{"id":"https://openalex.org/W7221079263","doi":"https://doi.org/10.48550/arxiv.2610.12037","title":"Hyperplane winning for bad in manifolds","display_name":"Hyperplane winning for bad in manifolds","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221079263","doi":"https://doi.org/10.48550/arxiv.2610.12037"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.12037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12037","pdf_url":"https://arxiv.org/pdf/2610.12037","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/2610.12037","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102744977","display_name":"Shreyasi Datta","orcid":"https://orcid.org/0000-0002-8937-5532","observed_orcids":["https://orcid.org/0000-0002-8937-5532"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Datta, Shreyasi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102553880","display_name":"Liyang Shao","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shao, Liyang","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":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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8223000168800354,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.8223000168800354,"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":0.07010000199079514,"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":0.03180000185966492,"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/diophantine-approximation","display_name":"Diophantine approximation","score":0.8679999709129333},{"id":"https://openalex.org/keywords/affine-subspaces","display_name":"affine subspaces","score":0.9909999966621399},{"id":"https://openalex.org/keywords/diophantine-condition","display_name":"Diophantine conditions","score":0.8610000014305115},{"id":"https://openalex.org/keywords/higher-dimensional-manifolds","display_name":"higher-dimensional manifolds","score":0.7549999952316284}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.9016000032424927},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7677000164985657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7578999996185303},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7317000031471252},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6729000210762024},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5631999969482422},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44999998807907104},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3903999924659729},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38359999656677246},{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.36899998784065247},{"id":"https://openalex.org/C207221997","wikidata":"https://www.wikidata.org/wiki/Q938614","display_name":"Affine combination","level":3,"score":0.3528999984264374},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.3086000084877014},{"id":"https://openalex.org/C169611556","wikidata":"https://www.wikidata.org/wiki/Q230689","display_name":"Contractible space","level":2,"score":0.30079999566078186},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C102966492","wikidata":"https://www.wikidata.org/wiki/Q1227061","display_name":"Diophantine approximation","level":3,"score":0.28349998593330383},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.275299996137619},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.26989999413490295}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.12037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12037","pdf_url":"https://arxiv.org/pdf/2610.12037","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.2610.12037","doi":"https://doi.org/10.48550/arxiv.2610.12037","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.12037","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:2610.12037","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12037","pdf_url":"https://arxiv.org/pdf/2610.12037","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":[{"id":"https://openalex.org/G7483793068","display_name":"The density of rational points near manifolds and applications","funder_award_id":"EP/Y016769/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221079263.pdf","grobid_xml":"https://content.openalex.org/works/W7221079263.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4384920020","https://openalex.org/W7220725084"],"related_works":["https://openalex.org/W7128718840","https://openalex.org/W2270682479","https://openalex.org/W2037384923","https://openalex.org/W2268075884","https://openalex.org/W3026314180","https://openalex.org/W2610817116","https://openalex.org/W3139516844","https://openalex.org/W4300451549","https://openalex.org/W2896057470","https://openalex.org/W7128709754"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2],"hyperplane":[3],"winning":[4],"property":[5],"of":[6,29],"weighted":[7],"badly":[8],"approximable":[9],"vectors":[10],"inside":[11],"nondegenerate":[12],"analytic":[13],"manifolds":[14],"and":[15],"affine":[16,35],"subspaces":[17],"satisfying":[18],"almost":[19],"optimal":[20],"Diophantine":[21],"conditions.":[22],"This,":[23],"in":[24,41],"particular,":[25],"answers":[26],"a":[27],"conjecture":[28],"Badziahin--Velani":[30],"for":[31],"higher-dimensional":[32],"manifolds,":[33],"including":[34],"cases":[36],"that":[37],"were":[38],"understood":[39],"only":[40],"$\\mathbb{R}^2$.":[42]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}
