{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:J7HNJRSVFBFHJGDM4KTC3BYI2O","short_pith_number":"pith:J7HNJRSV","schema_version":"1.0","canonical_sha256":"4fced4c655284a74986ce2a62d8708d3b6859362d83b047226178a2f488bf23d","source":{"kind":"arxiv","id":"1407.3166","version":1},"attestation_state":"computed","paper":{"title":"The Frobenius theorem for Banach distributions on infinite-dimensional manifolds and applications in infinite-dimensional Lie theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GR","authors_text":"Jan Milan Eyni","submitted_at":"2014-07-11T14:09:44Z","abstract_excerpt":"We prove a Frobenius theorem for Banach distributions on manifolds that are modelled over locally convex spaces. Moreover, we recall how Frobenius theorems can be applied to infinite-dimensional Lie groups and obtain, that given a Lie subalgebra of the Lie algebra of a Lie group that is modelled over a locally convex space that admits an exponential map, the Lie subalgebra is integrable if it is complemented as a topological vector space and a Banach space with the induced topology."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-07-11T14:09:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"d80e8d6bf377d8b2ed96ef51b54fc5ad7bbc3290d845f81be60e9094d1394dfb","abstract_canon_sha256":"3a4b275fc610d4f1da75dc9898c361ff20c2540b236ac313b72479a5bfb60a18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:51.871893Z","signature_b64":"XfkgAawv8Ebb6q+AgMQMzYPo8WbNXdrTUUVqiki0pVppQz0EEGvXflzEqVBuCupTamOHnAZo4zqME/NMRdKmDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fced4c655284a74986ce2a62d8708d3b6859362d83b047226178a2f488bf23d","last_reissued_at":"2026-05-18T02:47:51.871331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:51.871331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Frobenius theorem for Banach distributions on infinite-dimensional manifolds and applications in infinite-dimensional Lie theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GR","authors_text":"Jan Milan Eyni","submitted_at":"2014-07-11T14:09:44Z","abstract_excerpt":"We prove a Frobenius theorem for Banach distributions on manifolds that are modelled over locally convex spaces. Moreover, we recall how Frobenius theorems can be applied to infinite-dimensional Lie groups and obtain, that given a Lie subalgebra of the Lie algebra of a Lie group that is modelled over a locally convex space that admits an exponential map, the Lie subalgebra is integrable if it is complemented as a topological vector space and a Banach space with the induced topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3166","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.3166","created_at":"2026-05-18T02:47:51.871425+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3166v1","created_at":"2026-05-18T02:47:51.871425+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3166","created_at":"2026-05-18T02:47:51.871425+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7HNJRSVFBFH","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7HNJRSVFBFHJGDM","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7HNJRSV","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.22472","citing_title":"A Frobenius Theorem on Fr\\'echet Manifolds","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O","json":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O.json","graph_json":"https://pith.science/api/pith-number/J7HNJRSVFBFHJGDM4KTC3BYI2O/graph.json","events_json":"https://pith.science/api/pith-number/J7HNJRSVFBFHJGDM4KTC3BYI2O/events.json","paper":"https://pith.science/paper/J7HNJRSV"},"agent_actions":{"view_html":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O","download_json":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O.json","view_paper":"https://pith.science/paper/J7HNJRSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3166&json=true","fetch_graph":"https://pith.science/api/pith-number/J7HNJRSVFBFHJGDM4KTC3BYI2O/graph.json","fetch_events":"https://pith.science/api/pith-number/J7HNJRSVFBFHJGDM4KTC3BYI2O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O/action/storage_attestation","attest_author":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O/action/author_attestation","sign_citation":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O/action/citation_signature","submit_replication":"https://pith.science/pith/J7HNJRSVFBFHJGDM4KTC3BYI2O/action/replication_record"}},"created_at":"2026-05-18T02:47:51.871425+00:00","updated_at":"2026-05-18T02:47:51.871425+00:00"}