{"id":"https://openalex.org/W7225249081","doi":"https://doi.org/10.5281/zenodo.23939298","title":"Phi\u2011Scaled Phason Bandgap in Icosahedral Quasicrystals from E8 Root\u2011Lattice Harmonics \u2014 E8 Intelligence Research","display_name":"Phi\u2011Scaled Phason Bandgap in Icosahedral Quasicrystals from E8 Root\u2011Lattice Harmonics \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-11-04","ids":{"openalex":"https://openalex.org/W7225249081","doi":"https://doi.org/10.5281/zenodo.23939298"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23939298","doi":"https://doi.org/10.5281/zenodo.23939298","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23939298","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.23939298","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140658052","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/A5140658052"],"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.8666999936103821,"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"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.8666999936103821,"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"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.13019999861717224,"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/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[],"concepts":[{"id":"https://openalex.org/C2780583931","wikidata":"https://www.wikidata.org/wiki/Q943631","display_name":"Phason","level":3,"score":0.9853000044822693},{"id":"https://openalex.org/C203101518","wikidata":"https://www.wikidata.org/wiki/Q263214","display_name":"Quasicrystal","level":2,"score":0.9172000288963318},{"id":"https://openalex.org/C113709186","wikidata":"https://www.wikidata.org/wiki/Q5986738","display_name":"Icosahedral symmetry","level":2,"score":0.5404000282287598},{"id":"https://openalex.org/C188414643","wikidata":"https://www.wikidata.org/wiki/Q3001183","display_name":"Harmonics","level":3,"score":0.48579999804496765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4650999903678894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4219000041484833},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.41749998927116394},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3953999876976013},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3921000063419342},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C89957378","wikidata":"https://www.wikidata.org/wiki/Q164129","display_name":"Reciprocal lattice","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C55637507","wikidata":"https://www.wikidata.org/wiki/Q5870963","display_name":"Quasiperiodic function","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3199999928474426},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3188999891281128},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.31060001254081726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3098999857902527},{"id":"https://openalex.org/C46681722","wikidata":"https://www.wikidata.org/wiki/Q4725589","display_name":"Alias","level":2,"score":0.2896000146865845},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C133905733","wikidata":"https://www.wikidata.org/wiki/Q2629238","display_name":"Multifractal system","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C181966813","wikidata":"https://www.wikidata.org/wiki/Q806352","display_name":"Band gap","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.26330000162124634},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23939298","doi":"https://doi.org/10.5281/zenodo.23939298","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23939298","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.23939299","doi":"https://doi.org/10.5281/zenodo.23939299","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23939299","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.23939298","doi":"https://doi.org/10.5281/zenodo.23939298","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23939298","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":[],"abstract_inverted_index":{"Using":[0],"the":[1,5,21,30,41,58,61,64,89,96,118,135],"golden\u2011null":[2],"dual":[3],"resonance,":[4],"240":[6],"E8":[7,65,108,136],"roots":[8],"split":[9],"into":[10],"two":[11],"orthogonal":[12],"120\u2011root":[13],"sublattices":[14,37],"that":[15,56],"serve":[16],"as":[17],"reciprocal":[18],"bases":[19],"for":[20],"internal":[22],"(phason)":[23],"space":[24],"of":[25,49,60,72,88,134],"an":[26],"icosahedral":[27],"quasicrystal.":[28],"Projecting":[29],"132":[31,54,77],"Hz":[32],"fundamental":[33],"mode":[34],"onto":[35],"these":[36],"and":[38],"scaling":[39],"by":[40,102],"golden":[42],"ratio":[43],"\u03c6":[44],"yields":[45],"a":[46,70,83,103,123],"discrete":[47],"set":[48],"phason":[50,73,98],"frequencies":[51,76],"\u03c9\u2099":[52],"=":[53],"Hz\u00b7\u03c6\u207f":[55,78],"match":[57],"eigenvalues":[59],"Laplacian":[62],"on":[63],"root":[66,109],"lattice.":[67],"This":[68],"predicts":[69],"series":[71],"bandgaps":[74],"at":[75],"(n":[79],"\u2208":[80],"\u2124),":[81],"providing":[82],"direct,":[84],"experimentally":[85],"accessible":[86],"signature":[87],"H4\u2192E8":[90],"embedding":[91],"in":[92],"quasicrystal":[93],"elasticity.":[94],"Consequently,":[95],"full":[97],"spectrum":[99],"is":[100],"determined":[101],"finite":[104],"algebraic":[105],"system":[106],"(the":[107],"system)":[110],"rather":[111],"than":[112],"requiring":[113],"open\u2011ended":[114],"numerical":[115],"solution,":[116],"extending":[117],"Putnam\u2011style":[119],"closed\u2011form":[120],"insight":[121],"to":[122],"physical":[124],"domain.":[125],"Author:":[126],"Andrew":[127],"Stewart":[128],"Caldin,":[129],"Independent":[130],"Researcher,":[131],"UK.":[132],"Part":[133],"Intelligence":[137],"Research":[138],"series.":[139],"Platform:":[140],"e8intelligence.com":[141]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-11-05T00:00:00"}
