{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C5EOM7INH2RW56QUHER6NTQJ4B","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cf1489aa030faec0ecf83a8bed0a73d982a11da6fb24766ad882e606ea507cd9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2011-09-22T11:18:04Z","title_canon_sha256":"58da6ecf3c1fa4665506b63342e5fa5df0dfdc829b3bbeb9c2c449bcdc7f01c9"},"schema_version":"1.0","source":{"id":"1109.4772","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4772","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4772v2","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4772","created_at":"2026-05-18T04:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"C5EOM7INH2RW","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C5EOM7INH2RW56QU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C5EOM7IN","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:f9da3eed4193d8f3621ad394b1c6f01bd9c02065fcaf9931062db4a7c5a70555","target":"graph","created_at":"2026-05-18T04:03:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that a vector bundle $\\pi : E \\to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of Pursell-Shanks type but it is remarkable in the sense that it is the whole fibration that is characterized here. The proof relies on a theorem of [Lecomte P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same hypotheses. In particular, our characterization holds only for vector bundles of rank greater than 1.","authors_text":"Elie Zihindula Mushengezi, Pierre B.A. Lecomte, Thomas Leuther","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2011-09-22T11:18:04Z","title":"On a Lie Algebraic Characterization of Vector Bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4772","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:94e1922284c81e71ef007d0466ebe6b6b18079fc69d3505cc20c276d2499f7e0","target":"record","created_at":"2026-05-18T04:03:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cf1489aa030faec0ecf83a8bed0a73d982a11da6fb24766ad882e606ea507cd9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.DG","submitted_at":"2011-09-22T11:18:04Z","title_canon_sha256":"58da6ecf3c1fa4665506b63342e5fa5df0dfdc829b3bbeb9c2c449bcdc7f01c9"},"schema_version":"1.0","source":{"id":"1109.4772","kind":"arxiv","version":2}},"canonical_sha256":"1748e67d0d3ea36efa143923e6ce09e0789f3bec1553172425942f1bb496fd32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1748e67d0d3ea36efa143923e6ce09e0789f3bec1553172425942f1bb496fd32","first_computed_at":"2026-05-18T04:03:54.318429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:54.318429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/KBZdl+s/14M/w8Z+UcaqWHH7HeK1yLKCKPNcfOfHaW0u1rD2KgcJIWy8H4cBoWqBad4La+1ugsIzBVvVwACg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:54.319103Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4772","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94e1922284c81e71ef007d0466ebe6b6b18079fc69d3505cc20c276d2499f7e0","sha256:f9da3eed4193d8f3621ad394b1c6f01bd9c02065fcaf9931062db4a7c5a70555"],"state_sha256":"37941de38e25916205eaa536e5d7b95dd32cb8672c43e9f1afa0a3df437e10e3"}