{"id":"https://openalex.org/W1926392198","doi":"https://doi.org/10.1080/10586458.2015.1029599","title":"Verified Computations for Hyperbolic 3-Manifolds","display_name":"Verified Computations for Hyperbolic 3-Manifolds","publication_year":2015,"publication_date":"2015-10-09","ids":{"openalex":"https://openalex.org/W1926392198","doi":"https://doi.org/10.1080/10586458.2015.1029599","mag":"1926392198"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2015.1029599","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1029599","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hdl.handle.net/20.500.14446/336590","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064383647","display_name":"Neil Hoffman","orcid":"https://orcid.org/0000-0003-0662-3244"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Neil Hoffman","raw_affiliation_strings":["School of Mathematics and Statistics, University of Melbourne, Parkville, VIC Australia","University of Melbourne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of Melbourne, Parkville, VIC Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002087391","display_name":"Kazuhiro Ichihara","orcid":"https://orcid.org/0000-0001-5061-3276"},"institutions":[{"id":"https://openalex.org/I104946051","display_name":"Nihon University","ror":"https://ror.org/05jk51a88","country_code":"JP","type":"education","lineage":["https://openalex.org/I104946051"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhiro Ichihara","raw_affiliation_strings":["College of Humanities and Sciences, Nihon University, Tokyo, Japan","Nihon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Humanities and Sciences, Nihon University, Tokyo, Japan","institution_ids":["https://openalex.org/I104946051"]},{"raw_affiliation_string":"Nihon University","institution_ids":["https://openalex.org/I104946051"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110883917","display_name":"Masahide Kashiwagi","orcid":null},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masahide Kashiwagi","raw_affiliation_strings":["Department of Applied Mathematics, Waseda University, Tokyo, Japan","Department of Applied mathematics, Waseda University, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Applied mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102723460","display_name":"Hidetoshi Masai","orcid":"https://orcid.org/0000-0003-3033-9729"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hidetoshi Masai","raw_affiliation_strings":["Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan","Graduate School of Mathematical Sciences, #N#            The University of Tokyo, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]},{"raw_affiliation_string":"Graduate School of Mathematical Sciences, #N#            The University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063201472","display_name":"Shin\u2019ichi Oishi","orcid":"https://orcid.org/0000-0002-6582-265X"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shin\u2019ichi Oishi","raw_affiliation_strings":["Department of Applied Mathematics, Waseda University, Tokyo, Japan","Department of Applied mathematics, Waseda University, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Applied mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041793840","display_name":"Akitoshi Takayasu","orcid":"https://orcid.org/0009-0005-5087-4894"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Akitoshi Takayasu","raw_affiliation_strings":["Department of Applied Mathematics, Waseda University, Tokyo, Japan","Department of Applied mathematics, Waseda University, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Applied mathematics, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064383647"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":3.4862,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.91656651,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"25","issue":"1","first_page":"66","last_page":"78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9884999990463257,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8984527587890625},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.741583526134491},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6513817310333252},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6357437968254089},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5840418338775635},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.5517494678497314},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.48580169677734375},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39472696185112},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32664722204208374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27181196212768555},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2572935223579407},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1732066571712494},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16135764122009277}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8984527587890625},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.741583526134491},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6513817310333252},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6357437968254089},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5840418338775635},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.5517494678497314},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.48580169677734375},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39472696185112},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32664722204208374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27181196212768555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2572935223579407},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1732066571712494},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16135764122009277},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1080/10586458.2015.1029599","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2015.1029599","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:openresearch.okstate.edu:20.500.14446/336590","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.14446/336590","pdf_url":null,"source":{"id":"https://openalex.org/S4306402274","display_name":"SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.740.1243","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.740.1243","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1310.3410.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:728625","is_oa":false,"landing_page_url":"http://edoc.mpg.de/728625","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Experimental Mathematics, v.25, 66-78 (2016)","raw_type":"Article"},{"id":"pmh:oai:pure.mpg.de:item_3119602","is_oa":true,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0004-103D-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"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":"Experimental Mathematics","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:shareok.org:11244/336590","is_oa":true,"landing_page_url":"https://shareok.org/handle/11244/336590","pdf_url":null,"source":{"id":"https://openalex.org/S4306402274","display_name":"SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:openresearch.okstate.edu:20.500.14446/336590","is_oa":true,"landing_page_url":"https://hdl.handle.net/20.500.14446/336590","pdf_url":null,"source":{"id":"https://openalex.org/S4306402274","display_name":"SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University)","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1881225186","display_name":"\uff13\u6b21\u5143\u591a\u69d8\u4f53\u306e\u8af8\u6027\u8cea\u306e\u30e9\u30f3\u30c0\u30e0\u30cd\u30b9\u304b\u3089\u898b\u308b\u7279\u5fb4\u4ed8\u3051","funder_award_id":"15J08142","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6671449689","display_name":"Studies on verified numerical computations for nonlinear parabolic partial differential equations","funder_award_id":"15K17596","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G7073634014","display_name":"Cosmetic surgery conjecture for alternating knots","funder_award_id":"26400100","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W319832710","https://openalex.org/W364859224","https://openalex.org/W1528063838","https://openalex.org/W1530501787","https://openalex.org/W1532036648","https://openalex.org/W1589310148","https://openalex.org/W1890527156","https://openalex.org/W1915967525","https://openalex.org/W1965191089","https://openalex.org/W2014078287","https://openalex.org/W2016784563","https://openalex.org/W2022365359","https://openalex.org/W2044720368","https://openalex.org/W2053282530","https://openalex.org/W2082573213","https://openalex.org/W2112526218","https://openalex.org/W2170345902","https://openalex.org/W2963682115","https://openalex.org/W2963812834","https://openalex.org/W3101591590","https://openalex.org/W3185484028","https://openalex.org/W4206215385"],"related_works":["https://openalex.org/W2520934858","https://openalex.org/W2098412892","https://openalex.org/W2990487117","https://openalex.org/W43877154","https://openalex.org/W109635080","https://openalex.org/W4213384165","https://openalex.org/W2377262226","https://openalex.org/W2531534085","https://openalex.org/W4285295794","https://openalex.org/W34401233"],"abstract_inverted_index":{"For":[0],"a":[1,12,21,26,65],"given":[2],"cusped":[3],"3-manifold":[4],"M":[5,19,24],"admitting":[6],"an":[7,39,50],"ideal":[8],"triangulation,":[9],"we":[10],"describe":[11],"method":[13,37],"to":[14,35],"rigorously":[15],"prove":[16],"that":[17],"either":[18],"or":[20],"filling":[22],"of":[23,41],"admits":[25],"complete":[27],"hyperbolic":[28],"structure":[29],"via":[30],"verified":[31],"computer":[32],"calculations.":[33],"Central":[34],"our":[36],"is":[38],"implementation":[40],"interval":[42],"arithmetic":[43],"and":[44,68],"Krawczyk\u2019s":[45],"test.":[46],"These":[47],"techniques":[48],"represent":[49],"improvement":[51],"over":[52],"existing":[53],"algorithms":[54],"as":[55],"they":[56],"are":[57],"faster":[58],"while":[59],"accounting":[60],"for":[61],"error":[62],"accumulation":[63],"in":[64],"more":[66],"direct":[67],"user-friendly":[69],"way.":[70]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}