{"id":"https://openalex.org/W1545409775","doi":"https://doi.org/10.1007/11541868_8","title":"A HOL Theory of Euclidean Space","display_name":"A HOL Theory of Euclidean Space","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1545409775","doi":"https://doi.org/10.1007/11541868_8","mag":"1545409775"},"language":"en","primary_location":{"id":"doi:10.1007/11541868_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11541868_8","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010440892","display_name":"John Harrison","orcid":"https://orcid.org/0000-0001-5707-4631"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John Harrison","raw_affiliation_strings":["Intel Corporation, JF1-13, Hillsboro","Intel Corporation, JF1-13, Hillsboro, OR#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intel Corporation, JF1-13, Hillsboro","institution_ids":["https://openalex.org/I1343180700"]},{"raw_affiliation_string":"Intel Corporation, JF1-13, Hillsboro, OR#TAB#","institution_ids":["https://openalex.org/I1343180700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010440892"],"corresponding_institution_ids":["https://openalex.org/I1343180700"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.2544,"has_fulltext":false,"cited_by_count":77,"citation_normalized_percentile":{"value":0.5333453,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"114","last_page":"129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9965999722480774,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9925000071525574,"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":0.8869996070861816},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4745386838912964},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4670397639274597},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4602256417274475},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.44688668847084045},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4463019371032715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4337804913520813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3898216485977173},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38698989152908325},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.33196622133255005},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3245888650417328},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23446449637413025},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1379195749759674}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.8869996070861816},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4745386838912964},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4670397639274597},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4602256417274475},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.44688668847084045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4463019371032715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4337804913520813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3898216485977173},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38698989152908325},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.33196622133255005},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3245888650417328},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23446449637413025},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1379195749759674},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11541868_8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11541868_8","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W102301403","https://openalex.org/W588570749","https://openalex.org/W1519743817","https://openalex.org/W1532154335","https://openalex.org/W1539838732","https://openalex.org/W1561578951","https://openalex.org/W1774729455","https://openalex.org/W1967184028","https://openalex.org/W2022261955","https://openalex.org/W2050984357","https://openalex.org/W2097415784","https://openalex.org/W2162053995","https://openalex.org/W2504155696","https://openalex.org/W2595897327","https://openalex.org/W4235178139","https://openalex.org/W4249213567","https://openalex.org/W4285719527","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W1497011154","https://openalex.org/W1504680642","https://openalex.org/W4206694237","https://openalex.org/W2724703556","https://openalex.org/W3196544792","https://openalex.org/W2519051298","https://openalex.org/W2166178773","https://openalex.org/W1513403094","https://openalex.org/W2888810578","https://openalex.org/W2787637024"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}