{"id":"https://openalex.org/W7157731906","doi":"https://doi.org/10.48550/arxiv.2604.24797","title":"The Network Structure of Mathlib","display_name":"The Network Structure of Mathlib","publication_year":2026,"publication_date":"2026-04-26","ids":{"openalex":"https://openalex.org/W7157731906","doi":"https://doi.org/10.48550/arxiv.2604.24797"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.24797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.24797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.24797","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5134823556","display_name":"Xinze Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Xinze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030248499","display_name":"Nanyun Peng","orcid":"https://orcid.org/0000-0002-8509-6595"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Nanyun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064938440","display_name":"Simone Severini","orcid":"https://orcid.org/0000-0001-7305-6759"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Severini, Simone","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015419380","display_name":"Patrick Shafto","orcid":"https://orcid.org/0000-0002-6506-5644"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shafto, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10126","display_name":"Logic, programming, and type systems","score":0.1485999971628189,"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":0.1485999971628189,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.09830000251531601,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.07909999787807465,"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/centrality","display_name":"Centrality","score":0.7631999850273132},{"id":"https://openalex.org/keywords/network-science","display_name":"Network science","score":0.5655999779701233},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5246999859809875},{"id":"https://openalex.org/keywords/network-analysis","display_name":"Network analysis","score":0.4887999892234802},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4724999964237213},{"id":"https://openalex.org/keywords/network-structure","display_name":"Network structure","score":0.46140000224113464},{"id":"https://openalex.org/keywords/dependency-graph","display_name":"Dependency graph","score":0.4571000039577484},{"id":"https://openalex.org/keywords/dependency","display_name":"Dependency (UML)","score":0.4433000087738037},{"id":"https://openalex.org/keywords/network-theory","display_name":"Network theory","score":0.43309998512268066}],"concepts":[{"id":"https://openalex.org/C53811970","wikidata":"https://www.wikidata.org/wiki/Q5062194","display_name":"Centrality","level":2,"score":0.7631999850273132},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7067000269889832},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5975000262260437},{"id":"https://openalex.org/C137753397","wikidata":"https://www.wikidata.org/wiki/Q2434424","display_name":"Network science","level":3,"score":0.5655999779701233},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5246999859809875},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.4887999892234802},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4724999964237213},{"id":"https://openalex.org/C2988224531","wikidata":"https://www.wikidata.org/wiki/Q20830730","display_name":"Network structure","level":2,"score":0.46140000224113464},{"id":"https://openalex.org/C16311509","wikidata":"https://www.wikidata.org/wiki/Q4148050","display_name":"Dependency graph","level":3,"score":0.4571000039577484},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.4433000087738037},{"id":"https://openalex.org/C11804174","wikidata":"https://www.wikidata.org/wiki/Q1192971","display_name":"Network theory","level":2,"score":0.43309998512268066},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.42410001158714294},{"id":"https://openalex.org/C112953755","wikidata":"https://www.wikidata.org/wiki/Q739462","display_name":"Graph drawing","level":3,"score":0.3781000077724457},{"id":"https://openalex.org/C85407183","wikidata":"https://www.wikidata.org/wiki/Q1045785","display_name":"Semantic network","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C2987255567","wikidata":"https://www.wikidata.org/wiki/Q33002955","display_name":"Knowledge graph","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C21847791","wikidata":"https://www.wikidata.org/wiki/Q191081","display_name":"Logical conjunction","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.3046000003814697},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.30329999327659607},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.2924000024795532},{"id":"https://openalex.org/C64339825","wikidata":"https://www.wikidata.org/wiki/Q722659","display_name":"Graph property","level":5,"score":0.29010000824928284},{"id":"https://openalex.org/C558772884","wikidata":"https://www.wikidata.org/wiki/Q1508564","display_name":"Graph rewriting","level":3,"score":0.27810001373291016},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2718000113964081},{"id":"https://openalex.org/C99679407","wikidata":"https://www.wikidata.org/wiki/Q56761637","display_name":"Substructure","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.26510000228881836},{"id":"https://openalex.org/C106937863","wikidata":"https://www.wikidata.org/wiki/Q7236518","display_name":"Power graph analysis","level":3,"score":0.2628999948501587},{"id":"https://openalex.org/C2776542497","wikidata":"https://www.wikidata.org/wiki/Q5266672","display_name":"Development (topology)","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.25380000472068787}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.24797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.24797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.24797","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.24797","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"Preprint"},"sustainable_development_goals":[{"score":0.6466463208198547,"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"ongoing":[1],"development":[2],"of":[3,25,36,68,96,98],"Lean":[4],"4's":[5],"Mathlib":[6],"has":[7],"produced":[8],"a":[9,22,33,86,94],"macroscopic":[10],"structural":[11,66],"complexity":[12],"that":[13,49],"interweaves":[14],"logical,":[15],"mathematical,":[16],"and":[17,42],"infrastructural":[18],"dependencies.":[19],"We":[20],"present":[21],"network":[23,108],"analysis":[24,72],"this":[26],"library,":[27],"extracting":[28],"its":[29],"dependency":[30],"structure":[31],"into":[32],"multilayer":[34],"graph":[35,47],"308,129":[37],"declarations,":[38],"8.4":[39],"million":[40],"edges,":[41],"7,563":[43],"modules.":[44],"By":[45],"introducing":[46],"decompositions":[48],"isolate":[50],"explicit":[51],"edges":[52],"from":[53,82],"those":[54],"synthesized":[55],"by":[56,61,79],"the":[57,65,99],"compiler":[58],"or":[59],"driven":[60],"proofs,":[62],"we":[63],"quantify":[64],"properties":[67],"formalized":[69],"mathematics.":[70],"Our":[71],"reveals":[73],"three":[74],"findings.":[75],"First,":[76],"taxonomies":[77],"designed":[78],"humans":[80],"diverge":[81],"logical":[83],"structures,":[84],"exhibiting":[85],"50.9%":[87],"coupling":[88],"across":[89],"namespaces.":[90],"Second,":[91],"developers":[92],"utilize":[93],"median":[95],"1.6%":[97],"imported":[100],"scope.":[101],"Third,":[102],"formalization":[103],"compresses":[104],"semantic":[105],"hierarchies,":[106],"with":[107],"centrality":[109],"capturing":[110],"language":[111],"infrastructure":[112],"rather":[113],"than":[114],"mathematical":[115],"relevance.":[116]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-30T00:00:00"}