{"id":"https://openalex.org/W7225464894","doi":"https://doi.org/10.48550/arxiv.2611.10408","title":"Sharp Logarithmic-Product Bounds for List Replicability of Sign Matrices","display_name":"Sharp Logarithmic-Product Bounds for List Replicability of Sign Matrices","publication_year":2026,"publication_date":"2026-11-07","ids":{"openalex":"https://openalex.org/W7225464894","doi":"https://doi.org/10.48550/arxiv.2611.10408"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2611.10408","doi":"https://doi.org/10.48550/arxiv.2611.10408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.10408","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2611.10408","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101622483","display_name":"Guangjian Zhang","orcid":"https://orcid.org/0000-0002-4540-8179","observed_orcids":["https://orcid.org/0000-0002-4540-8179","https://orcid.org/0009-0007-5514-6524"]},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Zhang, Guangjian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101622483"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3571999967098236,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.3571999967098236,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.1768999993801117,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.155799999833107,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/sign-matrices","display_name":"sign matrices","score":0.906000018119812},{"id":"https://openalex.org/keywords/facial-width","display_name":"facial width","score":0.8109999895095825},{"id":"https://openalex.org/keywords/equivariant-index","display_name":"equivariant index","score":0.777999997138977},{"id":"https://openalex.org/keywords/learning-rules","display_name":"learning rules","score":0.5289999842643738},{"id":"https://openalex.org/keywords/combinatorial-bounds","display_name":"combinatorial bounds","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7541000247001648},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6492000222206116},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.628000020980835},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5770999789237976},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5485000014305115},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5446000099182129},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5195000171661377},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.47029998898506165},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.4268999993801117},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.40470001101493835},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3944999873638153},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.31679999828338623},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.2897999882698059},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2879999876022339}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.48550/arxiv.2611.10408","doi":"https://doi.org/10.48550/arxiv.2611.10408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.10408","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"},{"id":"doi:10.5281/zenodo.24025019","doi":"https://doi.org/10.5281/zenodo.24025019","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24025019","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24025020","doi":"https://doi.org/10.5281/zenodo.24025020","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24025020","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.48550/arxiv.2611.10408","doi":"https://doi.org/10.48550/arxiv.2611.10408","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.10408","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7212194465","https://openalex.org/W7222399478","https://openalex.org/W7165040182","https://openalex.org/W7163644034","https://openalex.org/W7223669425","https://openalex.org/W7202142863","https://openalex.org/W4416417318","https://openalex.org/W7133217296","https://openalex.org/W7110302772","https://openalex.org/W4415277502"],"abstract_inverted_index":{"List":[0],"replicability":[1,36,125,149],"measures":[2],"how":[3],"many":[4],"accurate":[5,113],"hypotheses":[6],"suffice":[7],"to":[8,177],"contain":[9],"the":[10,42,58,84,100,131,156,160,188],"output":[11],"of":[12,26,45,57,86,190],"a":[13,87,106],"learning":[14,117],"rule":[15],"with":[16,68,147],"arbitrarily":[17],"high":[18],"confidence.":[19],"We":[20,164],"prove":[21],"that":[22],"every":[23],"nonempty":[24],"class":[25],"$m$":[27],"binary":[28],"concepts":[29],"on":[30,183],"$n$":[31],"domain":[32],"points":[33],"has":[34],"list":[35,124,148],"at":[37],"most":[38],"$805\\ln(2m)\\ln(2n)$.":[39],"This":[40],"resolves":[41],"logarithmic-product":[43],"conjecture":[44],"Blondal,":[46],"Hatami,":[47,48],"Lalov,":[49],"and":[50,64,105,116,134,151,168,186],"Tretiak.":[51],"Hanner":[52],"matrices":[53,63],"give":[54,172],"lower":[55],"bounds":[56,175],"same":[59],"order,":[60],"for":[61,65],"square":[62],"explicit":[66,145],"families":[67],"unequal":[69],"logarithmic":[70],"aspect":[71],"ratios.":[72],"The":[73],"upper":[74,174],"bound":[75],"is":[76,162],"obtained":[77],"by":[78],"constructing":[79],"nested":[80],"acyclic":[81],"sets":[82,101],"in":[83],"faces":[85],"cube.":[88],"A":[89],"critical-point":[90],"estimate":[91],"supplies":[92],"highly":[93],"connected":[94],"regions,":[95],"weighted":[96],"cell":[97],"attachments":[98],"keep":[99],"compatible":[102],"across":[103],"faces,":[104],"cubical":[107],"carrier":[108],"theorem":[109],"converts":[110],"them":[111],"into":[112,126],"finite":[114],"covers":[115],"rules.":[118],"Appending":[119],"one":[120],"constant":[121],"coordinate":[122],"turns":[123],"an":[127],"exact":[128,138,181],"geometric":[129],"quantity,":[130],"face":[132],"width,":[133],"graph-orientation":[135],"classes":[136,146],"satisfy":[137],"product":[139],"formulas.":[140],"In":[141],"particular,":[142],"there":[143],"are":[144],"$4k+1$":[150],"equivariant":[152],"index":[153,189],"$3k$,":[154],"so":[155],"additive":[157],"gap":[158],"between":[159],"two":[161],"unbounded.":[163],"also":[165],"develop":[166],"entropy-tilting":[167],"two-sided":[169],"Gibbs":[170],"constructions,":[171],"combinatorial":[173],"adapted":[176],"structured":[178],"matrices,":[179],"compute":[180],"values":[182],"classical":[184],"families,":[185],"study":[187],"Paley":[191],"matrices.":[192]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-08T00:00:00"}
