{"id":"https://openalex.org/W7119216670","doi":"https://doi.org/10.1137/1.9781611978964.11","title":"Most Juntas Saturate the Hardcore Lemma","display_name":"Most Juntas Saturate the Hardcore Lemma","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7119216670","doi":"https://doi.org/10.1137/1.9781611978964.11"},"language":"en","primary_location":{"id":"doi:10.1137/1.9781611978964.11","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611978964.11","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2026 SIAM Symposium on Simplicity in Algorithms (SOSA)","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2510.25165","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057163359","display_name":"Vinayak M. Kumar","orcid":"https://orcid.org/0009-0002-7309-5648"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vinayak M. Kumar","raw_affiliation_strings":["University of Texas at Austin"],"affiliations":[{"raw_affiliation_string":"University of Texas at Austin","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057163359"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36038186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"142","last_page":"150"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9352999925613403,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9352999925613403,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.012900000438094139,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.005900000222027302,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.9208999872207642},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48829999566078186},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.25189998745918274},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.23170000314712524},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.2160000056028366}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.9208999872207642},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6428999900817871},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47609999775886536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46160000562667847},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3109000027179718},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.23170000314712524},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2160000056028366},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.20810000598430634}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/1.9781611978964.11","is_oa":false,"landing_page_url":"https://doi.org/10.1137/1.9781611978964.11","pdf_url":null,"source":{"id":"https://openalex.org/S4306463922","display_name":"Society for Industrial and Applied Mathematics eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2026 SIAM Symposium on Simplicity in Algorithms (SOSA)","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2510.25165","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.25165","pdf_url":"https://arxiv.org/pdf/2510.25165","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2510.25165","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.25165","pdf_url":"https://arxiv.org/pdf/2510.25165","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.45796433091163635}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Consider":[0],"a":[1,18,62,78],"function":[2,26],"that":[3,45,71],"is":[4,27,57,75],"mildly":[5],"hard":[6,29],"for":[7,30,77],"size-\\(s\\)":[8],"circuits.":[9],"For":[10],"sufficiently":[11],"large":[12],"\\(s\\),":[13],"Impagliazzo\u2019s":[14],"hardcore":[15,73],"lemma":[16,56,74],"provides":[17],"subset":[19],"of":[20,32,66],"inputs":[21],"on":[22],"which":[23],"the":[24,46,72],"same":[25],"extremely":[28],"circuits":[31],"size":[33,47],"\\(s'":[34],"\\ll":[35],"s\\).":[36],"Blanc,":[37],"Hayderi,":[38],"Koch,":[39],"and":[40],"Tan":[41],"[FOCS,":[42],"2024]":[43],"proved":[44],"degradation":[48],"from":[49],"\\(s\\)":[50],"to":[51],"\\(s'\\)":[52],"present":[53],"in":[54],"this":[55,67],"quantitatively":[58],"tight.":[59],"We":[60],"give":[61],"much":[63],"simpler":[64],"proof":[65],"fact":[68],"by":[69],"showing":[70],"tight":[76],"random":[79],"junta":[80],"with":[81],"high":[82],"probability.":[83]},"counts_by_year":[],"updated_date":"2026-01-08T20:10:11.968330","created_date":"2026-01-08T00:00:00"}