{"id":"https://openalex.org/W7224989652","doi":"https://doi.org/10.5281/zenodo.23830955","title":"No Primary Research Found on Spectral Geometry of Congruence Subgroups \u2014 E8 Intelligence Research","display_name":"No Primary Research Found on Spectral Geometry of Congruence Subgroups \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-10-31","ids":{"openalex":"https://openalex.org/W7224989652","doi":"https://doi.org/10.5281/zenodo.23830955"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23830955","doi":"https://doi.org/10.5281/zenodo.23830955","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830955","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.23830955","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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.478300005197525,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.478300005197525,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.3637999892234802,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.12600000202655792,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spectral-geometry","display_name":"spectral geometry","score":0.7950000166893005},{"id":"https://openalex.org/keywords/congruence-subgroups","display_name":"congruence subgroups","score":0.9829999804496765},{"id":"https://openalex.org/keywords/sl-2-z","display_name":"SL2(Z)","score":0.8529999852180481},{"id":"https://openalex.org/keywords/principal-congruence-subgroups","display_name":"principal congruence subgroups","score":0.8140000104904175},{"id":"https://openalex.org/keywords/laplacian-eigenvalues","display_name":"Laplacian eigenvalues","score":0.8169999718666077},{"id":"https://openalex.org/keywords/hyperbolic-3-manifolds","display_name":"hyperbolic 3-manifolds","score":0.9940000176429749},{"id":"https://openalex.org/keywords/hyperbolic-surfaces","display_name":"hyperbolic surfaces","score":0.8420000076293945},{"id":"https://openalex.org/keywords/weyl-s-law","display_name":"Weyl law","score":0.8849999904632568},{"id":"https://openalex.org/keywords/golden-ratio","display_name":"golden ratio","score":0.7549999952316284},{"id":"https://openalex.org/keywords/e8","display_name":"E8","score":0.7110000252723694}],"concepts":[{"id":"https://openalex.org/C132074034","wikidata":"https://www.wikidata.org/wiki/Q154210","display_name":"Congruence (geometry)","level":2,"score":0.847100019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7684000134468079},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7114999890327454},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5530999898910522},{"id":"https://openalex.org/C2777941758","wikidata":"https://www.wikidata.org/wiki/Q5161000","display_name":"Congruence subgroup","level":2,"score":0.5091999769210815},{"id":"https://openalex.org/C51364350","wikidata":"https://www.wikidata.org/wiki/Q3123529","display_name":"Spectral geometry","level":2,"score":0.4851999878883362},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4138000011444092},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.4108999967575073},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.36970001459121704},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.358599990606308},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3310000002384186},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28859999775886536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2653000056743622}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23830955","doi":"https://doi.org/10.5281/zenodo.23830955","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830955","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.23830956","doi":"https://doi.org/10.5281/zenodo.23830956","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830956","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.23830955","doi":"https://doi.org/10.5281/zenodo.23830955","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23830955","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/W1978196560","https://openalex.org/W130842547","https://openalex.org/W2962705131","https://openalex.org/W2079332612","https://openalex.org/W7100266821","https://openalex.org/W1988085365","https://openalex.org/W167563646","https://openalex.org/W127598205","https://openalex.org/W7172147306","https://openalex.org/W2006370736"],"abstract_inverted_index":{"FINDING:":[0],"The":[1,37,94,142,152],"search":[2],"returned":[3],"no":[4],"primary":[5],"research":[6],"on":[7,66,123],"the":[8,55,61,64,90,104,116,121,135,169],"spectral":[9,57],"geometry":[10],"of":[11,14,19,63,73,85,120,168],"congruence":[12,48,126],"subgroups":[13,49],"SL\u2082(Z)":[15],"or":[16,81],"Laplace":[17],"eigenvalues":[18,71],"hyperbolic":[20],"3-manifolds":[21],"\u2014":[22],"only":[23,38],"tangential":[24],"lecture":[25],"titles":[26],"and":[27,45],"one":[28],"unrelated":[29],"particle-physics":[30],"paper.":[31],"|":[32,92],"MATH:":[33],"No":[34],"equations":[35],"extractable.":[36],"concrete":[39],"mathematical":[40],"object":[41,58],"named":[42],"is":[43,87,112],"SL_n(Z)":[44],"its":[46],"principal":[47],"\u0393(N)":[50],"=":[51,75,79,132,156],"ker(SL_n(Z)":[52],"\u2192":[53],"SL_n(Z/NZ));":[54],"relevant":[56],"would":[59],"be":[60],"spectrum":[62],"Laplacian":[65,122],"\u0393\\\u210d\u00b3":[67],"(or":[68],"\u0393\\\u210d\u00b2),":[69],"i.e.":[70],"\u03bb":[72,78],"\u0394\u03c6":[74],"\u03bb\u03c6":[76],"with":[77,134],"s(2\u2212s)":[80],"s(1\u2212s)":[82],"parametrization.":[83],"None":[84],"this":[86,99],"developed":[88],"in":[89,98,103],"sources.":[91],"CONNECTION:":[93],"genuine":[95],"geometric-harmony":[96],"link":[97],"domain":[100],"(not":[101],"present":[102],"sources,":[105],"so":[106],"flagged":[107],"as":[108],"context,":[109],"not":[110],"evidence)":[111],"Selberg's":[113],"3/16":[114,131],"theorem:":[115],"first":[117],"nonzero":[118],"eigenvalue":[119,146],"\u0393\\\u210d\u00b2":[124],"for":[125,150],"\u0393":[127],"satisfies":[128],"\u03bb\u2081":[129,139],"\u2265":[130,140],"0.1875,":[133],"conjectured":[136],"optimal":[137],"bound":[138],"1/4.":[141],"Weyl":[143],"law":[144],"gives":[145],"density":[147],"~":[148],"(Vol/4\u03c0)\u00b7\u03bb":[149],"surfaces.":[151],"golden":[153],"ratio":[154],"\u03c6":[155],"1.618":[157],"appears":[158],"i":[159],"Author:":[160],"Andrew":[161],"Stewart":[162],"Caldin,":[163],"Independent":[164],"Researcher,":[165],"UK.":[166],"Part":[167],"E8":[170],"Intelligence":[171],"Research":[172],"series.":[173],"Platform:":[174],"e8intelligence.com":[175]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-11-01T00:00:00"}
