{"id":"https://openalex.org/W7143343046","doi":"https://doi.org/10.5281/zenodo.19326063","title":"The \"Duality\" Hidden in Numbers: Numbers are both \"Quantity\" and \"Wave\"","display_name":"The \"Duality\" Hidden in Numbers: Numbers are both \"Quantity\" and \"Wave\"","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7143343046","doi":"https://doi.org/10.5281/zenodo.19326063"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.19326063","doi":"https://doi.org/10.5281/zenodo.19326063","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19326063","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.19326063","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130719835","display_name":"Shinya Iida","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I149737473","display_name":"Seirei Christopher University","ror":"https://ror.org/02cd6sx47","country_code":"JP","type":"education","lineage":["https://openalex.org/I149737473"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Iida, Shinya","raw_affiliation_strings":["Seirei Christopher University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seirei Christopher University","institution_ids":["https://openalex.org/I149737473"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5130719835"],"corresponding_institution_ids":["https://openalex.org/I149737473"],"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":0.7109000086784363,"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":0.7109000086784363,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.27730000019073486,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.004699999932199717,"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/prime-numbers","display_name":"prime numbers","score":0.9539999961853027},{"id":"https://openalex.org/keywords/prime-number-distribution","display_name":"prime number distribution","score":0.44999998807907104},{"id":"https://openalex.org/keywords/wave-interference","display_name":"wave interference","score":0.6830000281333923},{"id":"https://openalex.org/keywords/composite-numbers","display_name":"composite numbers","score":0.5360000133514404},{"id":"https://openalex.org/keywords/number-theory","display_name":"number theory","score":0.37599998712539673},{"id":"https://openalex.org/keywords/phase-locking","display_name":"phase locking","score":0.3790000081062317},{"id":"https://openalex.org/keywords/imaginary-dimension","display_name":"imaginary dimension","score":0.5609999895095825},{"id":"https://openalex.org/keywords/transition-state","display_name":"transition state","score":0.5630000233650208}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.6934999823570251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6567000150680542},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6269999742507935},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6191999912261963},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.5188999772071838},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.4844000041484833},{"id":"https://openalex.org/C207673951","wikidata":"https://www.wikidata.org/wiki/Q1303150","display_name":"Compounding","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.41909998655319214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39969998598098755},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.3783999979496002},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.3361000120639801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3222000002861023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2955999970436096},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2741999924182892},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2621000111103058}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.19326063","doi":"https://doi.org/10.5281/zenodo.19326063","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19326063","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.19326064","doi":"https://doi.org/10.5281/zenodo.19326064","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19326064","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.19326063","doi":"https://doi.org/10.5281/zenodo.19326063","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.19326063","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":0,"referenced_works":[],"related_works":["https://openalex.org/W7162617776","https://openalex.org/W7149331466","https://openalex.org/W7149623132","https://openalex.org/W7165554229","https://openalex.org/W6930695682","https://openalex.org/W7094948948","https://openalex.org/W7106227401","https://openalex.org/W6968149858","https://openalex.org/W7104282990","https://openalex.org/W6912055199"],"abstract_inverted_index":{"This":[0,74],"paper":[1],"proposes":[2],"a":[3,28,77,100],"fundamental":[4,29],"redefinition":[5],"of":[6,18,83,90,96],"integers,":[7],"shifting":[8],"the":[9,15,36,71,81,88],"paradigm":[10],"from":[11],"discrete":[12],"units":[13],"to":[14],"emergent":[16],"results":[17],"continuous":[19],"wave":[20],"interference.":[21],"By":[22],"conceptualizing":[23],"each":[24],"prime":[25,52,55],"p":[26],"as":[27,64],"frequency":[30],"(a":[31],"\"prime":[32],"wave\"),":[33],"we":[34],"elucidate":[35],"mechanism":[37],"by":[38],"which":[39],"their":[40],"superposition":[41],"generates":[42],"\"chemically":[43],"resonant":[44],"compounding":[45],"peaks\"":[46],"at":[47,54],"composite":[48],"numbers":[49,91],"and":[50,85],"\"atomic":[51],"valleys\"":[53],"coordinates.":[56],"Through":[57],"this":[58],"lens,":[59],"non-integer":[60],"regions":[61],"are":[62],"interpreted":[63],"\"transition":[65],"states\"":[66],"where":[67],"energy":[68],"disperses":[69],"into":[70],"imaginary":[72],"dimension.":[73],"framework":[75],"provides":[76],"physical":[78],"necessity":[79],"for":[80],"emergence":[82],"primes":[84],"suggests":[86],"that":[87],"distribution":[89],"is":[92],"an":[93],"observable":[94],"manifestation":[95],"phase-locked":[97],"singularities":[98],"within":[99],"complex":[101],"manifold.":[102]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-03-31T00:00:00"}
