{"id":"https://openalex.org/W7213392138","doi":"https://doi.org/10.5281/zenodo.22790074","title":"\u6784\u9020\u6570\u5b66\u8ba4\u8bc1\u6807\u51c6:\u516c\u7406\u5316\u6784\u9020\u7684\u8bc4\u4ef7\u6846\u67b6 / Constructive Mathematics: A Certification Standard for Axiomatic Constructions","display_name":"\u6784\u9020\u6570\u5b66\u8ba4\u8bc1\u6807\u51c6:\u516c\u7406\u5316\u6784\u9020\u7684\u8bc4\u4ef7\u6846\u67b6 / Constructive Mathematics: A Certification Standard for Axiomatic Constructions","publication_year":2026,"publication_date":"2026-09-16","ids":{"openalex":"https://openalex.org/W7213392138","doi":"https://doi.org/10.5281/zenodo.22790074"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22790074","doi":"https://doi.org/10.5281/zenodo.22790074","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22790074","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22790074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5141198945","display_name":"Chao Qin","orcid":"https://orcid.org/0009-0006-2000-5644","observed_orcids":["https://orcid.org/0009-0006-2000-5644"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qin, Chao","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0006-2000-5644","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5141198945"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":73.8295,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.99858393,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.7494999766349792,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.7494999766349792,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.03530000150203705,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.030700000002980232,"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/constructive-mathematics","display_name":"constructive mathematics","score":0.9940000176429749},{"id":"https://openalex.org/keywords/axiomatic-construction","display_name":"axiomatic construction","score":0.8330000042915344},{"id":"https://openalex.org/keywords/certification-standards","display_name":"certification standards","score":0.8299999833106995},{"id":"https://openalex.org/keywords/assessment-framework","display_name":"evaluation framework","score":0.8709999918937683},{"id":"https://openalex.org/keywords/formalization","display_name":"formalization","score":0.6359999775886536},{"id":"https://openalex.org/keywords/self-construction","display_name":"self-construction","score":0.5120000243186951},{"id":"https://openalex.org/keywords/construction-difficulties","display_name":"construction difficulties","score":0.49399998784065247},{"id":"https://openalex.org/keywords/proof-verification","display_name":"proof verification","score":0.31200000643730164},{"id":"https://openalex.org/keywords/provenance-comparison","display_name":"provenance comparison","score":0.4309999942779541},{"id":"https://openalex.org/keywords/error-correction-mechanism","display_name":"error correction mechanism","score":0.3479999899864197}],"concepts":[{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6977999806404114},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.651199996471405},{"id":"https://openalex.org/C46304622","wikidata":"https://www.wikidata.org/wiki/Q374814","display_name":"Certification","level":2,"score":0.555400013923645},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5285999774932861},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.4934000074863434},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4156000018119812},{"id":"https://openalex.org/C556429856","wikidata":"https://www.wikidata.org/wiki/Q5164501","display_name":"Constructive set theory","level":5,"score":0.40689998865127563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39160001277923584},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3531999886035919},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.33660000562667847},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.289000004529953},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2558000087738037}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.5281/zenodo.22790074","doi":"https://doi.org/10.5281/zenodo.22790074","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22790074","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.5281/zenodo.22790075","doi":"https://doi.org/10.5281/zenodo.22790075","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22790075","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Report"},{"id":"doi:10.5281/zenodo.22858723","doi":"https://doi.org/10.5281/zenodo.22858723","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22858723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Report"},{"id":"doi:10.5281/zenodo.22867678","doi":"https://doi.org/10.5281/zenodo.22867678","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22867678","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Report"},{"id":"doi:10.5281/zenodo.22874646","doi":"https://doi.org/10.5281/zenodo.22874646","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22874646","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22790074","doi":"https://doi.org/10.5281/zenodo.22790074","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22790074","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W7213353187","https://openalex.org/W7213423059","https://openalex.org/W7213431119","https://openalex.org/W7213432159","https://openalex.org/W7213869965"],"related_works":["https://openalex.org/W3186482227","https://openalex.org/W7022565633","https://openalex.org/W7214001059","https://openalex.org/W7100157541","https://openalex.org/W1516030196","https://openalex.org/W107651900","https://openalex.org/W34143232","https://openalex.org/W2526483358","https://openalex.org/W608501865","https://openalex.org/W374266323"],"abstract_inverted_index":{"\u6784\u9020\u6570\u5b66\u8ba4\u8bc1\u6807\u51c6:\u516c\u7406\u5316\u6784\u9020\u7684\u8bc4\u4ef7\u6846\u67b6\u3002\u672c\u6587\u516c\u5f00\u4e00\u5957\u9488\u5bf9\"\u6784\u9020\u6570\u5b66\"\u7684\u8ba4\u8bc1\u6807\u51c6:\u5bf9\u6ee1\u8db3\"\u4ece\u89c2\u5bdf\u5f52\u7eb3\u516c\u7406\u96c6\u3001\u5bf9\u8c61\u5b87\u5b99\u81ea\u6784\u9020\u751f\u957f\u3001\u6807\u51c6\u6570\u5b66\u53ef\u4f5c\u4e3a\u5176\u7279\u4f8b\u5bfc\u51fa\"\u4e09\u8981\u7d20\u7684\u6570\u5b66\u6784\u9020,\u7ed9\u51fa\u53ef\u516c\u5f00\u5ba1\u67e5\u7684\u6210\u5458\u5224\u636e(C1":[0],"\u89c2\u5bdf\u8d77\u6e90/C2":[1],"\u516c\u7406\u5316\u72ec\u7acb\u6027\u9884\u68c0/C3":[2],"\u5bf9\u8c61\u81ea\u6784\u9020\u5206\u6c34\u5cad/C4":[3],"\u7279\u4f8b\u5316\u738b\u51a0/C5":[4],"\u81ea\u8db3\u6027\u5206\u5c42/C6":[5],"\u673a\u5668\u53ef\u68c0\u9a8c\u6027\u786c\u5224\u636e[\u5f62\u5f0f\u5316+\u96f6":[6],"sorry,kernel":[7],"\u552f\u4e00\u5173\u53e3,\u8bc1\u660e\u4f5c\u8005\u8eab\u4efd\u4e0d\u8bbe\u9650]/C7":[8],"\u6eaf\u6e90\u5bf9\u7167)\u4e0e\u8ba4\u8bc1\u6d41\u7a0b(\u4e09\u6863\u7ed3\u8bba+\u4e94\u60c5\u5f62\u5206\u6d41+\u7ea0\u9519\u673a\u5236)\u3002\u542b\u5df2\u8ba4\u8bc1\u6210\u5458\u76ee\u5f55\u5feb\u7167:\u56db\u5c42\u6784\u9020\u6570\u5b66\u6210\u5458(\u6570/\u5173\u7cfb/\u52a8/\u51e0\u4f55)\u4e0e\u5355\u5217\u8868\u793a\u6570\u5b66\u5e8f\u5217,\u5168\u90e8\u7ecf\u9010\u6761\u5ba1\u67e5\u4e14":[9],"C6":[10,95,158],"\u8fbe\u786c\u5224\u636e\u3002\u540c\u65f6\u516c\u5f00\u6784\u9020\u96be\u5ea6\u7684\u6210\u5206\u5206\u89e3(\u56db\u9053\u4e32\u8054\u6ee4\u7f51\u4e0e":[11],"12:0":[12,174],"\u5b9e\u6d4b\u6dd8\u6c70\u7387\u2014\u2014\u62d2\u7edd\u96be\u5ea6\u6570\u5b57\u7684\u4f2a\u7cbe\u786e\u6807\u5b9a)\u4e0e\u629b\u9898\u4e09\u7ef4\u5206\u7ea7\u89c4\u8303(\u9884\u671f\u6295\u5165":[13],"D/\u89c2\u5bdf\u4f9d\u8d56":[14],"O/\u5224\u5b9a\u65b9\u5f0f":[15],"J)\u3002\u672c\u6587\u663e\u5f0f\u533a\u5206\u672c\u6846\u67b6\u7684\u6784\u9020\u6570\u5b66\u4e0e":[16],"Bishop":[17,217],"\u4f20\u7edf\u7684":[18],"constructive":[19,27,208,213],"mathematics(1967):\u4e24\u8005\u6b63\u4ea4\u4e92\u8865\u2014\u2014\u540e\u8005\u7ea6\u675f\u8bc1\u660e\u7684\u903b\u8f91\u65b9\u6cd5,\u672c\u6846\u67b6\u8bc4\u4ef7\u6570\u5b66\u5bf9\u8c61\u7684\u6784\u9020\u65b9\u5f0f\u3002\u4fee\u8ba2\u7ecf":[20],"Zenodo":[21,243],"\u7248\u672c\u94fe\u8fdb\u884c\u3002\u4e2d\u6587\u4e3b\u7248\u3002":[22],"The":[23,201],"certification":[24,39,122],"standard":[25,40,61],"of":[26,114,168,215,229],"mathematics:":[28],"an":[29,48,54],"evaluation":[30],"framework":[31,232],"for":[32,41,187,261],"axiomatic":[33,79],"constructions.":[34],"This":[35],"document":[36,202],"publishes":[37,164],"a":[38,65,99,147,165,183],"mathematical":[42,235],"constructions":[43],"satisfying":[44],"three":[45],"criteria":[46,73],"\u2014":[47,68,177,222,254],"axiom":[49],"set":[50],"induced":[51],"from":[52],"observation,":[53],"object":[55],"universe":[56],"grown":[57],"by":[58,155],"self-construction,":[59],"and":[60,120,182],"mathematics":[62,209,214],"recoverable":[63],"as":[64,98,107],"special":[66],"case":[67],"with":[69,157],"publicly":[70],"reviewable":[71],"membership":[72],"(C1":[74],"observational":[75,195],"origin":[76],"/":[77,82,86,90,94,116,139,141,143,193,197],"C2":[78],"independence":[80],"pre-check":[81],"C3":[83],"self-construction":[84],"watershed":[85],"C4":[87],"specialization":[88],"crown":[89],"C5":[91],"layered":[92],"self-containedness":[93],"machine":[96],"checkability":[97],"hard":[100],"criterion":[101],"[formalization":[102],"+":[103],"zero":[104],"sorry,":[105],"kernel":[106],"the":[108,121,131,160,212,216,223,226,242],"sole":[109],"gate,":[110],"author":[111],"identity":[112],"out":[113],"scope]":[115],"C7":[117],"provenance":[118],"comparison)":[119],"process":[123],"(three-valued":[124],"conclusions,":[125],"five-case":[126],"triage,":[127],"correction":[128],"mechanisms).":[129],"Includes":[130],"certified-membership":[132],"catalog":[133],"snapshot:":[134],"four":[135],"constructive-mathematics":[136],"members":[137],"(number":[138],"relation":[140],"motion":[142],"geometry":[144],"layers)":[145],"plus":[146],"separately":[148],"listed":[149],"representation-mathematics":[150],"series,":[151],"all":[152],"reviewed":[153],"item":[154,156],"at":[159],"hard-criterion":[161],"level.":[162],"Also":[163],"component":[166],"decomposition":[167],"construction":[169],"difficulty":[170,180],"(four":[171],"serial":[172],"filters,":[173],"measured":[175],"elimination":[176],"refusing":[178],"pseudo-precise":[179],"numbers)":[181],"three-dimensional":[184],"grading":[185],"specification":[186],"posed":[188],"problems":[189],"(D":[190],"expected":[191],"investment":[192],"O":[194],"dependence":[196],"J":[198],"verification":[199],"mode).":[200],"states":[203],"explicitly":[204],"how":[205,234],"this":[206,231],"framework's":[207],"relates":[210],"to":[211],"tradition":[218],"(1967):":[219],"orthogonally":[220],"complementary":[221],"latter":[224],"constrains":[225],"logical":[227],"methods":[228],"proof,":[230],"evaluates":[233],"objects":[236],"are":[237],"constructed.":[238],"Revisions":[239],"proceed":[240],"through":[241],"version":[244],"chain.":[245],"English":[246],"edition.":[247],"v1.3":[248],"(2026-09-21):":[249],"\u00a74.1.1":[250],"non-derivation":[251],"self-check":[252],"added":[253],"new-member":[255],"applications":[256],"must":[257],"carry":[258],"negative":[259],"evidence":[260],"E1\u2013E6":[262],"(completion/derivation":[263],"rerouted,":[264],"no":[265],"new":[266],"register":[267],"row).":[268],"Form:":[269],"application-template":[270],"v0.2.":[271]},"counts_by_year":[{"year":2026,"cited_by_count":9}],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-17T00:00:00"}
