{"id":"https://openalex.org/W7141758171","doi":"https://doi.org/10.48550/arxiv.2603.24890","title":"Inconsistency Probability of Sparse Equations over F2","display_name":"Inconsistency Probability of Sparse Equations over F2","publication_year":2026,"publication_date":"2026-03-26","ids":{"openalex":"https://openalex.org/W7141758171","doi":"https://doi.org/10.48550/arxiv.2603.24890"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.24890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24890","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.24890","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130804646","display_name":"P. Horak","orcid":null},"institutions":[{"id":"https://openalex.org/I4210150356","display_name":"University of Washington Tacoma","ror":"https://ror.org/05n8t2628","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701","https://openalex.org/I4210150356"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Horak, P.","raw_affiliation_strings":["University of Washington, Tacoma, USA"],"affiliations":[{"raw_affiliation_string":"University of Washington, Tacoma, USA","institution_ids":["https://openalex.org/I4210150356"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086199716","display_name":"Igor Semaev","orcid":null},"institutions":[{"id":"https://openalex.org/I4432739","display_name":"University of Bergen","ror":"https://ror.org/03zga2b32","country_code":"NO","type":"education","lineage":["https://openalex.org/I4432739"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Semaev, I.","raw_affiliation_strings":["University of Bergen, Bergen, Norway"],"affiliations":[{"raw_affiliation_string":"University of Bergen, Bergen, Norway","institution_ids":["https://openalex.org/I4432739"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5130804646"],"corresponding_institution_ids":["https://openalex.org/I4210150356"],"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/T11435","display_name":"Polynomial and algebraic computation","score":0.8125,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.8125,"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/T11130","display_name":"Coding theory and cryptography","score":0.05550000071525574,"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/T10237","display_name":"Cryptography and Data Security","score":0.02419999986886978,"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/conjecture","display_name":"Conjecture","score":0.5794000029563904},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5706999897956848},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5120999813079834},{"id":"https://openalex.org/keywords/system-of-polynomial-equations","display_name":"System of polynomial equations","score":0.4408999979496002},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.4341000020503998},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.3330000042915344},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.3262999951839447}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7893000245094299},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5794000029563904},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5706999897956848},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5151000022888184},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5120999813079834},{"id":"https://openalex.org/C105335568","wikidata":"https://www.wikidata.org/wiki/Q7663735","display_name":"System of polynomial equations","level":3,"score":0.4408999979496002},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4345000088214874},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4341000020503998},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4074999988079071},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C77346573","wikidata":"https://www.wikidata.org/wiki/Q484637","display_name":"Linear equation","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C2984179964","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Probability model","level":2,"score":0.26030001044273376},{"id":"https://openalex.org/C158557763","wikidata":"https://www.wikidata.org/wiki/Q5166603","display_name":"Convolution of probability distributions","level":4,"score":0.25429999828338623}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.24890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24890","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.24890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.24890","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7495154142379761,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"n":[1],"denote":[2],"the":[3,9,19,24,34,47,53,61,93],"number":[4,10,48],"of":[5,11,27,49,69],"variables":[6,45,50],"and":[7,46,76,84,102,107,109,122],"m":[8],"equations":[12],"in":[13],"a":[14,56,111],"sparse":[15,30],"polynomial":[16,31],"system":[17,54],"over":[18,33],"binary":[20,35],"field.":[21],"We":[22],"study":[23],"inconsistency":[25,62],"probability":[26,63],"randomly":[28],"generated":[29],"systems":[32],"field,":[36],"where":[37],"each":[38],"equation":[39],"depends":[40,64],"on":[41,66,74],"at":[42],"most":[43],"k":[44],"grows.":[51],"Associating":[52],"with":[55],"hypergraph,":[57,71],"we":[58,80,96],"show":[59],"that":[60],"strongly":[65],"structural":[67],"properties":[68],"this":[70],"not":[72],"only":[73],"n,m,":[75],"k.":[77],"Using":[78],"inclusion--exclusion,":[79],"derive":[81],"general":[82],"bounds":[83],"obtain":[85],"tight":[86],"asymptotics":[87],"for":[88,100,113,119],"complete":[89],"k-uniform":[90],"hypergraphs.":[91],"In":[92],"2-sparse":[94],"case,":[95],"provide":[97],"explicit":[98],"formulas":[99],"paths":[101],"stars,":[103],"characterize":[104],"extremal":[105],"trees":[106],"forests,":[108],"conjecture":[110],"formula":[112],"cycles.":[114],"These":[115],"results":[116],"have":[117],"implications":[118],"SAT":[120],"solving":[121],"cryptanalysis.":[123]},"counts_by_year":[],"updated_date":"2026-03-28T06:16:51.555046","created_date":"2026-03-28T00:00:00"}
