{"id":"https://openalex.org/W2587411512","doi":"https://doi.org/10.3233/com-160065","title":"Computable copies of \u2113p","display_name":"Computable copies of \u2113p","publication_year":2016,"publication_date":"2016-09-06","ids":{"openalex":"https://openalex.org/W2587411512","doi":"https://doi.org/10.3233/com-160065","mag":"2587411512"},"language":"en","primary_location":{"id":"doi:10.3233/com-160065","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160065","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lib.dr.iastate.edu/math_pubs/259","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057460107","display_name":"Timothy H. McNicholl","orcid":"https://orcid.org/0000-0001-8334-4367"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Timothy H. McNicholl","raw_affiliation_strings":["Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA","Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA. mcnichol@iastate.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA. mcnichol@iastate.edu","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057460107"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":null,"apc_paid":null,"fwci":1.8023,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87444552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"6","issue":"4","first_page":"391","last_page":"408"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9743000268936157,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.972599983215332,"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/mathematics","display_name":"Mathematics","score":0.4565562307834625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4035149812698364}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4565562307834625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4035149812698364}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/com-160065","is_oa":false,"landing_page_url":"https://doi.org/10.3233/com-160065","pdf_url":null,"source":{"id":"https://openalex.org/S4210231662","display_name":"Computability","issn_l":"2211-3568","issn":["2211-3568","2211-3576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computability","raw_type":"journal-article"},{"id":"pmh:oai:lib.dr.iastate.edu:math_pubs-1269","is_oa":true,"landing_page_url":"https://lib.dr.iastate.edu/math_pubs/259","pdf_url":"https://lib.dr.iastate.edu/math_pubs/259","source":{"id":"https://openalex.org/S4377196104","display_name":"Iowa State University Digital Repository (Iowa State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173911158","host_organization_name":"Iowa State University","host_organization_lineage":["https://openalex.org/I173911158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:lib.dr.iastate.edu:math_pubs-1269","is_oa":true,"landing_page_url":"https://lib.dr.iastate.edu/math_pubs/259","pdf_url":"https://lib.dr.iastate.edu/math_pubs/259","source":{"id":"https://openalex.org/S4377196104","display_name":"Iowa State University Digital Repository (Iowa State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I173911158","host_organization_name":"Iowa State University","host_organization_lineage":["https://openalex.org/I173911158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Publications","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2587411512.pdf","grobid_xml":"https://content.openalex.org/works/W2587411512.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1426436400","https://openalex.org/W1497475168","https://openalex.org/W1519861729","https://openalex.org/W1982821787","https://openalex.org/W2019044359","https://openalex.org/W2068855023","https://openalex.org/W2484528249","https://openalex.org/W2549647330","https://openalex.org/W2963063031","https://openalex.org/W4243563333"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Suppose":[0],"p":[1],"is":[2,12,34,40,83,88,99,104,111],"a":[3,20,65,105,113],"computable":[4,27,51],"real":[5,122],"so":[6],"that":[7,14,37,43,60,63,102,110],"[Formula:":[8,30,45,54,80,84,95],"see":[9,31,46,55,81,85,96],"text].":[10,32,97],"It":[11,33,98],"shown":[13,36],"the":[15,58,71,76,121],"halting":[16,77],"set":[17],"can":[18],"compute":[19,75],"surjective":[21],"linear":[22,66],"isometry":[23,67],"between":[24],"any":[25,61],"two":[26,50],"copies":[28,52],"of":[29,53,68],"also":[35,74,100],"this":[38],"result":[39],"optimal":[41],"in":[42,119],"when":[44],"text]":[47,56,82],"there":[48,103],"are":[49],"with":[57],"property":[59],"oracle":[62],"computes":[64],"one":[69],"onto":[70],"other":[72],"must":[73],"set.":[78],"Thus,":[79],"text]-categorical":[86],"and":[87,92,123],"computably":[89,106],"categorical":[90,107],"if":[91,94],"only":[93],"demonstrated":[101],"Banach":[108],"space":[109],"not":[112],"Hilbert":[114],"space.":[115],"These":[116],"results":[117],"hold":[118],"both":[120],"complex":[124],"case.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
