{"id":"https://openalex.org/W7213495303","doi":"https://doi.org/10.48550/arxiv.2609.17795","title":"An elementary way to find a counterexample to the Jacobian Conjecture","display_name":"An elementary way to find a counterexample to the Jacobian Conjecture","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213495303","doi":"https://doi.org/10.48550/arxiv.2609.17795"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17795","pdf_url":"https://arxiv.org/pdf/2609.17795","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.17795","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027596937","display_name":"Arno van den Essen","orcid":"https://orcid.org/0000-0003-4212-5728","observed_orcids":["https://orcid.org/0000-0003-4212-5728"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Essen, Arno van den","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5027596937"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.6172000169754028,"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":0.6172000169754028,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.1307000070810318,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.11289999634027481,"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/jacobian-conjecture","display_name":"Jacobian conjecture","score":0.9900000095367432},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.9739999771118164},{"id":"https://openalex.org/keywords/polynomial-maps","display_name":"polynomial maps","score":0.6740000247955322},{"id":"https://openalex.org/keywords/injectivity-of-polynomial-maps","display_name":"injectivity of polynomial maps","score":0.5299999713897705},{"id":"https://openalex.org/keywords/coordinate-transformation","display_name":"coordinate transformation","score":0.4059999883174896}],"concepts":[{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.9696999788284302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7563999891281128},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.733299970626831},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5152000188827515},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44909998774528503},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3874000012874603},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.375},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.325300008058548},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2329999953508377}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17795","pdf_url":"https://arxiv.org/pdf/2609.17795","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.17795","doi":"https://doi.org/10.48550/arxiv.2609.17795","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17795","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17795","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17795","pdf_url":"https://arxiv.org/pdf/2609.17795","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213495303.pdf","grobid_xml":"https://content.openalex.org/works/W7213495303.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7172413910"],"related_works":["https://openalex.org/W7169793437","https://openalex.org/W126242048","https://openalex.org/W2963967086","https://openalex.org/W2145311877","https://openalex.org/W2044419029","https://openalex.org/W2751910890","https://openalex.org/W4407130495","https://openalex.org/W7030157957","https://openalex.org/W1562855000","https://openalex.org/W4402012655"],"abstract_inverted_index":{"We":[0],"show":[1],"how":[2],"a":[3],"counterexample":[4],"to":[5],"the":[6,25],"Jacobian":[7],"Conjecture":[8],"can":[9],"be":[10],"found":[11,27],"by":[12,28],"elementary":[13],"mathematics.":[14],"The":[15],"example":[16,26],"we":[17],"find":[18],"is,":[19],"apart":[20],"from":[21],"linear":[22],"coordinate":[23],"changes":[24],"Levent":[29],"Alp\u00f6ge.":[30]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}