{"id":"https://openalex.org/W1525612270","doi":"https://doi.org/10.1007/s10817-017-9404-x","title":"A Formally Verified Proof of the Central Limit Theorem","display_name":"A Formally Verified Proof of the Central Limit Theorem","publication_year":2017,"publication_date":"2017-02-08","ids":{"openalex":"https://openalex.org/W1525612270","doi":"https://doi.org/10.1007/s10817-017-9404-x","mag":"1525612270"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-017-9404-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-017-9404-x","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1405.7012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003483051","display_name":"Jeremy Avigad","orcid":"https://orcid.org/0000-0003-1275-315X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jeremy Avigad","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037209402","display_name":"Johannes H\u00f6lzl","orcid":"https://orcid.org/0000-0003-0869-9250"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johannes H\u00f6lzl","raw_affiliation_strings":["Technische Universit\u00e4t M\u00fcnchen, Munich, Germany","Technische Universit\u00e4t M\u00fcnchen Munich Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technische Universit\u00e4t M\u00fcnchen Munich Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035018862","display_name":"Luke Serafin","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luke Serafin","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie Mellon University, Pittsburgh, USA"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003483051"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.2077,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.60840785,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"59","issue":"4","first_page":"389","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"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":0.994700014591217,"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/T10142","display_name":"Formal Methods in Verification","score":0.9936000108718872,"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/central-limit-theorem","display_name":"Central limit theorem","score":0.7779554128646851},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6828860640525818},{"id":"https://openalex.org/keywords/proof-assistant","display_name":"Proof assistant","score":0.6130931377410889},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.49877262115478516},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.47651970386505127},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.4720350503921509},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.42789462208747864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42602285742759705},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4174345135688782},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41345474123954773},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33553093671798706},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.3330872356891632},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.26303812861442566},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.26018857955932617},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.20954516530036926},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1063908040523529},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07571211457252502},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.059416353702545166}],"concepts":[{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.7779554128646851},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6828860640525818},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.6130931377410889},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.49877262115478516},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.47651970386505127},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4720350503921509},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.42789462208747864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42602285742759705},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4174345135688782},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41345474123954773},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33553093671798706},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.3330872356891632},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26303812861442566},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.26018857955932617},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.20954516530036926},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1063908040523529},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07571211457252502},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.059416353702545166},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10817-017-9404-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-017-9404-x","pdf_url":null,"source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1405.7012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.7012","pdf_url":"https://arxiv.org/pdf/1405.7012","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1525612270","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1405.7012.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1405.7012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1405.7012","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":"pmh:oai:arXiv.org:1405.7012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1405.7012","pdf_url":"https://arxiv.org/pdf/1405.7012","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6299999952316284}],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3982656328","display_name":null,"funder_award_id":"FA9550-12-1-0370","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4753822615","display_name":null,"funder_award_id":"FA9550-15-1-0053","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6071252945","display_name":null,"funder_award_id":"FA9550-12","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7641317265","display_name":"Proof Mining and Formal Verification","funder_award_id":"1068829","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7999580237","display_name":null,"funder_award_id":"FA9550-12-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1525612270.pdf","grobid_xml":"https://content.openalex.org/works/W1525612270.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W112168304","https://openalex.org/W166580360","https://openalex.org/W178927145","https://openalex.org/W836255558","https://openalex.org/W1511527545","https://openalex.org/W1532290481","https://openalex.org/W1537220347","https://openalex.org/W1647616909","https://openalex.org/W1755481569","https://openalex.org/W1996404651","https://openalex.org/W2105518356","https://openalex.org/W2143235494","https://openalex.org/W2174838357","https://openalex.org/W2483648716","https://openalex.org/W2496670332","https://openalex.org/W2981616527","https://openalex.org/W4242174109","https://openalex.org/W4250846042","https://openalex.org/W6822732606"],"related_works":["https://openalex.org/W3183065824","https://openalex.org/W1937733667","https://openalex.org/W2268143451","https://openalex.org/W2776461454","https://openalex.org/W1525483008","https://openalex.org/W1588278029","https://openalex.org/W3104046540","https://openalex.org/W2168509624","https://openalex.org/W287250049","https://openalex.org/W1836725053","https://openalex.org/W136503236","https://openalex.org/W1600124086","https://openalex.org/W241023240","https://openalex.org/W2038861555","https://openalex.org/W1969211016","https://openalex.org/W2625677324","https://openalex.org/W1491975900","https://openalex.org/W1556405916","https://openalex.org/W1498428138","https://openalex.org/W1585467680"],"abstract_inverted_index":null,"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}