{"id":"https://openalex.org/W7129627264","doi":"https://doi.org/10.48550/arxiv.2602.13247","title":"Integral Curves and Flows on Banach Manifolds in Lean","display_name":"Integral Curves and Flows on Banach Manifolds in Lean","publication_year":2026,"publication_date":"2026-02-02","ids":{"openalex":"https://openalex.org/W7129627264","doi":"https://doi.org/10.48550/arxiv.2602.13247"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2602.13247","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.13247","pdf_url":"https://arxiv.org/pdf/2602.13247","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2602.13247","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126243745","display_name":"Weichen Winston Yin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Weichen Winston","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5042404953","display_name":"Yury Kudryashov","orcid":"https://orcid.org/0000-0003-4286-9276","observed_orcids":["https://orcid.org/0000-0003-4286-9276"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kudryashov, Yury","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":0.673799991607666,"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":0.673799991607666,"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/T13806","display_name":"Mathematical and Computational Methods","score":0.025499999523162842,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.024800000712275505,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/integral-curves","display_name":"integral curves","score":0.9269999861717224},{"id":"https://openalex.org/keywords/vector-fields","display_name":"vector fields","score":0.6899999976158142},{"id":"https://openalex.org/keywords/banach-manifolds","display_name":"Banach manifolds","score":0.9990000128746033},{"id":"https://openalex.org/keywords/picard-lindelof-theorem","display_name":"Picard-Lindel\u00f6f theorem","score":0.8690000176429749},{"id":"https://openalex.org/keywords/gronwall-s-inequality","display_name":"Gronwall inequality","score":0.9330000281333923},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7549999952316284},{"id":"https://openalex.org/keywords/lean-theorem-prover","display_name":"Lean theorem prover","score":0.7749999761581421},{"id":"https://openalex.org/keywords/formalization-of-mathematics","display_name":"mathematical formalization","score":0.7870000004768372},{"id":"https://openalex.org/keywords/dynamical-systems","display_name":"dynamical systems","score":0.8230000138282776},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"differential geometry","score":0.8840000033378601}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742000222206116},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6377999782562256},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5437999963760376},{"id":"https://openalex.org/C165593952","wikidata":"https://www.wikidata.org/wiki/Q3554819","display_name":"Banach manifold","level":4,"score":0.5324000120162964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4837000072002411},{"id":"https://openalex.org/C19496378","wikidata":"https://www.wikidata.org/wiki/Q846542","display_name":"C0-semigroup","level":3,"score":0.47600001096725464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4214000105857849},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C155940","wikidata":"https://www.wikidata.org/wiki/Q7886967","display_name":"Uniqueness theorem for Poisson's equation","level":3,"score":0.3919000029563904},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3617999851703644},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C206929604","wikidata":"https://www.wikidata.org/wiki/Q530152","display_name":"Picard\u2013Lindel\u00f6f theorem","level":3,"score":0.35100001096725464},{"id":"https://openalex.org/C184908153","wikidata":"https://www.wikidata.org/wiki/Q2226650","display_name":"Eberlein\u2013\u0160mulian theorem","level":4,"score":0.3427000045776367},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.31369999051094055},{"id":"https://openalex.org/C86177461","wikidata":"https://www.wikidata.org/wiki/Q837551","display_name":"Frobenius theorem (differential topology)","level":5,"score":0.3070000112056732},{"id":"https://openalex.org/C43987214","wikidata":"https://www.wikidata.org/wiki/Q931001","display_name":"Inverse function theorem","level":4,"score":0.305400013923645},{"id":"https://openalex.org/C2776548862","wikidata":"https://www.wikidata.org/wiki/Q2694495","display_name":"Existence theorem","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C2781106287","wikidata":"https://www.wikidata.org/wiki/Q806066","display_name":"Banach algebra","level":3,"score":0.27730000019073486},{"id":"https://openalex.org/C80739010","wikidata":"https://www.wikidata.org/wiki/Q6029720","display_name":"Infinite-dimensional vector function","level":5,"score":0.26809999346733093},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.25690001249313354},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2602.13247","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.13247","pdf_url":"https://arxiv.org/pdf/2602.13247","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2602.13247","doi":"https://doi.org/10.48550/arxiv.2602.13247","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.13247","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2602.13247","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2602.13247","pdf_url":"https://arxiv.org/pdf/2602.13247","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2490518206","https://openalex.org/W2008267169","https://openalex.org/W1997143827","https://openalex.org/W2580583895","https://openalex.org/W108320751","https://openalex.org/W2735645504","https://openalex.org/W7220552332","https://openalex.org/W2057307765","https://openalex.org/W1967822815","https://openalex.org/W2077402709"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2],"formalisation":[3],"of":[4,10,13,28],"the":[5,20,37,52,68],"existence":[6],"and":[7,40,42,54,57,73,81],"uniqueness":[8],"theorems":[9],"integral":[11,55],"curves":[12],"vector":[14],"fields":[15],"on":[16,31],"Banach":[17,32,48,58],"manifolds":[18,59],"in":[19,61],"Lean":[21],"theorem":[22],"prover.":[23],"First,":[24],"we":[25],"formalize":[26],"properties":[27],"differential":[29,53,74],"equations":[30],"spaces":[33],"(the":[34],"Picard-Lindel\u00f6f":[35],"theorem,":[36],"Gr\u00f6nwall":[38],"inequality,":[39],"corollaries),":[41],"then":[43],"transfer":[44],"results":[45],"to":[46,66,83],"abstract":[47],"manifolds.":[49],"Built":[50],"upon":[51],"calculus":[56],"libraries":[60,76],"Mathlib,":[62],"our":[63],"work":[64],"aims":[65],"lay":[67],"foundation":[69],"for":[70],"dynamical":[71],"systems":[72],"geometry":[75],"that":[77],"are":[78],"general,":[79],"robust,":[80],"friendly":[82],"classical":[84],"mathematicians.":[85]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-02-18T00:00:00"}
