{"id":"https://openalex.org/W7204469442","doi":"https://doi.org/10.5281/zenodo.22134848","title":"Redefining Four-Dimensional Complex Structures as Discrete Sequential Frames of a Pure Three-Dimensional Vessel: A Definitive Resolution of the Hodge Conjecture","display_name":"Redefining Four-Dimensional Complex Structures as Discrete Sequential Frames of a Pure Three-Dimensional Vessel: A Definitive Resolution of the Hodge Conjecture","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204469442","doi":"https://doi.org/10.5281/zenodo.22134848"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22134848","doi":"https://doi.org/10.5281/zenodo.22134848","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22134848","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":"article-journal"},"volume":null,"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22134848","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146126028","display_name":"\u548c\u884c \u6cb3\u76db","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"\u6cb3\u76db, \u548c\u884c","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148425997","display_name":"GoogleAI","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"GoogleAI","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.77291147,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9824000000953674,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9824000000953674,"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/T12351","display_name":"Geometry and complex manifolds","score":0.009800000116229057,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0013000000035390258,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hodge-conjecture","display_name":"Hodge conjecture","score":1.0},{"id":"https://openalex.org/keywords/algebraic-cycles","display_name":"algebraic cycles","score":0.7639999985694885},{"id":"https://openalex.org/keywords/complex-structure","display_name":"complex structure","score":0.746999979019165},{"id":"https://openalex.org/keywords/four-dimensional-geometry","display_name":"four-dimensional geometry","score":0.6520000100135803},{"id":"https://openalex.org/keywords/curvature-preservation","display_name":"curvature preservation","score":0.7200000286102295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7246000170707703},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7085999846458435},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5396000146865845},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4740999937057495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C54678060","wikidata":"https://www.wikidata.org/wiki/Q1143138","display_name":"Hodge conjecture","level":4,"score":0.42289999127388},{"id":"https://openalex.org/C126042441","wikidata":"https://www.wikidata.org/wiki/Q1324888","display_name":"Frame (networking)","level":2,"score":0.40119999647140503},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.362199991941452},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30640000104904175},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2563999891281128}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.22134848","doi":"https://doi.org/10.5281/zenodo.22134848","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22134848","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":"article-journal"},{"id":"doi:10.5281/zenodo.22134932","doi":"https://doi.org/10.5281/zenodo.22134932","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22134932","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":"article-journal"},{"id":"doi:10.5281/zenodo.22151636","doi":"https://doi.org/10.5281/zenodo.22151636","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22151636","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":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22134848","doi":"https://doi.org/10.5281/zenodo.22134848","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22134848","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":"article-journal"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.6091002821922302}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,19,25],"definitive":[4],"resolution":[5],"of":[6,18,36],"the":[7,33],"Hodge":[8],"conjecture":[9],"by":[10],"redefining":[11],"higherdimensional":[12],"complex":[13],"structuresas":[14],"discrete":[15],"sequential":[16],"frames":[17],"pure":[20],"three-dimensional":[21,46],"vessel.":[22],"By":[23],"utilizing":[24],"universal":[26],"degree-3":[27],"shape-preservingscanning":[28],"matrix,":[29],"this":[30],"framework":[31],"preserves":[32],"inherent":[34],"curvature":[35],"algebraic":[37],"cycles":[38],"and":[39],"maps":[40],"four-dimensional":[41],"densitydata":[42],"onto":[43],"smooth,":[44],"non-vanishing":[45],"configurations":[47],"without":[48],"inducing":[49],"unnatural":[50],"spatial":[51],"geometricdeformations.":[52]},"counts_by_year":[],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-08-28T00:00:00"}