{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IZMZXR5P46I56XFPYSPZFJ4SXL","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":"d5bfd3d7345f5f72e438ef7c0cb4eefc53b759a06b4effbe91fc21ad50c87129","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-14T11:06:00Z","title_canon_sha256":"e2874c9bc25d5dd71df1222a2b5eaf86ff3abc7c7f730ae1e0955c6fe6bbd58c"},"schema_version":"1.0","source":{"id":"1308.3086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3086","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3086v1","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3086","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"IZMZXR5P46I5","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IZMZXR5P46I56XFP","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IZMZXR5P","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:9d776323e58b86e666aa8e55454302f6871767e6fced459b1a77f6b5b741067d","target":"graph","created_at":"2026-05-18T03:14:38Z","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 study natural lifting operations from a bundle E over R to the dual bundle of its first-jet bundle. The main purpose is to define a complete lift of a type (1,1) tensor field on E and to understand all features of its construction. Various other lifting operations of tensorial objects on E are needed for that purpose. We prove that the complete lift of a type (1,1) tensor with vanishing Nijenhuis torsion gives rise to a Poisson-Nijenhuis structure on the dual of the first-jet bundle, and discuss in detail how the construction of associated Darboux-Nijenhuis coordinates can be carried out.","authors_text":"Goedele Waeyaert, Willy Sarlet","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-14T11:06:00Z","title":"Lifting geometric objects to the dual of the first jet bundle of a bundle fibred over R"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3086","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":"sha256:463c41c48faaa054f741a2d1234fa9b74a1684ac6a48d456d4dfb79dbb5ca388","target":"record","created_at":"2026-05-18T03:14:38Z","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":"d5bfd3d7345f5f72e438ef7c0cb4eefc53b759a06b4effbe91fc21ad50c87129","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-08-14T11:06:00Z","title_canon_sha256":"e2874c9bc25d5dd71df1222a2b5eaf86ff3abc7c7f730ae1e0955c6fe6bbd58c"},"schema_version":"1.0","source":{"id":"1308.3086","kind":"arxiv","version":1}},"canonical_sha256":"46599bc7afe791df5cafc49f92a792baf6947004fb1148536bb7b58906f89178","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46599bc7afe791df5cafc49f92a792baf6947004fb1148536bb7b58906f89178","first_computed_at":"2026-05-18T03:14:38.786632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:38.786632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QFPHQGuby+pbHyKfGUrOSzYZOjUSISCbrI5WXpvpEBkUgQ3i7ZwS27YP3utmz5+lyOF+BbFSaHSKnPyyKfI+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:38.787121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:463c41c48faaa054f741a2d1234fa9b74a1684ac6a48d456d4dfb79dbb5ca388","sha256:9d776323e58b86e666aa8e55454302f6871767e6fced459b1a77f6b5b741067d"],"state_sha256":"7f6c505257de8464eed9ce73039a80cee70fc7bddf1c8e2b067bb3cf399ad16e"}