{"id":"https://openalex.org/W7219620784","doi":"https://doi.org/10.5281/zenodo.23131674","title":"Golden Oscillator: Fibonacci-Quantized Spectra via Quantum Calculus \u2014 E8 Intelligence Research","display_name":"Golden Oscillator: Fibonacci-Quantized Spectra via Quantum Calculus \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7219620784","doi":"https://doi.org/10.5281/zenodo.23131674"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23131674","doi":"https://doi.org/10.5281/zenodo.23131674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23131674","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.23131674","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5155309988","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5155309988"],"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":0.9994999766349792,"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":0.9994999766349792,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":9.999999747378752e-05,"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":[{"id":"https://openalex.org/keywords/quantum-harmonic-oscillator","display_name":"quantum harmonic oscillator","score":0.9860000014305115},{"id":"https://openalex.org/keywords/fibonacci-sequence","display_name":"Fibonacci numbers","score":0.8149999976158142},{"id":"https://openalex.org/keywords/q-calculus","display_name":"q-calculus","score":0.703000009059906},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.9049999713897705},{"id":"https://openalex.org/keywords/silver-ratio","display_name":"silver ratio","score":0.9980000257492065},{"id":"https://openalex.org/keywords/pell-numbers","display_name":"Pell numbers","score":0.7549999952316284},{"id":"https://openalex.org/keywords/supersymmetry","display_name":"supersymmetry","score":0.8240000009536743},{"id":"https://openalex.org/keywords/fock-space","display_name":"Fock space","score":0.8399999737739563},{"id":"https://openalex.org/keywords/binet-s-formula","display_name":"Binet formula","score":0.7089999914169312}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.873199999332428},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.5536999702453613},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5375000238418579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5368000268936157},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C122332657","wikidata":"https://www.wikidata.org/wiki/Q677864","display_name":"Quantum harmonic oscillator","level":3,"score":0.43799999356269836},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4212000072002411},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C2983197053","wikidata":"https://www.wikidata.org/wiki/Q654182","display_name":"Energy spectrum","level":2,"score":0.38179999589920044},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.33799999952316284},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.3125},{"id":"https://openalex.org/C63630878","wikidata":"https://www.wikidata.org/wiki/Q902336","display_name":"Creation and annihilation operators","level":3,"score":0.30630001425743103},{"id":"https://openalex.org/C15353042","wikidata":"https://www.wikidata.org/wiki/Q7269009","display_name":"Quantum algebra","level":4,"score":0.2883000075817108},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.28760001063346863},{"id":"https://openalex.org/C137019171","wikidata":"https://www.wikidata.org/wiki/Q2623817","display_name":"Quantum algorithm","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.2827000021934509},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.2581999897956848},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23131674","doi":"https://doi.org/10.5281/zenodo.23131674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23131674","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.23131675","doi":"https://doi.org/10.5281/zenodo.23131675","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23131675","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.23131674","doi":"https://doi.org/10.5281/zenodo.23131674","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23131674","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":[],"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":{"FINDING:":[0],"The":[1,42],"arXiv":[2],"paper":[3],"(2410.04169v2)":[4],"introduces":[5],"a":[6,10,35],"\"golden":[7],"oscillator\"":[8],"\u2014":[9,97],"quantum":[11,23],"harmonic":[12],"oscillator":[13,80],"whose":[14],"energy":[15],"spectrum":[16,81],"is":[17],"quantized":[18],"via":[19],"Fibonacci":[20,99,156],"divisors":[21],"and":[22,30,52],"calculus":[24],"with":[25],"bases":[26],"\u03c6":[27],"(golden":[28],"ratio)":[29],"\u03c8":[31,135],"(silver":[32],"ratio),":[33],"yielding":[34],"supersymmetric":[36],"hierarchy":[37],"of":[38,180],"fermion-boson":[39],"entangled":[40],"states.":[41],"YouTube":[43],"results":[44],"are":[45],"standard":[46],"QHO":[47],"pedagogy":[48],"(E_n":[49],"=":[50,62,72,75,87,93,106,114,117,123,127,130,136,141,147,161],"(n+\u00bd)\u0127\u03c9)":[51],"add":[53],"no":[54],"novel":[55],"mathematics.":[56],"MATH:":[57],"-":[58,78,102,132,152,169],"Standard":[59],"QHO:":[60],"E_n":[61,84],"\u0127\u03c9(n":[63],"+":[64],"\u00bd),":[65],"n":[66],"\u2208":[67],"\u2115\u2080.":[68],"Partition":[69],"function":[70],"Z":[71],"\u03a3":[73],"exp(\u2212\u03b2E_n)":[74],"1/[2":[76],"sinh(\u03b2\u0127\u03c9/2)].":[77],"Golden":[79],"(from":[82],"abstract):":[83],"\u221d":[85],"[n]_\u03c6":[86],"(\u03c6^n":[88,94],"\u2212":[89,91,95,108,110,119,121,143,145,163],"(\u2212\u03c6)^\u2212n)/(\u03c6":[90],"(\u2212\u03c6)^\u22121)":[92],"(\u2212\u03c6)^\u2212n)/\u221a5":[96],"the":[98,181],"number":[100,158],"F_n.":[101],"Quantum":[103],"calculus:":[104],"[n]_q":[105],"(1":[107],"q^n)/(1":[109],"q).":[111],"For":[112],"q":[113],"\u03c6\u00b2,":[115],"[n]_{\u03c6\u00b2}":[116],"(\u03c6^{2n}":[118],"1)/(\u03c6\u00b2":[120],"1)":[122,146],"F_{2n}/\u03c6":[124],"(using":[125],"\u03c6\u00b2":[126],"\u03c6+1,":[128],"\u03c6\u00b2\u22121":[129],"\u03c6).":[131],"Silver":[133],"ratio:":[134],"1+\u221a2":[137],"\u2248":[138],"2.414;":[139],"[n]_{\u03c8\u00b2}":[140],"(\u03c8^{2n}":[142],"1)/(\u03c8\u00b2":[144],"Pell":[148],"numbers":[149],"/":[150],"(2\u03c8).":[151],"Binet":[153],"formula":[154],"for":[155],"divisor":[157],"operator:":[159],"N_\u03c6":[160],"(\u03c6^N":[162],"(\u2212\u03c6)^\u2212N)/\u221a5,":[164],"acting":[165],"on":[166],"Fock":[167],"space.":[168],"Supersymmetric":[170],"hierar":[171],"Author:":[172],"Andrew":[173],"Stewart":[174],"Caldin,":[175],"Independent":[176],"Researcher,":[177],"UK.":[178],"Part":[179],"E8":[182],"Intelligence":[183],"Research":[184],"series.":[185],"Platform:":[186],"e8intelligence.com":[187]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-10-05T00:00:00"}