{"id":"https://openalex.org/W7220660690","doi":"https://doi.org/10.48550/arxiv.2610.05474","title":"Presenting a proof of the Kannan-Lovasz-Simonovits conjecture","display_name":"Presenting a proof of the Kannan-Lovasz-Simonovits conjecture","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220660690","doi":"https://doi.org/10.48550/arxiv.2610.05474"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05474","pdf_url":"https://arxiv.org/pdf/2610.05474","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/2610.05474","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058817276","display_name":"Pierre Bizeul","orcid":"https://orcid.org/0009-0002-5744-4254","observed_orcids":["https://orcid.org/0009-0002-5744-4254"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bizeul, Pierre","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059794784","display_name":"Bo\u2019az Klartag","orcid":"https://orcid.org/0000-0001-5488-2115","observed_orcids":["https://orcid.org/0000-0001-5488-2115"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Klartag, Boaz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5067369217","display_name":"Joseph Lehec","orcid":"https://orcid.org/0000-0001-6182-9427","observed_orcids":["https://orcid.org/0000-0001-6182-9427"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lehec, Joseph","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":10,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0003000000142492354,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/high-dimensional-geometry","display_name":"high-dimensional geometry","score":0.5410000085830688},{"id":"https://openalex.org/keywords/higher-order-derivatives","display_name":"higher-order derivatives","score":0.9470000267028809},{"id":"https://openalex.org/keywords/convex-bodies","display_name":"convex bodies","score":0.7149999737739563},{"id":"https://openalex.org/keywords/isotropic-convex-bodies","display_name":"isotropic convex bodies","score":0.5669999718666077},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"isoperimetric inequality","score":0.4690000116825104}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7354999780654907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.630299985408783},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3894999921321869},{"id":"https://openalex.org/C2779844322","wikidata":"https://www.wikidata.org/wiki/Q2919140","display_name":"Tilt (camera)","level":2,"score":0.36570000648498535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35420000553131104},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.34869998693466187},{"id":"https://openalex.org/C2777045944","wikidata":"https://www.wikidata.org/wiki/Q12170198","display_name":"Zh\u00e0ng","level":3,"score":0.34549999237060547},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C2776190703","wikidata":"https://www.wikidata.org/wiki/Q488148","display_name":"Slicing","level":2,"score":0.32330000400543213},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.31769999861717224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28850001096725464},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2822999954223633},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.2759000062942505},{"id":"https://openalex.org/C94461902","wikidata":"https://www.wikidata.org/wiki/Q2762418","display_name":"Formal proof","level":3,"score":0.2651999890804291},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05474","pdf_url":"https://arxiv.org/pdf/2610.05474","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.2610.05474","doi":"https://doi.org/10.48550/arxiv.2610.05474","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05474","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:2610.05474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05474","pdf_url":"https://arxiv.org/pdf/2610.05474","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/W7220660690.pdf","grobid_xml":"https://content.openalex.org/works/W7220660690.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W4405354901","https://openalex.org/W4414938463","https://openalex.org/W6910583003","https://openalex.org/W7171532221","https://openalex.org/W7171550111","https://openalex.org/W7172327716","https://openalex.org/W7203636665","https://openalex.org/W7215101012","https://openalex.org/W7216026011"],"related_works":["https://openalex.org/W4285545993","https://openalex.org/W2480131018","https://openalex.org/W4414688519","https://openalex.org/W4234947007","https://openalex.org/W2971022007","https://openalex.org/W7126290777","https://openalex.org/W426148383","https://openalex.org/W2148736677","https://openalex.org/W2825825416","https://openalex.org/W7214928649"],"abstract_inverted_index":{"Together":[0],"with":[1],"Bourgain's":[2],"slicing":[3],"problem":[4],"and":[5,49],"the":[6,9,40,43],"variance":[7],"conjecture,":[8],"Kannan-Lov\u00e1sz-Simonovits":[10],"(KLS)":[11],"conjecture":[12],"has":[13],"been":[14],"a":[15,31],"driving":[16],"force":[17],"for":[18],"mathematical":[19],"developments":[20],"in":[21,25,39],"high":[22],"dimensional":[23],"geometry":[24],"recent":[26,45],"decades.":[27],"We":[28],"present":[29],"here":[30],"proof":[32,41],"of":[33,54],"this":[34],"conjecture.":[35],"The":[36],"crucial":[37],"step":[38],"is":[42],"very":[44],"criterion":[46],"from":[47],"Song":[48],"Zhang":[50],"involving":[51],"high-order":[52],"derivatives":[53],"tilt":[55],"averages.":[56]},"counts_by_year":[{"year":2026,"cited_by_count":10}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-10-07T00:00:00"}