{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UCIULH4YZB3BBUSU4CR2CL3KFJ","short_pith_number":"pith:UCIULH4Y","schema_version":"1.0","canonical_sha256":"a091459f98c87610d254e0a3a12f6a2a7e6c3ca1c888c37a49ad139b4b30d7c8","source":{"kind":"arxiv","id":"1904.05809","version":1},"attestation_state":"computed","paper":{"title":"Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexei Kotov, Thomas Strobl","submitted_at":"2019-04-11T16:10:33Z","abstract_excerpt":"Consider an anchored bundle $(E,\\rho)$, i.e. a vector bundle $E\\to M$ equipped with a bundle map $\\rho \\colon E \\to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid $FR(E)\\supset E$. We adapt his construction to the case of an anchored bundle equipped with an arbitrary connection, $(E,\\nabla)$, and show that it gives rise to a unique connection $\\tilde \\nabla$ on $FR(E)$ which is compatible with its Lie algebroid structure, thus turning $(FR(E), \\tilde \\n"},"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":"1904.05809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-11T16:10:33Z","cross_cats_sorted":[],"title_canon_sha256":"2792364a8f8b7e2b1236859d6fc43d78abefe6dc9a2c6164e2ecb99178fe4915","abstract_canon_sha256":"20b8a9ebab1a723704474b90b5b108f665e34dfea3b38808fe591c63190b8185"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:48.378853Z","signature_b64":"RIKt/Y5GyNo7C3LAXQme4aqsRNcvtvjQPZukg8rnD9mzR21PTOYxSUc+3Pe6foLg3mDQ8nCLun8T4hsyJDy5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a091459f98c87610d254e0a3a12f6a2a7e6c3ca1c888c37a49ad139b4b30d7c8","last_reissued_at":"2026-05-17T23:48:48.378310Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:48.378310Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alexei Kotov, Thomas Strobl","submitted_at":"2019-04-11T16:10:33Z","abstract_excerpt":"Consider an anchored bundle $(E,\\rho)$, i.e. a vector bundle $E\\to M$ equipped with a bundle map $\\rho \\colon E \\to TM$ covering the identity. M.~Kapranov showed in the context of Lie-Rinehard algebras that there exists an extension of this anchored bundle to an infinite rank universal free Lie algebroid $FR(E)\\supset E$. We adapt his construction to the case of an anchored bundle equipped with an arbitrary connection, $(E,\\nabla)$, and show that it gives rise to a unique connection $\\tilde \\nabla$ on $FR(E)$ which is compatible with its Lie algebroid structure, thus turning $(FR(E), \\tilde \\n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05809","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":"1904.05809","created_at":"2026-05-17T23:48:48.378392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.05809v1","created_at":"2026-05-17T23:48:48.378392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05809","created_at":"2026-05-17T23:48:48.378392+00:00"},{"alias_kind":"pith_short_12","alias_value":"UCIULH4YZB3B","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UCIULH4YZB3BBUSU","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UCIULH4Y","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ","json":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ.json","graph_json":"https://pith.science/api/pith-number/UCIULH4YZB3BBUSU4CR2CL3KFJ/graph.json","events_json":"https://pith.science/api/pith-number/UCIULH4YZB3BBUSU4CR2CL3KFJ/events.json","paper":"https://pith.science/paper/UCIULH4Y"},"agent_actions":{"view_html":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ","download_json":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ.json","view_paper":"https://pith.science/paper/UCIULH4Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.05809&json=true","fetch_graph":"https://pith.science/api/pith-number/UCIULH4YZB3BBUSU4CR2CL3KFJ/graph.json","fetch_events":"https://pith.science/api/pith-number/UCIULH4YZB3BBUSU4CR2CL3KFJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ/action/storage_attestation","attest_author":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ/action/author_attestation","sign_citation":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ/action/citation_signature","submit_replication":"https://pith.science/pith/UCIULH4YZB3BBUSU4CR2CL3KFJ/action/replication_record"}},"created_at":"2026-05-17T23:48:48.378392+00:00","updated_at":"2026-05-17T23:48:48.378392+00:00"}