{"id":"https://openalex.org/W7225609642","doi":"https://doi.org/10.5281/zenodo.24074390","title":"The E\u2086 genus of the shorter Conway\u2013Wales lattice","display_name":"The E\u2086 genus of the shorter Conway\u2013Wales lattice","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225609642","doi":"https://doi.org/10.5281/zenodo.24074390"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24074390","doi":"https://doi.org/10.5281/zenodo.24074390","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24074390","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.24074390","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001357359","display_name":"Gerald H\u00f6hn","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I189590672","display_name":"Kansas State University","ror":"https://ror.org/05p1j8758","country_code":"US","type":"education","lineage":["https://openalex.org/I189590672"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H\u00f6hn, Gerald","raw_affiliation_strings":["Kansas State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kansas State University","institution_ids":["https://openalex.org/I189590672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001357359"],"corresponding_institution_ids":["https://openalex.org/I189590672"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9014000296592712,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9014000296592712,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.07240000367164612,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.00279999990016222,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/e6-lattice","display_name":"E6 lattice","score":0.3919999897480011},{"id":"https://openalex.org/keywords/gaussian-integers","display_name":"Gaussian integers","score":0.8410000205039978},{"id":"https://openalex.org/keywords/albert-algebra","display_name":"Albert algebra","score":0.7620000243186951},{"id":"https://openalex.org/keywords/cubic-forms","display_name":"cubic forms","score":0.6460000276565552},{"id":"https://openalex.org/keywords/cuspidal-cohomology","display_name":"cuspidal cohomology","score":0.953000009059906},{"id":"https://openalex.org/keywords/mass-formula","display_name":"mass formula","score":0.7770000100135803},{"id":"https://openalex.org/keywords/automorphism-groups","display_name":"automorphism groups","score":0.8090000152587891},{"id":"https://openalex.org/keywords/e7","display_name":"E7","score":0.7639999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8797000050544739},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.7484999895095825},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.613099992275238},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5612999796867371},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4674000144004822},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3215000033378601},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29589998722076416},{"id":"https://openalex.org/C2776196297","wikidata":"https://www.wikidata.org/wiki/Q17138781","display_name":"Twist","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.25679999589920044}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24074390","doi":"https://doi.org/10.5281/zenodo.24074390","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24074390","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.24074391","doi":"https://doi.org/10.5281/zenodo.24074391","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24074391","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.24074390","doi":"https://doi.org/10.5281/zenodo.24074390","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24074390","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/W1550937419","https://openalex.org/W2150164926","https://openalex.org/W1531760852","https://openalex.org/W2029890711","https://openalex.org/W2039588777","https://openalex.org/W2140518239","https://openalex.org/W2789947186","https://openalex.org/W2016473741","https://openalex.org/W7125970925","https://openalex.org/W7214220253"],"abstract_inverted_index":{"We":[0,137],"classify":[1],"the":[2,10,19,23,38,48,61,91,103,124,130,140,149,159,166],"definite":[3],"integral":[4,25,146],"structures":[5],"of":[6,22,37,50,57,110,129,145,148,153,165],"type":[7],"\\({}^2E_6\\)":[8],"over":[9,134],"Gaussian":[11],"integers":[12],"which":[13],"are":[14,60],"everywhere":[15],"locally":[16],"isomorphic":[17],"to":[18],"trace-parity":[20],"shortening":[21],"standard":[24],"Albert":[26],"algebra.":[27],"The":[28,54,74,113,155],"genus":[29],"has":[30,116],"exactly":[31],"eight":[32,141],"classes,":[33],"two":[34,55],"at":[35],"each":[36],"heights":[39],"\\(1\\),":[40],"\\(2\\),":[41],"\\(4\\)":[42],"and":[43,45,65,97,106,119],"\\(5\\),":[44],"we":[46],"determine":[47],"orders":[49],"their":[51,71],"automorphism":[52],"groups.":[53],"classes":[56,142],"height":[58,87],"five":[59],"shorter":[62],"Conway\u2013Wales":[63],"lattice":[64],"its":[66,120],"complex":[67],"conjugate,":[68],"equipped":[69],"with":[70],"cubic":[72],"forms.":[73],"classification":[75],"is":[76,85,99],"proved":[77],"by":[78,102,107],"a":[79,86],"Venkov-type":[80],"argument":[81],"whose":[82],"modular":[83,132],"input":[84],"bound":[88],"obtained":[89],"from":[90],"exceptional":[92,114],"theta":[93],"lift":[94,115],"for":[95,162],"\\(E_6\\times\\mathrm{SU}(2,1)\\),":[96],"it":[98],"confirmed":[100],"independently":[101],"mass":[104],"formula":[105],"an":[108],"enumeration":[109],"dyadic":[111],"neighbours.":[112],"five-dimensional":[117],"image,":[118],"cuspidal":[121,126],"part":[122],"spans":[123],"two-dimensional":[125],"cohomology":[127],"\\(H^2_{\\mathrm{cusp}}(\\Gamma_{\\mathrm{Pic}},V_{(3,3)})\\)":[128],"Picard":[131],"group":[133],"\\(\\mathbb":[135],"Z[i]\\).":[136],"also":[138],"describe":[139],"as":[143],"orbits":[144],"markings":[147],"rank-\\(56\\)":[150],"Freudenthal":[151],"module":[152],"\\(E_7\\).":[154],"archive":[156],"e6_certificate.zip":[157],"contains":[158],"computational":[160],"certificate":[161],"Section":[163],"6":[164],"paper.":[167]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
