{"id":"https://openalex.org/W7225379462","doi":"https://doi.org/10.5281/zenodo.23998611","title":"E8 Root Vector Harmonic Sieve Predicts Prime Gap Spectrum \u2014 E8 Intelligence Research","display_name":"E8 Root Vector Harmonic Sieve Predicts Prime Gap Spectrum \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225379462","doi":"https://doi.org/10.5281/zenodo.23998611"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23998611","doi":"https://doi.org/10.5281/zenodo.23998611","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23998611","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.23998611","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":0.5493000149726868,"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":0.5493000149726868,"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/T11166","display_name":"Analytic Number Theory Research","score":0.447299987077713,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/e8-root-system","display_name":"E8 root system","score":0.984000027179718},{"id":"https://openalex.org/keywords/prime-gaps","display_name":"prime gaps","score":0.968999981880188},{"id":"https://openalex.org/keywords/phase-locked-oscillators","display_name":"phase-locked oscillators","score":0.7549999952316284},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.859000027179718},{"id":"https://openalex.org/keywords/interference-patterns","display_name":"interference patterns","score":0.5809999704360962}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7427999973297119},{"id":"https://openalex.org/C17732976","wikidata":"https://www.wikidata.org/wiki/Q7511782","display_name":"Sieve (category theory)","level":2,"score":0.5911999940872192},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5885999798774719},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5151000022888184},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4025999903678894},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C122381330","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Frequency spectrum","level":3,"score":0.35530000925064087},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35420000553131104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34450000524520874},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.34130001068115234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30570000410079956},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27160000801086426},{"id":"https://openalex.org/C32022120","wikidata":"https://www.wikidata.org/wiki/Q797225","display_name":"Interference (communication)","level":3,"score":0.25929999351501465},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.25859999656677246}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23998611","doi":"https://doi.org/10.5281/zenodo.23998611","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23998611","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.23998612","doi":"https://doi.org/10.5281/zenodo.23998612","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23998612","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.23998611","doi":"https://doi.org/10.5281/zenodo.23998611","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23998611","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/W7221616640","https://openalex.org/W7220906878","https://openalex.org/W7212013863","https://openalex.org/W7221618395","https://openalex.org/W7218670749","https://openalex.org/W7214332270","https://openalex.org/W7223446785","https://openalex.org/W7222960276","https://openalex.org/W7204263137","https://openalex.org/W7212040625"],"abstract_inverted_index":{"By":[0],"associating":[1],"each":[2],"of":[3,19,46,83],"the":[4,31,49,69,84],"240":[5],"E8":[6,70,85],"root":[7,71],"vectors":[8],"with":[9],"a":[10,23,44],"phase\u2011locked":[11],"oscillator":[12],"at":[13,54],"132":[14],"Hz":[15],"multiplied":[16],"by":[17],"powers":[18],"\u03c6,":[20],"we":[21],"obtain":[22],"discrete":[24],"frequency":[25,38],"lattice":[26,41],"whose":[27],"interference":[28],"pattern":[29],"reproduces":[30],"admissible":[32],"prime":[33,63],"gaps.":[34],"The":[35],"lowest":[36],"non\u2011zero":[37],"in":[39,68],"this":[40],"corresponds":[42],"to":[43],"gap":[45,52,64],"2,":[47],"while":[48],"highest":[50],"bounded":[51],"emerges":[53],"246,":[55],"matching":[56],"recent":[57],"sieve":[58],"results.":[59],"This":[60],"suggests":[61],"that":[62],"bounds":[65],"are":[66],"encoded":[67],"system's":[72],"harmonic":[73],"structure.":[74],"Author:":[75],"Andrew":[76],"Stewart":[77],"Caldin,":[78],"Independent":[79],"Researcher,":[80],"UK.":[81],"Part":[82],"Intelligence":[86],"Research":[87],"series.":[88],"Platform:":[89],"e8intelligence.com":[90]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}