{"id":"https://openalex.org/W7224129043","doi":"https://doi.org/10.48550/arxiv.2610.37634","title":"UPP$^{\\text{cc}}$ is Not Closed Under Intersection","display_name":"UPP$^{\\text{cc}}$ is Not Closed Under Intersection","publication_year":2026,"publication_date":"2026-10-27","ids":{"openalex":"https://openalex.org/W7224129043","doi":"https://doi.org/10.48550/arxiv.2610.37634"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37634","pdf_url":"https://arxiv.org/pdf/2610.37634","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.37634","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066860235","display_name":"Mark Bun","orcid":"https://orcid.org/0000-0002-5855-8045","observed_orcids":["https://orcid.org/0000-0002-5855-8045"]},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bun, Mark","raw_affiliation_strings":["Boston University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston University","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012729003","display_name":"Mandar Juvekar","orcid":"https://orcid.org/0000-0002-1603-1843","observed_orcids":["https://orcid.org/0000-0002-1603-1843"]},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Juvekar, Mandar","raw_affiliation_strings":["Boston University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Boston University","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9916999936103821,"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":0.9916999936103821,"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":0.0013000000035390258,"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"}},{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.0012000000569969416,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rotational-symmetry","display_name":"rotational symmetry","score":0.5400000214576721},{"id":"https://openalex.org/keywords/sign-matrices","display_name":"sign matrices","score":0.44999998807907104},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.3919999897480011}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8248000144958496},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.7581999897956848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7020999789237976},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.6287999749183655},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5544000267982483},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5374000072479248},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.48330000042915344},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.477400004863739},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4726000130176544},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.46380001306533813},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.39899998903274536},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.3508000075817108},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3077999949455261},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.30730000138282776},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.2856999933719635},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2800000011920929},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.27300000190734863},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.2711000144481659},{"id":"https://openalex.org/C44083865","wikidata":"https://www.wikidata.org/wiki/Q3853443","display_name":"Mean reciprocal rank","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2619999945163727}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.37634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37634","pdf_url":"https://arxiv.org/pdf/2610.37634","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.2610.37634","doi":"https://doi.org/10.48550/arxiv.2610.37634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37634","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.37634","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37634","pdf_url":"https://arxiv.org/pdf/2610.37634","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224129043.pdf","grobid_xml":"https://content.openalex.org/works/W7224129043.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2949181974","https://openalex.org/W2949826851","https://openalex.org/W6910510361","https://openalex.org/W2117822564","https://openalex.org/W2021360967","https://openalex.org/W1754706138","https://openalex.org/W2575583391","https://openalex.org/W2888350691","https://openalex.org/W3046506586","https://openalex.org/W1507889269"],"abstract_inverted_index":{"The":[0,100],"sign":[1,41,50,82,113,142,155,172,178,190],"rank":[2,12,42,51,83,114],"of":[3,13,61,75,81,115,122,124,140,195],"a":[4,14,116,135],"${\\pm":[5],"1}$-valued":[6],"matrix":[7,16,33,60,117],"$A$":[8,20,34,67],"is":[9,57,95,107],"the":[10,58,62,73,76,79,91,112,119,145,164,177],"minimum":[11],"real":[15],"that":[17,45,90],"agrees":[18],"with":[19,35],"entrywise":[21],"in":[22],"sign.":[23],"For":[24],"every":[25],"sufficiently":[26],"large":[27],"$d$,":[28],"we":[29],"give":[30],"an":[31,158],"explicit":[32,188],"$2^{\u0398(d^2)}$":[36],"rows":[37,126],"and":[38,40,71,127,131],"columns":[39,128],"$\u0398(d)$":[43],"such":[44],"$A":[46,54],"\\land":[47,55],"A$":[48,56],"has":[49],"$2^{\u0398(d)}$.":[52],"Here,":[53],"communication":[59,86,92],"problem":[63,152],"obtained":[64],"by":[65,129],"evaluating":[66],"on":[68,144,163],"disjoint":[69],"inputs":[70],"taking":[72],"conjunction":[74],"results.":[77],"As":[78],"logarithm":[80],"characterizes":[84],"unbounded-error":[85],"complexity,":[87],"this":[88,151],"implies":[89],"class":[93],"$\\mathsf{UPP}^{\\mathsf{cc}}$":[94],"not":[96],"closed":[97],"under":[98],"intersection.":[99],"starting":[101],"point":[102],"for":[103,138],"our":[104],"lower":[105],"bound":[106,162,168],"Forster's":[108],"method,":[109],"which":[110],"relates":[111],"to":[118,153,184,187],"average":[120,165],"margin":[121],"representations":[123],"its":[125],"points":[130],"halfspaces.":[132,197],"We":[133],"study":[134],"continuous":[136],"analog":[137],"conjunctions":[139],"inner-product":[141],"tests":[143],"unit":[146],"sphere.":[147],"Rotational":[148],"symmetry":[149],"connects":[150],"polynomial":[154],"representations,":[156],"yielding":[157],"exponentially":[159],"small":[160],"upper":[161],"margin.":[166],"This":[167],"holds":[169],"even":[170],"when":[171],"constraints":[173],"are":[174],"relaxed":[175],"near":[176],"tests'":[179],"decision":[180],"boundary,":[181],"allowing":[182],"us":[183],"transfer":[185],"it":[186],"finite":[189],"matrices":[191],"arising":[192],"from":[193],"intersections":[194],"integer":[196]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-29T00:00:00"}
