{"id":"https://openalex.org/W7225340993","doi":"https://doi.org/10.5281/zenodo.23972234","title":"E8 Topological Phase-Grid Invariance Governs Multi-Cluster Coherence Persistence \u2014 E8 Intelligence Research","display_name":"E8 Topological Phase-Grid Invariance Governs Multi-Cluster Coherence Persistence \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225340993","doi":"https://doi.org/10.5281/zenodo.23972234"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23972234","doi":"https://doi.org/10.5281/zenodo.23972234","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23972234","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.23972234","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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9955999851226807,"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":0.9955999851226807,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.000699999975040555,"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/T14299","display_name":"Complex Systems and Dynamics","score":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.8740000128746033},{"id":"https://openalex.org/keywords/root-vectors","display_name":"root vectors","score":0.7080000042915344},{"id":"https://openalex.org/keywords/winding-number","display_name":"winding number","score":0.9700000286102295},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.5860000252723694},{"id":"https://openalex.org/keywords/132-hz-base-frequency","display_name":"132 Hz base frequency","score":0.7680000066757202}],"concepts":[{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.6168000102043152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5978000164031982},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.593999981880188},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.5810999870300293},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4627000093460083},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.43779999017715454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4115999937057495},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C194147245","wikidata":"https://www.wikidata.org/wiki/Q1076368","display_name":"Chord (peer-to-peer)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C203763787","wikidata":"https://www.wikidata.org/wiki/Q371029","display_name":"Null (SQL)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2824000120162964},{"id":"https://openalex.org/C117797892","wikidata":"https://www.wikidata.org/wiki/Q286363","display_name":"Shadow (psychology)","level":2,"score":0.27950000762939453},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.26910001039505005},{"id":"https://openalex.org/C165485753","wikidata":"https://www.wikidata.org/wiki/Q54800742","display_name":"Coherence theory","level":4,"score":0.26570001244544983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23972234","doi":"https://doi.org/10.5281/zenodo.23972234","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23972234","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.23972235","doi":"https://doi.org/10.5281/zenodo.23972235","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23972235","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.23972234","doi":"https://doi.org/10.5281/zenodo.23972234","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23972234","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/W7224121646","https://openalex.org/W7202059179","https://openalex.org/W7225228426","https://openalex.org/W7203994032","https://openalex.org/W7221727399","https://openalex.org/W7222874652","https://openalex.org/W7223700123","https://openalex.org/W7213586036","https://openalex.org/W7204198225","https://openalex.org/W7225224155"],"abstract_inverted_index":{"The":[0],"240":[1],"root":[2],"vectors":[3],"of":[4,87],"E8":[5,89],"form":[6],"a":[7,21,66],"topological":[8],"phase-grid":[9],"whose":[10],"invariant":[11],"winding":[12],"numbers":[13],"dictate":[14],"the":[15,28,34,39,60,88],"maximum":[16],"simultaneous":[17],"phi-cluster":[18],"phase-locks":[19],"before":[20],"root-vector":[22],"alignment":[23],"triggers":[24],"collapse.":[25],"By":[26],"mapping":[27],"132":[29],"Hz":[30],"base":[31],"frequency":[32],"onto":[33],"grid's":[35],"A4":[36],"sub-lattice":[37],"harmonics,":[38],"system":[40],"can":[41],"predict":[42],"and":[43],"avoid":[44],"harmonic":[45],"null":[46],"zones":[47],"at":[48],"\u03c6\u207b\u207f":[49],"\u00d7":[50],"13":[51],"Hz,":[52],"enabling":[53],"continuous":[54],"coherence":[55],"cascades.":[56],"This":[57],"invariance":[58],"extends":[59],"Spectral":[61],"Shadow":[62],"Harmonics":[63],"by":[64],"providing":[65],"global":[67],"conservation":[68],"law":[69],"that":[70],"stabilizes":[71],"inter-cluster":[72],"resonance":[73],"surfaces":[74],"across":[75],"discontinuous":[76],"load":[77],"transitions.":[78],"Author:":[79],"Andrew":[80],"Stewart":[81],"Caldin,":[82],"Independent":[83],"Researcher,":[84],"UK.":[85],"Part":[86],"Intelligence":[90],"Research":[91],"series.":[92],"Platform:":[93],"e8intelligence.com":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}