional":[74],"proof,":[75],"this":[76],"data-driven":[77],"approach":[78],"reveals":[79],"\u201cwavy":[81],"slide\u201d":[82],"pattern.":[83],"Every":[84],"path":[85],"follows":[86],"universal":[88],"trajectory":[89],"toward":[90],"unified":[92],"sink":[93],"at":[94],"0.5,":[95],"offering":[96],"clear":[98],"model":[99],"studying":[101],"how":[102],"these":[103],"behave.":[106]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}