{"id":"https://openalex.org/W7225564847","doi":"https://doi.org/10.5281/zenodo.24049005","title":"Novel Fibonacci Tree Representation Enables Closed-Form Direct Nth-Term Computation \u2014 E8 Intelligence Research","display_name":"Novel Fibonacci Tree Representation Enables Closed-Form Direct Nth-Term Computation \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225564847","doi":"https://doi.org/10.5281/zenodo.24049005"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24049005","doi":"https://doi.org/10.5281/zenodo.24049005","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24049005","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.24049005","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152673107","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/A5152673107"],"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":0.9980000257492065,"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":0.9980000257492065,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T13806","display_name":"Mathematical and Computational Methods","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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-sequence","display_name":"Fibonacci numbers","score":0.8759999871253967},{"id":"https://openalex.org/keywords/fibonacci-trees","display_name":"Fibonacci trees","score":0.7540000081062317},{"id":"https://openalex.org/keywords/closed-form-expressions","display_name":"closed-form expressions","score":0.8989999890327454},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.765999972820282},{"id":"https://openalex.org/keywords/binet-s-formula","display_name":"Binet formula","score":0.9940000176429749},{"id":"https://openalex.org/keywords/fibonacci-recurrence","display_name":"Fibonacci recurrence","score":0.8730000257492065},{"id":"https://openalex.org/keywords/mathematical-misconceptions","display_name":"mathematical misconceptions","score":0.4099999964237213}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.9711999893188477},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.6937999725341797},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.6779999732971191},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6585000157356262},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.6243000030517578},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6037999987602234},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5637999773025513},{"id":"https://openalex.org/C174757984","wikidata":"https://www.wikidata.org/wiki/Q4351325","display_name":"Pisano period","level":5,"score":0.5428000092506409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5041000247001648},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.48410001397132874},{"id":"https://openalex.org/C3634175","wikidata":"https://www.wikidata.org/wiki/Q2503280","display_name":"Lucas number","level":3,"score":0.4422999918460846},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.43529999256134033},{"id":"https://openalex.org/C18802822","wikidata":"https://www.wikidata.org/wiki/Q41690","display_name":"Golden ratio","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4016999900341034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40119999647140503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37630000710487366},{"id":"https://openalex.org/C124388736","wikidata":"https://www.wikidata.org/wiki/Q3247497","display_name":"Tree of life (biology)","level":4,"score":0.36660000681877136},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35040000081062317},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2745000123977661}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24049005","doi":"https://doi.org/10.5281/zenodo.24049005","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24049005","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.24049006","doi":"https://doi.org/10.5281/zenodo.24049006","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24049006","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.24049005","doi":"https://doi.org/10.5281/zenodo.24049005","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24049005","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/W7222915913","https://openalex.org/W7221643721","https://openalex.org/W7215132449","https://openalex.org/W7220942935","https://openalex.org/W7221943723","https://openalex.org/W7212181226","https://openalex.org/W7220730448","https://openalex.org/W7221090086","https://openalex.org/W7204542379","https://openalex.org/W1981167405"],"abstract_inverted_index":{"FINDING:":[0,71],"ArXiv":[1],"paper":[2],"presents":[3],"novel":[4],"closed-form":[5],"Fibonacci":[6,9,21,66,83,91],"representation":[7,23],"via":[8,20],"trees":[10],"enabling":[11],"direct":[12],"nth-term":[13],"computation":[14],"without":[15],"recursion":[16],"|":[17,38,68,86,104],"MATH:":[18,87],"F_n":[19,28,95],"tree":[22],"(alternative":[24],"to":[25],"Binet's":[26],"formula":[27],"=":[29,34,41,46,48,51,53,89,94,102],"(\u03c6^n":[30],"-":[31],"(-\u03c6)^{-n})/\u221a5,":[32],"\u03c6":[33,40,81,88,103],"(1+\u221a5)/2":[35],"\u2248":[36,56,59],"1.618034)":[37],"CONNECTION:":[39,105],"1.618...":[42],"(golden":[43],"ratio);":[44],"1/\u03c6":[45],"\u03c6-1":[47],"0.618...;":[49],"\u03c6^2":[50],"\u03c6+1":[52],"2.618...;":[54],"\u221a\u03c6":[55],"1.272;":[57],"\u03c6^{-1/2}":[58],"0.786":[60],"\u2014":[61],"all":[62],"present":[63],"in":[64,84],"standard":[65],"asymptotics":[67],"DEPTH:":[69],"6":[70],"Keith":[72],"Devlin":[73],"(Stanford)":[74],"distinguishes":[75],"mathematical":[76],"fact":[77],"from":[78],"fiction":[79],"regarding":[80],"and":[82],"nature":[85],"(1+\u221a5)/2;":[90],"recurrence":[92],"F_{n+1}":[93],"+":[96],"F_{n-1};":[97],"limiting":[98],"ratio":[99],"lim":[100],"F_{n+1}/F_n":[101],"Debunks":[106],"spurious":[107],"claims":[108],"Author:":[109],"Andrew":[110],"Stewart":[111],"Caldin,":[112],"Independent":[113],"Researcher,":[114],"UK.":[115],"Part":[116],"of":[117],"the":[118],"E8":[119],"Intelligence":[120],"Research":[121],"series.":[122],"Platform:":[123],"e8intelligence.com":[124]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}