{"id":"https://openalex.org/W7224990856","doi":"https://doi.org/10.5281/zenodo.23830936","title":"Fibonacci Anyons Realize Golden Ratio as Braiding Eigenvalue via Pentagon Geometry \u2014 E8 Intelligence Research","display_name":"Fibonacci Anyons Realize Golden Ratio as Braiding Eigenvalue via Pentagon Geometry \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7224990856","doi":"https://doi.org/10.5281/zenodo.23830936"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23830936","doi":"https://doi.org/10.5281/zenodo.23830936","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830936","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.23830936","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153285007","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/A5153285007"],"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":0.9214000105857849,"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":0.9214000105857849,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.04309999942779541,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.010700000450015068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-anyons","display_name":"Fibonacci anyons","score":1.0},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.9879999756813049},{"id":"https://openalex.org/keywords/topological-quantum-computation","display_name":"topological quantum computation","score":0.5910000205039978},{"id":"https://openalex.org/keywords/anyon-braiding","display_name":"anyon braiding","score":0.7749999761581421},{"id":"https://openalex.org/keywords/pentagon-equation","display_name":"pentagon equation","score":0.8669999837875366},{"id":"https://openalex.org/keywords/f-matrix","display_name":"F-matrix","score":0.6460000276565552},{"id":"https://openalex.org/keywords/quantum-dimension","display_name":"quantum dimension","score":0.8349999785423279},{"id":"https://openalex.org/keywords/jones-polynomial","display_name":"Jones polynomial","score":0.8870000243186951},{"id":"https://openalex.org/keywords/pentagon-geometry","display_name":"pentagon geometry","score":0.8140000104904175},{"id":"https://openalex.org/keywords/icosahedral-symmetry","display_name":"icosahedral symmetry","score":0.8730000257492065},{"id":"https://openalex.org/keywords/topological-phases","display_name":"topological phases","score":0.546999990940094}],"concepts":[{"id":"https://openalex.org/C2779965921","wikidata":"https://www.wikidata.org/wiki/Q127840","display_name":"Pentagon","level":2,"score":0.9879000186920166},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9387999773025513},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.9071000218391418},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4936000108718872},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4846999943256378},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4749999940395355},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.47440001368522644},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.446399986743927},{"id":"https://openalex.org/C187483380","wikidata":"https://www.wikidata.org/wiki/Q7825042","display_name":"Topological quantum computer","level":3,"score":0.4147999882698059},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3580999970436096},{"id":"https://openalex.org/C2777446375","wikidata":"https://www.wikidata.org/wiki/Q5528","display_name":"Anyon","level":4,"score":0.33379998803138733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.31349998712539673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31310001015663147},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.2816999852657318},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23830936","doi":"https://doi.org/10.5281/zenodo.23830936","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830936","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.23830937","doi":"https://doi.org/10.5281/zenodo.23830937","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830937","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.23830936","doi":"https://doi.org/10.5281/zenodo.23830936","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830936","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/W7204048752","https://openalex.org/W7172000126","https://openalex.org/W7204056796","https://openalex.org/W7223061353","https://openalex.org/W7204038450","https://openalex.org/W7218443595","https://openalex.org/W7204048384","https://openalex.org/W7224251290","https://openalex.org/W7219783064","https://openalex.org/W7171027074"],"abstract_inverted_index":{"FINDING:":[0,97],"Fibonacci":[1,27],"anyons":[2],"realize":[3],"the":[4,12,105,110,174],"golden":[5,111],"ratio":[6,100],"as":[7,20],"a":[8,21],"braiding":[9,40],"eigenvalue":[10],"\u2014":[11,104],"same":[13],"\u03d5":[14,37,102,117],"that":[15],"governs":[16],"pentagon":[17,49,69,92,132],"geometry":[18],"appears":[19],"topological":[22],"quantum":[23,33],"phase.":[24],"|":[25,63,94,113,143],"MATH:":[26,114],"fusion":[28],"rule":[29],"\u03c4\u2297\u03c4":[30],"=":[31,36,38,44,47,71,85,116,118,124,128,130,138,141,146,149,152,155],"1\u2295\u03c4;":[32],"dimension":[34],"d_\u03c4":[35],"(1+\u221a5)/2;":[39],"R-matrix":[41],"eigenvalues":[42],"R\u2081":[43],"e^{-4\u03c0i/5},":[45],"R_\u03c4":[46],"e^{3\u03c0i/5};":[48],"equation":[50,66],"constrains":[51],"F-matrix":[52,73],"elements":[53],"to":[54,158],"\u03d5-powers;":[55],"hexagon":[56],"equations":[57],"fix":[58],"R":[59],"via":[60],"(R_\u03c4)^?":[61],"relations.":[62],"CONNECTION:":[64,144],"Pentagon":[65,98],"\u2194":[67,91],"regular":[68],"diagonal/side":[70],"\u03d5;":[72],"entries":[74],"are":[75],"\u03d5^{-1},":[76],"\u03d5^{-1/2};":[77],"SU(2)\u2083":[78],"WZW":[79],"/":[80],"Jones":[81],"polynomial":[82],"at":[83],"q":[84],"e^{2\u03c0i/5}":[86],"(5th":[87],"root":[88],"of":[89,109,173],"unity":[90],"symmetry).":[93],"DEPTH:":[95],"9":[96],"diagonal-to-side":[99],"equals":[101],"exactly":[103],"defining":[106],"geometric":[107],"origin":[108],"ratio.":[112],"d/s":[115],"(1+\u221a5)/2":[119],"\u2248":[120],"1.6180339887;":[121],"cos":[122,126],"36\u00b0":[123,154],"\u03d5/2;":[125],"72\u00b0":[127],"(\u03d5\u22121)/2":[129],"1/(2\u03d5);":[131],"angles":[133],"108\u00b0,":[134],"72\u00b0,":[135],"36\u00b0;":[136],"\u03d5\u00b2":[137],"\u03d5+1,":[139],"\u03d5\u207b\u00b9":[140],"\u03d5\u22121.":[142],"0.618":[145],"\u03d5\u207b\u00b9,":[147],"0.382":[148],"\u03d5\u207b\u00b2,":[150],"2.618":[151],"\u03d5\u00b2;":[153],"\u03c0/5":[156],"links":[157],"5-fold":[159],"crystallographic":[160],"(icosahedral)":[161],"symmetry;":[162],"forbidden":[163],"in":[164],"Author:":[165],"Andrew":[166],"Stewart":[167],"Caldin,":[168],"Independent":[169],"Researcher,":[170],"UK.":[171],"Part":[172],"E8":[175],"Intelligence":[176],"Research":[177],"series.":[178],"Platform:":[179],"e8intelligence.com":[180]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}
