{"id":"https://openalex.org/W7134832333","doi":"https://doi.org/10.48550/arxiv.2603.08693","title":"Improved Certificates for Independence Number in Semirandom Hypergraphs","display_name":"Improved Certificates for Independence Number in Semirandom Hypergraphs","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134832333","doi":"https://doi.org/10.48550/arxiv.2603.08693"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.08693","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08693","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.08693","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128653307","display_name":"Pravesh Kothari","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kothari, Pravesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059653613","display_name":"Anand Louis","orcid":"https://orcid.org/0000-0002-4727-9219"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Louis, Anand","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040520265","display_name":"Rameesh Paul","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul, Rameesh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101701586","display_name":"Prasad Raghavendra","orcid":"https://orcid.org/0009-0009-7851-0653"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raghavendra, Prasad","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":false,"cited_by_count":0,"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/T12303","display_name":"Tensor decomposition and applications","score":0.6830000281333923,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T12303","display_name":"Tensor decomposition and applications","score":0.6830000281333923,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational 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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.08330000191926956,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.04670000076293945,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.8513000011444092},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6875},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6064000129699707},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5177000164985657},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.45559999346733093},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4537000060081482},{"id":"https://openalex.org/keywords/independence-number","display_name":"Independence number","score":0.3935000002384186},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3824000060558319},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.3792000114917755}],"concepts":[{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.8513000011444092},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6848999857902527},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6064000129699707},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.536300003528595},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.45559999346733093},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4537000060081482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44679999351501465},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.3935000002384186},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35589998960494995},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.35120001435279846},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3149999976158142},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3018999993801117},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.29600000381469727},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.28630000352859497},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.08693","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08693","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.08693","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.08693","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,76],"study":[1],"the":[2,30,71,89,110,151,184,211],"problem":[3,111,185],"of":[4,12,74,116,170,186,233,246],"efficiently":[5],"certifying":[6],"upper":[7],"bounds":[8,61,152,219],"on":[9,167],"independence":[10,31],"number":[11,32],"$\\ell$-uniform":[13],"hypergraphs":[14],"in":[15,37,66,139,148,192,202,220],"semirandom":[16],"models.":[17],"This":[18,200],"is":[19,100,174,201,213],"a":[20,46,106,123,162,188,206,221,239],"notoriously":[21],"hard":[22],"problem,":[23],"with":[24,229],"efficient":[25],"algorithms":[26],"failing":[27],"to":[28,42,112,154,181,204,237],"approximate":[29],"within":[33],"an":[34,230,234],"$n^{1-\u03b5}$":[35],"factor":[36],"worst-case.":[38],"A":[39],"folklore":[40],"reduction":[41],"graph":[43],"case":[44,99],"yields":[45],"weak":[47],"$O(\\sqrt{n/p})$":[48],"bound,":[49],"and":[50,68],"spectral":[51],"certificates[GKM22]":[52],"achieve":[53],"$O(\\sqrt{n}.polylog(n)/p^{2/\\ell})$.":[54],"In":[55],"this":[56,136,182],"work,":[57,183],"we":[58,104,127,134,144,160],"prove":[59],"sharper":[60],"that":[62,173],"eliminate":[63],"logarithmic":[64,124],"factors":[65],"$n$":[67],"nearly":[69],"attain":[70],"optimal":[72],"threshold":[73,212],"$O(\\sqrt{n}/p^{1/\\ell})$.":[75],"also":[77],"show":[78],"matching":[79],"low-degree":[80,175],"polynomial":[81],"lower":[82,218],"bounds.":[83],"Our":[84],"certificates":[85,147,227],"are":[86],"designed":[87],"using":[88,129],"proofs-to-algorithms":[90],"paradigm":[91],"via":[92],"degree-$2\\ell$":[93],"Sum-of-Squares(SoS)":[94],"relaxation.":[95],"The":[96],"technically":[97],"challenging":[98],"odd-arity":[101],"hypergraphs,":[102],"where":[103,210],"employ":[105],"tensor-based":[107],"analysis":[108],"reducing":[109],"bounding":[113],"operator":[114],"norm":[115],"random":[117,178],"chaos":[118],"matrices.":[119],"Previous":[120],"bounds[AMP21,RT23]":[121],"have":[122],"dependence,":[125],"which":[126],"remove":[128],"recent":[130],"matrix":[131],"concentration":[132],"inequalities[BBvH23,BLNvH25];":[133],"believe":[135],"maybe":[137],"useful":[138],"other":[140],"hypergraph":[141],"problems.":[142],"Since":[143],"deploy":[145],"our":[146,226],"SoS":[149,231],"framework,":[150],"continue":[153],"hold":[155],"for":[156,198],"monotone":[157],"adversaries.":[158],"Additionally,":[159],"construct":[161],"'quiet'":[163],"planted":[164,190,207,240],"distribution":[165,191],"supported":[166],"independent":[168,208],"sets":[169],"size":[171],"$k=o(\\sqrt{n}/p^{1/\\ell})$":[172],"indistinguishable":[176],"from":[177],"hypergraphs.":[179],"Prior":[180],"constructing":[187],"quiet":[189],"sparse":[193],"regimes":[194],"was":[195],"open":[196],"even":[197],"graphs[JPR+22,Pot22].":[199],"contrast":[203],"recovering":[205],"set,":[209],"$k":[214],"\\gtrsim":[215],"\\sqrt{n}/p^{1/2(\\ell-1)}$":[216],"(matching":[217],"concurrent":[222],"work[FS26]).":[223],"As":[224],"application,":[225],"combine":[228],"relaxation":[232],"r-coloring":[235],"system":[236],"recover":[238],"r-colorable":[241],"subhypergraph":[242],"under":[243],"strong":[244],"adversaries":[245],"[LPR25].":[247]},"counts_by_year":[],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2026-03-11T00:00:00"}