{"id":"https://openalex.org/W70939740","doi":"https://doi.org/10.1007/978-3-642-15582-6_29","title":"A Formal Proof of Pick\u2019s Theorem","display_name":"A Formal Proof of Pick\u2019s Theorem","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W70939740","doi":"https://doi.org/10.1007/978-3-642-15582-6_29","mag":"70939740"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-15582-6_29","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-15582-6_29","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, 2111 NE 25th Avenue, Hillsboro, OR, 97124, USA","Intel Corporation, Hillsboro, OR#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Intel Corporation, JF1-13, 2111 NE 25th Avenue, Hillsboro, OR, 97124, USA","institution_ids":["https://openalex.org/I1343180700"]},{"raw_affiliation_string":"Intel Corporation, 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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02322662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"152","last_page":"154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11106","display_name":"Data Management and Algorithms","score":0.9423999786376953,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9423999786376953,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T12504","display_name":"Mathematics and Applications","score":0.939300000667572,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9221000075340271,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematical-proof","display_name":"Mathematical proof","score":0.6558900475502014},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6330585479736328},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48139476776123047},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.4694720506668091},{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.457346647977829},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4542539417743683},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43928736448287964},{"id":"https://openalex.org/keywords/computer-assisted-proof","display_name":"Computer-assisted proof","score":0.4106858968734741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1811681091785431},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11138316988945007},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08775782585144043}],"concepts":[{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6558900475502014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6330585479736328},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48139476776123047},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.4694720506668091},{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.457346647977829},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4542539417743683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43928736448287964},{"id":"https://openalex.org/C173613240","wikidata":"https://www.wikidata.org/wiki/Q1150675","display_name":"Computer-assisted proof","level":3,"score":0.4106858968734741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1811681091785431},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11138316988945007},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08775782585144043},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-15582-6_29","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-15582-6_29","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1487979635","https://openalex.org/W1497011154","https://openalex.org/W1518486998","https://openalex.org/W1528908721","https://openalex.org/W1978174880","https://openalex.org/W2096749529","https://openalex.org/W2316735436","https://openalex.org/W2326886964","https://openalex.org/W2328261313","https://openalex.org/W2405679748","https://openalex.org/W2512656699","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2534028225","https://openalex.org/W3098927713","https://openalex.org/W2963742580","https://openalex.org/W2938239299","https://openalex.org/W1500659951","https://openalex.org/W3100311625","https://openalex.org/W1858809161","https://openalex.org/W2483392883","https://openalex.org/W1545756543","https://openalex.org/W1941966748"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
