{"id":"https://openalex.org/W3109254761","doi":"https://doi.org/10.3390/e24050679","title":"Gull\u2019s Theorem Revisited","display_name":"Gull\u2019s Theorem Revisited","publication_year":2022,"publication_date":"2022-05-11","ids":{"openalex":"https://openalex.org/W3109254761","doi":"https://doi.org/10.3390/e24050679","mag":"3109254761","pmid":"https://pubmed.ncbi.nlm.nih.gov/35626563"},"language":"en","primary_location":{"id":"doi:10.3390/e24050679","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050679","pdf_url":"https://www.mdpi.com/1099-4300/24/5/679/pdf?version=1652337809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/5/679/pdf?version=1652337809","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042561088","display_name":"Richard D. Gill","orcid":"https://orcid.org/0000-0001-5821-9986"},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Richard D. Gill","raw_affiliation_strings":["Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands"],"raw_orcid":"https://orcid.org/0000-0001-5821-9986","affiliations":[{"raw_affiliation_string":"Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042561088"],"corresponding_institution_ids":["https://openalex.org/I121797337"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.8616,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.69483005,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"5","first_page":"679","last_page":"679"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10622","display_name":"Quantum Mechanics and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.991100013256073,"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":0.9635000228881836,"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/randomness","display_name":"Randomness","score":0.6349837183952332},{"id":"https://openalex.org/keywords/argument","display_name":"Argument (complex analysis)","score":0.5412883162498474},{"id":"https://openalex.org/keywords/hidden-variable-theory","display_name":"Hidden variable theory","score":0.4689734876155853},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4577942490577698},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4559098780155182},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.45448067784309387},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4524397850036621},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4453304708003998},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41836249828338623},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3250684440135956},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2875083088874817},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.20329606533050537}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.6349837183952332},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.5412883162498474},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.4689734876155853},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4577942490577698},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4559098780155182},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.45448067784309387},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4524397850036621},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4453304708003998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41836249828338623},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3250684440135956},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2875083088874817},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.20329606533050537},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.3390/e24050679","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050679","pdf_url":"https://www.mdpi.com/1099-4300/24/5/679/pdf?version=1652337809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2012.00719","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.00719","pdf_url":"https://arxiv.org/pdf/2012.00719","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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmid:35626563","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35626563","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:44b61673abfb4a16805de8813234d7c4","is_oa":true,"landing_page_url":"https://doaj.org/article/44b61673abfb4a16805de8813234d7c4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 24, Iss 5, p 679 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/24/5/679/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e24050679","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy; Volume 24; Issue 5; Pages: 679","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:9140976","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9140976","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:scholarlypublications.universiteitleiden.nl:item_3514966","is_oa":true,"landing_page_url":"https://hdl.handle.net/1887/3514966","pdf_url":null,"source":{"id":"https://openalex.org/S4306400850","display_name":"Leiden Repository (Leiden University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I121797337","host_organization_name":"Leiden University","host_organization_lineage":["https://openalex.org/I121797337"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Article / Letter to editor"},{"id":"pmh:ul:oai:scholarlypublications.universiteitleiden.nl:item_3514966","is_oa":true,"landing_page_url":"http://hdl.handle.net/1887/3514966","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, 24(5):679. MDPI","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/e24050679","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24050679","pdf_url":"https://www.mdpi.com/1099-4300/24/5/679/pdf?version=1652337809","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3109254761.pdf"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1563590311","https://openalex.org/W1709784975","https://openalex.org/W1877373460","https://openalex.org/W1980739194","https://openalex.org/W1982965844","https://openalex.org/W1986407511","https://openalex.org/W2001561850","https://openalex.org/W2025073632","https://openalex.org/W2028815089","https://openalex.org/W2059858750","https://openalex.org/W2091785906","https://openalex.org/W2115403962","https://openalex.org/W2117149141","https://openalex.org/W2135830616","https://openalex.org/W2226728039","https://openalex.org/W2484987773","https://openalex.org/W2486886792","https://openalex.org/W2505677996","https://openalex.org/W2522295346","https://openalex.org/W2998123347","https://openalex.org/W3010143612","https://openalex.org/W3097599855","https://openalex.org/W3099819226","https://openalex.org/W3102592148","https://openalex.org/W3104564933","https://openalex.org/W3106413244","https://openalex.org/W3139301977","https://openalex.org/W3217793055","https://openalex.org/W4212911762","https://openalex.org/W4285719527","https://openalex.org/W6722135110","https://openalex.org/W6724555332","https://openalex.org/W6727623715"],"related_works":["https://openalex.org/W3034924094","https://openalex.org/W3094954546","https://openalex.org/W1488708774","https://openalex.org/W1982811510","https://openalex.org/W4391100477","https://openalex.org/W2402189625","https://openalex.org/W4327779705","https://openalex.org/W4310560702","https://openalex.org/W3006682748","https://openalex.org/W1561563106"],"abstract_inverted_index":{"In":[0,57],"2016,":[1],"Steve":[2],"Gull":[3],"has":[4,6],"outlined":[5,7],"a":[8,24,34,38,82,86,111,144,168,178],"proof":[9,164],"of":[10,88,122,133,136,143,147,149,158,161,177],"Bell's":[11,20,101],"theorem":[12,21,36],"using":[13],"Fourier":[14],"theory.":[15],"Gull's":[16,163],"philosophy":[17],"is":[18],"that":[19,107],"(or":[22],"perhaps":[23],"key":[25],"lemma":[26],"in":[27,40,66,72,79,100,140],"its":[28],"proof)":[29],"can":[30],"be":[31],"seen":[32],"as":[33,174],"no-go":[35],"for":[37],"project":[39],"distributed":[41],"computing":[42],"with":[43],"classical,":[44],"not":[45],"quantum,":[46],"computers.":[47,126],"We":[48,69],"present":[49],"his":[50,58,80],"argument,":[51,59],"correcting":[52],"misprints":[53],"and":[54,124],"filling":[55],"gaps.":[56],"there":[60],"were":[61],"two":[62,93,97],"completely":[63],"separated":[64],"computers":[65,94],"the":[67,77,92,96,116,134,141,154,159,175,182],"network.":[68],"need":[70,130],"three":[71],"order":[73],"to":[74,91],"fill":[75],"all":[76],"gaps":[78],"proof:":[81],"third":[83,169],"computer":[84,108],"supplies":[85],"stream":[87],"random":[89],"numbers":[90,119],"representing":[95],"measurement":[98],"stations":[99],"work.":[102],"One":[103],"could":[104],"also":[105],"imagine":[106],"replaced":[109],"by":[110],"cloned,":[112],"virtual":[113],"computer,":[114],"generating":[115],"same":[117],"pseudo-random":[118],"within":[120],"each":[121],"Alice":[123],"Bob's":[125],"Either":[127],"way,":[128],"we":[129],"an":[131,172],"assumption":[132],"presence":[135],"shared":[137],"i.i.d.":[138,150],"randomness":[139],"form":[142],"synchronised":[145],"sequence":[146,160],"realisations":[148],"hidden":[151,183],"variables":[152],"underlying":[153],"otherwise":[155],"deterministic":[156],"physics":[157],"trials.":[162],"then":[165],"just":[166],"needs":[167],"step:":[170],"rewriting":[171],"expectation":[173,176,180],"conditional":[179],"given":[181],"variables.":[184]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}