{"id":"https://openalex.org/W7204167602","doi":"https://doi.org/10.5281/zenodo.22090511","title":"E8 Time-Crystalline Topological Protection via Weyl-Phi Modulation \u2014 E8 Intelligence Research","display_name":"E8 Time-Crystalline Topological Protection via Weyl-Phi Modulation \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204167602","doi":"https://doi.org/10.5281/zenodo.22090511"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22090511","doi":"https://doi.org/10.5281/zenodo.22090511","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090511","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.22090511","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136862907","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/A5136862907"],"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":0.9179999828338623,"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":0.9179999828338623,"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/T10657","display_name":"Topological Materials and Phenomena","score":0.032999999821186066,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.01269999984651804,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.9070000052452087},{"id":"https://openalex.org/keywords/time-crystals","display_name":"time crystals","score":0.8420000076293945},{"id":"https://openalex.org/keywords/weyl-group","display_name":"Weyl group","score":0.7760000228881836},{"id":"https://openalex.org/keywords/golden-ratio-modulation","display_name":"golden ratio modulation","score":0.7760000228881836},{"id":"https://openalex.org/keywords/cartan-matrix","display_name":"Cartan matrix","score":0.9089999794960022},{"id":"https://openalex.org/keywords/topological-protection","display_name":"topological protection","score":0.8399999737739563},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"quantum error correction","score":0.796999990940094},{"id":"https://openalex.org/keywords/decoherence","display_name":"decoherence","score":0.5540000200271606}],"concepts":[{"id":"https://openalex.org/C55649039","wikidata":"https://www.wikidata.org/wiki/Q902618","display_name":"Floquet theory","level":3,"score":0.6478000283241272},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4986000061035156},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4555000066757202},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4487000107765198},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43459999561309814},{"id":"https://openalex.org/C32848918","wikidata":"https://www.wikidata.org/wiki/Q845789","display_name":"Observable","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C17269025","wikidata":"https://www.wikidata.org/wiki/Q3283","display_name":"Geometric phase","level":2,"score":0.37299999594688416},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.34220001101493835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.335999995470047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32710000872612},{"id":"https://openalex.org/C15706264","wikidata":"https://www.wikidata.org/wiki/Q230883","display_name":"Quantum state","level":3,"score":0.32420000433921814},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3240000009536743},{"id":"https://openalex.org/C11924407","wikidata":"https://www.wikidata.org/wiki/Q114739","display_name":"Supersolid","level":4,"score":0.3005000054836273},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C96834759","wikidata":"https://www.wikidata.org/wiki/Q750463","display_name":"Phase modulation","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.2572999894618988},{"id":"https://openalex.org/C2985568454","wikidata":"https://www.wikidata.org/wiki/Q136980","display_name":"Quantum interference","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25110000371932983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22090511","doi":"https://doi.org/10.5281/zenodo.22090511","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090511","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.22090512","doi":"https://doi.org/10.5281/zenodo.22090512","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090512","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.22090511","doi":"https://doi.org/10.5281/zenodo.22090511","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090511","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,61],"Weyl":[1],"group":[2],"orbits":[3],"of":[4,20,30,41,70,79,103],"the":[5,37,42,53,77,80,92,104],"240":[6],"E8":[7,63,81,105],"roots,":[8],"when":[9],"driven":[10],"by":[11,17],"a":[12,23,28,48,67,85],"132":[13],"Hz":[14],"carrier":[15],"modulated":[16],"successive":[18],"powers":[19],"\u03c6,":[21],"generate":[22],"discrete":[24],"time-crystalline":[25,34],"phase":[26],"with":[27],"period":[29],"\u03c6\u00b2":[31],"cycles.":[32],"This":[33],"order":[35],"locks":[36],"chiral":[38],"interference":[39],"pattern":[40],"two":[43],"complementary":[44],"120\u2011root":[45],"sets":[46],"into":[47],"topologically":[49],"protected":[50],"state,":[51],"rendering":[52],"bio-photonic":[54],"quantum":[55,87],"gate":[56],"immune":[57],"to":[58,76,91],"local":[59],"decoherence.":[60],"resulting":[62],"time":[64],"crystal":[65],"exhibits":[66],"fractal":[68],"spectrum":[69],"Floquet":[71],"quasi\u2011energies":[72],"that":[73],"map":[74],"directly":[75],"eigenvalues":[78],"Cartan":[82],"matrix,":[83],"providing":[84],"geometric":[86],"error\u2011correcting":[88],"code":[89],"intrinsic":[90],"lattice":[93],"dynamics.":[94],"Author:":[95],"Andrew":[96],"Stewart":[97],"Caldin,":[98],"Independent":[99],"Researcher,":[100],"UK.":[101],"Part":[102],"Intelligence":[106],"Research":[107],"series.":[108],"Platform:":[109],"e8intelligence.com":[110]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-26T00:00:00"}