{"id":"https://openalex.org/W4389978614","doi":"https://doi.org/10.1007/s10817-023-09689-9","title":"A Formalization of the CHSH Inequality and Tsirelson\u2019s Upper-bound in Isabelle/HOL","display_name":"A Formalization of the CHSH Inequality and Tsirelson\u2019s Upper-bound in Isabelle/HOL","publication_year":2023,"publication_date":"2023-12-19","ids":{"openalex":"https://openalex.org/W4389978614","doi":"https://doi.org/10.1007/s10817-023-09689-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-023-09689-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-023-09689-9","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04740770/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010578735","display_name":"Mnacho Echenim","orcid":"https://orcid.org/0000-0001-5765-0758"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210113150","display_name":"Laboratoire Interdisciplinaire de Physique","ror":"https://ror.org/023n9q531","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113150","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mnacho Echenim","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d\u2019H\u00e8res, France","Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d'H\u00e8res, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d\u2019H\u00e8res, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I4210113150","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d'H\u00e8res, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022852175","display_name":"Mehdi Mhalla","orcid":"https://orcid.org/0000-0003-4178-5396"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210113150","display_name":"Laboratoire Interdisciplinaire de Physique","ror":"https://ror.org/023n9q531","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210113150","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mehdi Mhalla","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d\u2019H\u00e8res, France","Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d'H\u00e8res, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d\u2019H\u00e8res, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I4210113150","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering Univ. Grenoble Alpes), LIG, 700 avenue Centrale, 38400, Saint Martin d'H\u00e8res, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5010578735","https://openalex.org/A5022852175"],"corresponding_institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I4210113150","https://openalex.org/I899635006"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.289,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51931273,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"68","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10020","display_name":"Quantum Information and Cryptography","score":0.9998000264167786,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9995999932289124,"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/hol","display_name":"HOL","score":0.7320510149002075},{"id":"https://openalex.org/keywords/chsh-inequality","display_name":"CHSH inequality","score":0.6943698525428772},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6722997426986694},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.5624126195907593},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.4943709373474121},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44809746742248535},{"id":"https://openalex.org/keywords/hidden-variable-theory","display_name":"Hidden variable theory","score":0.44780951738357544},{"id":"https://openalex.org/keywords/bell-test-experiments","display_name":"Bell test experiments","score":0.4209050238132477},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3821749985218048},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3787945508956909},{"id":"https://openalex.org/keywords/bells-theorem","display_name":"Bell's theorem","score":0.3560269773006439},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34911131858825684},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1671331524848938},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15877068042755127},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1121913492679596}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.7320510149002075},{"id":"https://openalex.org/C134265032","wikidata":"https://www.wikidata.org/wiki/Q5011347","display_name":"CHSH inequality","level":5,"score":0.6943698525428772},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6722997426986694},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.5624126195907593},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.4943709373474121},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44809746742248535},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.44780951738357544},{"id":"https://openalex.org/C11511207","wikidata":"https://www.wikidata.org/wiki/Q1054240","display_name":"Bell test experiments","level":5,"score":0.4209050238132477},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3821749985218048},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3787945508956909},{"id":"https://openalex.org/C128108043","wikidata":"https://www.wikidata.org/wiki/Q388525","display_name":"Bell's theorem","level":4,"score":0.3560269773006439},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34911131858825684},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1671331524848938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15877068042755127},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1121913492679596},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10817-023-09689-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10817-023-09689-9","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:HAL:hal-04740770v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04740770","pdf_url":"https://hal.science/hal-04740770/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Automated Reasoning, 2023, 68 (1), pp.2. &#x27E8;10.1007/s10817-023-09689-9&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04740770v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04740770","pdf_url":"https://hal.science/hal-04740770/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Automated Reasoning, 2023, 68 (1), pp.2. &#x27E8;10.1007/s10817-023-09689-9&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G1190173965","display_name":null,"funder_award_id":"France2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2191957979","display_name":"Etude de la pile quantique : Algorithmes, mod\u00e8les de calcul et simulation pour l\u2019informatique quantique","funder_award_id":"ANR-22-PETQ-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4389978614.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W32507011","https://openalex.org/W189715775","https://openalex.org/W1579218062","https://openalex.org/W1709784975","https://openalex.org/W1986407511","https://openalex.org/W1988340599","https://openalex.org/W1992074575","https://openalex.org/W1995439665","https://openalex.org/W2005719714","https://openalex.org/W2006638080","https://openalex.org/W2013644039","https://openalex.org/W2028815089","https://openalex.org/W2061969020","https://openalex.org/W2122187744","https://openalex.org/W2135830616","https://openalex.org/W2136286557","https://openalex.org/W2208188898","https://openalex.org/W2256286306","https://openalex.org/W2466331000","https://openalex.org/W2763721972","https://openalex.org/W2787461609","https://openalex.org/W2792039802","https://openalex.org/W2806477068","https://openalex.org/W2957722170","https://openalex.org/W2964428331","https://openalex.org/W3037170129","https://openalex.org/W3113530183","https://openalex.org/W3114289179","https://openalex.org/W3126077699","https://openalex.org/W3136504866","https://openalex.org/W3145563287","https://openalex.org/W3156224329","https://openalex.org/W3209192400","https://openalex.org/W4242617599","https://openalex.org/W4250850800","https://openalex.org/W4376130945","https://openalex.org/W4386525688"],"related_works":["https://openalex.org/W2553524804","https://openalex.org/W2062204191","https://openalex.org/W2371657894","https://openalex.org/W2001882148","https://openalex.org/W4318156255","https://openalex.org/W1808697997","https://openalex.org/W4385189851","https://openalex.org/W2385300201","https://openalex.org/W3098290704","https://openalex.org/W4388213449"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
