{"id":"https://openalex.org/W7223808065","doi":"https://doi.org/10.5281/zenodo.23684394","title":"196884: The Numerical Bridge Between the Monster Group and Modular Forms \u2014 E8 Intelligence Research","display_name":"196884: The Numerical Bridge Between the Monster Group and Modular Forms \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7223808065","doi":"https://doi.org/10.5281/zenodo.23684394"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23684394","doi":"https://doi.org/10.5281/zenodo.23684394","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23684394","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.23684394","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/T11428","display_name":"Advanced Mathematical Identities","score":0.43869999051094055,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.43869999051094055,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.14090000092983246,"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/T10849","display_name":"Finite Group Theory Research","score":0.13210000097751617,"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/monster-group","display_name":"Monster group","score":0.8140000104904175},{"id":"https://openalex.org/keywords/monstrous-moonshine","display_name":"monstrous moonshine","score":0.9490000009536743},{"id":"https://openalex.org/keywords/modular-forms","display_name":"modular forms","score":0.7020000219345093},{"id":"https://openalex.org/keywords/leech-lattice","display_name":"Leech lattice","score":0.8259999752044678},{"id":"https://openalex.org/keywords/kissing-number","display_name":"kissing number","score":0.8799999952316284},{"id":"https://openalex.org/keywords/e8-root-system","display_name":"E8 root system","score":0.9010000228881836},{"id":"https://openalex.org/keywords/lattice-vertex-operator-algebras","display_name":"lattice vertex operator algebras","score":0.6140000224113464},{"id":"https://openalex.org/keywords/cholesky-decomposition","display_name":"Cholesky decomposition","score":0.7620000243186951}],"concepts":[{"id":"https://openalex.org/C2778626061","wikidata":"https://www.wikidata.org/wiki/Q6902671","display_name":"Monster","level":2,"score":0.8442999720573425},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.608299970626831},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5971999764442444},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5849999785423279},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.5221999883651733},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47049999237060547},{"id":"https://openalex.org/C2776420598","wikidata":"https://www.wikidata.org/wiki/Q25289","display_name":"Cornish","level":2,"score":0.40619999170303345},{"id":"https://openalex.org/C180746962","wikidata":"https://www.wikidata.org/wiki/Q243147","display_name":"Leech","level":2,"score":0.400299996137619},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38609999418258667},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.36480000615119934},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.362199991941452},{"id":"https://openalex.org/C2779478453","wikidata":"https://www.wikidata.org/wiki/Q6889748","display_name":"Modularity (biology)","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.3481000065803528},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.336899995803833},{"id":"https://openalex.org/C205724471","wikidata":"https://www.wikidata.org/wiki/Q208454","display_name":"Abacus (architecture)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C204160518","wikidata":"https://www.wikidata.org/wiki/Q122653","display_name":"Numeral system","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.31189998984336853},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3050000071525574},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.29109999537467957},{"id":"https://openalex.org/C2778120072","wikidata":"https://www.wikidata.org/wiki/Q2858150","display_name":"Aside","level":2,"score":0.2815000116825104},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2791999876499176},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.26019999384880066},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23684394","doi":"https://doi.org/10.5281/zenodo.23684394","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23684394","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.23684395","doi":"https://doi.org/10.5281/zenodo.23684395","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23684395","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.23684394","doi":"https://doi.org/10.5281/zenodo.23684394","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23684394","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7220400423","https://openalex.org/W7170085325","https://openalex.org/W7223150195","https://openalex.org/W7170160953","https://openalex.org/W7169752944","https://openalex.org/W7223241671","https://openalex.org/W7220466585","https://openalex.org/W7169879112","https://openalex.org/W7219862636","https://openalex.org/W7214223680"],"abstract_inverted_index":{"FINDING:":[0,151],"196884":[1,13,48,62,66,89],"is":[2,98,156],"the":[3,8,19,30,92,99,114,172],"first":[4],"nontrivial":[5,59],"coefficient":[6],"of":[7,32,57,171],"modular":[9,27,94],"j-invariant,":[10],"whose":[11],"decomposition":[12,153],"=":[14,38,49,54,63,67,73,80,124,128,130],"196883":[15,50,53],"+":[16,40,42,44,46,51,69],"1":[17],"links":[18],"Monster":[20,60],"group's":[21],"smallest":[22,58],"faithful":[23],"representation":[24],"(196883)":[25],"to":[26,110,146],"forms":[28],"\u2014":[29,139],"seed":[31],"Monstrous":[33],"Moonshine.":[34],"|":[35,82,148],"MATH:":[36],"j(\u03c4)":[37],"q\u207b\u00b9":[39],"744":[41],"196884q":[43],"21493760q\u00b2":[45],"\u2026;":[47],"1;":[52],"47\u00b759\u00b771":[55],"(dimension":[56],"irrep);":[61],"2\u00b2\u00b73\u00b761\u00b7269;":[64],"also":[65],"196560":[68,72,84,138],"324":[70,79],"where":[71],"Leech":[74,96,137],"lattice":[75,97,103],"kissing":[76,86,134],"number":[77,135,162],"and":[78,88,126],"18\u00b2.":[81],"CONNECTION:":[83],"(Leech":[85],"number)":[87],"sit":[90],"in":[91,108,113,142],"same":[93],"coefficient;":[95],"24-dim":[100],"even":[101],"unimodular":[102],"with":[104],"no":[105],"roots,":[106],"dual":[107],"moonshine":[109],"E8's":[111],"role":[112],"8-dim":[115],"case.":[116],"E8":[117,133,173],"root":[118],"system":[119],"has":[120],"240":[121,123],"roots;":[122],"2\u00b7120,":[125],"120":[127],"8\u00b715":[129],"8\u00b7T\u2085":[131],"(triangular).":[132],"240,":[136],"both":[140],"appear":[141],"lattice/VOA":[143],"structures":[144],"tied":[145],"moonshine.":[147],"DEPTH:":[149],"9":[150],"Triangular":[152],"(LU,":[154],"Cholesky-style)":[155],"a":[157],"general":[158],"linear-algebra":[159],"factorization;":[160],"triangular":[161],"Author:":[163],"Andrew":[164],"Stewart":[165],"Caldin,":[166],"Independent":[167],"Researcher,":[168],"UK.":[169],"Part":[170],"Intelligence":[174],"Research":[175],"series.":[176],"Platform:":[177],"e8intelligence.com":[178]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-28T00:00:00"}
