{"id":"https://openalex.org/W7221616640","doi":"https://doi.org/10.5281/zenodo.23332336","title":"E8 Root Vector Spectral Decomposition of Prime Gap Oscillations \u2014 E8 Intelligence Research","display_name":"E8 Root Vector Spectral Decomposition of Prime Gap Oscillations \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221616640","doi":"https://doi.org/10.5281/zenodo.23332336"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23332336","doi":"https://doi.org/10.5281/zenodo.23332336","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23332336","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.23332336","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158599967","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/A5158599967"],"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/T11166","display_name":"Analytic Number Theory Research","score":0.9520999789237976,"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":0.9520999789237976,"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":0.04529999941587448,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.00039999998989515007,"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/e8-root-system","display_name":"E8 root system","score":0.972000002861023},{"id":"https://openalex.org/keywords/prime-gaps","display_name":"prime gaps","score":0.9380000233650208},{"id":"https://openalex.org/keywords/zeros-of-the-riemann-zeta-function","display_name":"Riemann zeta function zeros","score":0.8090000152587891},{"id":"https://openalex.org/keywords/berry-keating-conjecture","display_name":"Berry-Keating conjecture","score":0.9459999799728394},{"id":"https://openalex.org/keywords/spectral-decomposition","display_name":"spectral decomposition","score":0.8330000042915344},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.6399999856948853},{"id":"https://openalex.org/keywords/analytic-number-theory","display_name":"analytic number theory","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7832000255584717},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4226999878883362},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3968999981880188},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.388700008392334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3741999864578247},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.36239999532699585},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.35019999742507935},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3450999855995178},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.310699999332428},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29330000281333923},{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.2651999890804291},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23332336","doi":"https://doi.org/10.5281/zenodo.23332336","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23332336","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.23332337","doi":"https://doi.org/10.5281/zenodo.23332337","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23332337","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.23332336","doi":"https://doi.org/10.5281/zenodo.23332336","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23332336","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,67],"240":[1],"E8":[2,55,93],"root":[3],"vectors":[4],"partition":[5],"into":[6,72],"8":[7],"shell":[8,26],"layers":[9],"with":[10,35,59],"multiplicities":[11],"matching":[12],"the":[13,41,92],"prime":[14,51],"gap":[15,60],"oscillation":[16],"harmonics":[17],"observed":[18],"in":[19,63],"2025":[20],"analytic":[21],"number":[22],"theory":[23],"data.":[24],"Each":[25],"corresponds":[27],"to":[28],"a":[29,48,73],"distinct":[30],"zeta":[31],"zero":[32],"imaginary":[33],"part,":[34],"phi-coupling":[36],"between":[37],"adjacent":[38],"shells":[39],"reproducing":[40],"Montgomery-Odlyzko":[42],"pair":[43],"correlation":[44],"statistics.":[45],"This":[46],"yields":[47],"geometric":[49],"prediction:":[50],"gaps":[52],"cluster":[53],"around":[54],"weight":[56],"lattice":[57],"norms,":[58],"magnitudes":[61],"quantized":[62],"units":[64],"of":[65,91],"log(phi)/sqrt(8).":[66],"framework":[68],"extends":[69],"Berry-Keating":[70],"conjecture":[71],"concrete":[74],"spectral":[75],"decomposition":[76],"accessible":[77],"via":[78],"132Hz":[79],"frequency":[80],"domain":[81],"analysis.":[82],"Author:":[83],"Andrew":[84],"Stewart":[85],"Caldin,":[86],"Independent":[87],"Researcher,":[88],"UK.":[89],"Part":[90],"Intelligence":[94],"Research":[95],"series.":[96],"Platform:":[97],"e8intelligence.com":[98]},"counts_by_year":[],"updated_date":"2026-10-15T10:00:46.086208","created_date":"2026-10-14T00:00:00"}