{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:66LDNJKUJA6AR3MN4XTXBDE4O2","short_pith_number":"pith:66LDNJKU","canonical_record":{"source":{"id":"1410.8804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-05T07:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"0a887a530941b89b455445bbff5073cbef120201450d72a42139d6e8dceafd14","abstract_canon_sha256":"b40a638ebbc0b6817f0a3aa6466959f1e2b826475f2d597a5360e78e5451334b"},"schema_version":"1.0"},"canonical_sha256":"f79636a554483c08ed8de5e7708c9c76a496d06fda20ee2cb93c2975e4c3258a","source":{"kind":"arxiv","id":"1410.8804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8804","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8804v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8804","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"66LDNJKUJA6A","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"66LDNJKUJA6AR3MN","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"66LDNJKU","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:66LDNJKUJA6AR3MN4XTXBDE4O2","target":"record","payload":{"canonical_record":{"source":{"id":"1410.8804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-05T07:43:02Z","cross_cats_sorted":[],"title_canon_sha256":"0a887a530941b89b455445bbff5073cbef120201450d72a42139d6e8dceafd14","abstract_canon_sha256":"b40a638ebbc0b6817f0a3aa6466959f1e2b826475f2d597a5360e78e5451334b"},"schema_version":"1.0"},"canonical_sha256":"f79636a554483c08ed8de5e7708c9c76a496d06fda20ee2cb93c2975e4c3258a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:53.660729Z","signature_b64":"NgiGDaPwcZj1NWE3VmBe4W8Ggvpkiw3In0wHA8JPbfOVkHx7wtLCupZm1qXmwixFKKS2C0QL2x+iPLVCA2HOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f79636a554483c08ed8de5e7708c9c76a496d06fda20ee2cb93c2975e4c3258a","last_reissued_at":"2026-05-18T02:38:53.660294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:53.660294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.8804","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXhE8vscVyrgLPs+sgKdkaHLH+ygpHom9HDpiH6yeyypECT5gCujHSLsdibo2aRKdQNw+Bcv5ygxAxZaKGOxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:26:52.412144Z"},"content_sha256":"3bea4daf4dcaaab1a64cf5556c5bef337bf65be43dbbcf56762ebe24343d60d3","schema_version":"1.0","event_id":"sha256:3bea4daf4dcaaab1a64cf5556c5bef337bf65be43dbbcf56762ebe24343d60d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:66LDNJKUJA6AR3MN4XTXBDE4O2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C. M. Arcu\\c{s}, E. Peyghan, L. Nourmohammadifar","submitted_at":"2014-10-05T07:43:02Z","abstract_excerpt":"Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of exterior differential calculus for generalized Lie algebroids, a covariant derivative for exterior forms of a (dual) vector bundle is introduced. Using this covariant derivative, the complete lift of an arbitrary section of a (dual) vector bundle is discovered. A theory of Legendre type and Legendre duality between vertical and complete lifts is presented. Finally,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8804","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qS9Gcg/WzI3VbTOB8gEPth5ut/5InDtWfmyLMkuQZJ1WeVGIcBIZX1CSCDvPlDSYWN+4j2SkCt7Ktw72lVrEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:26:52.412838Z"},"content_sha256":"4337a65f6a5592ebeae85c3a4c17aa7446f21bac35e2378ab216345390acac6b","schema_version":"1.0","event_id":"sha256:4337a65f6a5592ebeae85c3a4c17aa7446f21bac35e2378ab216345390acac6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/bundle.json","state_url":"https://pith.science/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T07:26:52Z","links":{"resolver":"https://pith.science/pith/66LDNJKUJA6AR3MN4XTXBDE4O2","bundle":"https://pith.science/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/bundle.json","state":"https://pith.science/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66LDNJKUJA6AR3MN4XTXBDE4O2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:66LDNJKUJA6AR3MN4XTXBDE4O2","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":"b40a638ebbc0b6817f0a3aa6466959f1e2b826475f2d597a5360e78e5451334b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-05T07:43:02Z","title_canon_sha256":"0a887a530941b89b455445bbff5073cbef120201450d72a42139d6e8dceafd14"},"schema_version":"1.0","source":{"id":"1410.8804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.8804","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1410.8804v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.8804","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"66LDNJKUJA6A","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"66LDNJKUJA6AR3MN","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"66LDNJKU","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4337a65f6a5592ebeae85c3a4c17aa7446f21bac35e2378ab216345390acac6b","target":"graph","created_at":"2026-05-18T02:38:53Z","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":"Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of exterior differential calculus for generalized Lie algebroids, a covariant derivative for exterior forms of a (dual) vector bundle is introduced. Using this covariant derivative, the complete lift of an arbitrary section of a (dual) vector bundle is discovered. A theory of Legendre type and Legendre duality between vertical and complete lifts is presented. Finally,","authors_text":"C. M. Arcu\\c{s}, E. Peyghan, L. Nourmohammadifar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-05T07:43:02Z","title":"Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.8804","kind":"arxiv","version":1},"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":"sha256:3bea4daf4dcaaab1a64cf5556c5bef337bf65be43dbbcf56762ebe24343d60d3","target":"record","created_at":"2026-05-18T02:38:53Z","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":"b40a638ebbc0b6817f0a3aa6466959f1e2b826475f2d597a5360e78e5451334b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-05T07:43:02Z","title_canon_sha256":"0a887a530941b89b455445bbff5073cbef120201450d72a42139d6e8dceafd14"},"schema_version":"1.0","source":{"id":"1410.8804","kind":"arxiv","version":1}},"canonical_sha256":"f79636a554483c08ed8de5e7708c9c76a496d06fda20ee2cb93c2975e4c3258a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f79636a554483c08ed8de5e7708c9c76a496d06fda20ee2cb93c2975e4c3258a","first_computed_at":"2026-05-18T02:38:53.660294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:53.660294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NgiGDaPwcZj1NWE3VmBe4W8Ggvpkiw3In0wHA8JPbfOVkHx7wtLCupZm1qXmwixFKKS2C0QL2x+iPLVCA2HOAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:53.660729Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.8804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bea4daf4dcaaab1a64cf5556c5bef337bf65be43dbbcf56762ebe24343d60d3","sha256:4337a65f6a5592ebeae85c3a4c17aa7446f21bac35e2378ab216345390acac6b"],"state_sha256":"447e2a8d888b3727944f0d9e112e79973e95e0d34414bf53ed560e3e797ab5c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kx6574U/K1yGReEo3A+MgWXyTMhoVtVQBWZLblGDl6ipZM2uEy7HzcIXy9TziXrnAOqRRLD+33DfVVnweKPGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:26:52.417776Z","bundle_sha256":"3e476fe5d31cc53b472548cdad067f37949f3cca64bd12ee0d71823a7a64aeed"}}