{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HZSQ27MAV2555QIRZCWZYCHR2G","short_pith_number":"pith:HZSQ27MA","schema_version":"1.0","canonical_sha256":"3e650d7d80aebbdec111c8ad9c08f1d1b08045c52d423feca0cc68c10c5e1197","source":{"kind":"arxiv","id":"1407.4968","version":1},"attestation_state":"computed","paper":{"title":"Lifted tensors and Hamilton-Jacobi separability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"G. Waeyaert, W. Sarlet","submitted_at":"2014-07-18T12:17:35Z","abstract_excerpt":"Starting from a bundle E over R, the dual of the first jet bundle, which is a co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. Based on previous work, we recall properties of the complete lifts of a type (1,1) tensor R on E to both of these manifolds. We discuss how an interplay between these lifted tensors leads to the identification of related distributions on both manifolds. The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditi"},"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":"1407.4968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-07-18T12:17:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"31604d92049851791da3194199a034beab519e38ab295e286d0f2ae6f825a891","abstract_canon_sha256":"dd1ff16f3ad2600d5cbc948a15af18621e34a740c9216b4ee88167ee45e80e4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:41.876761Z","signature_b64":"Q+aJrxPsaVIJIa29n2UEPlc/IY6RMN5UQ/DiAqoePRc9lKnLq5wTRiX0qlVTCOj7Y9NVPd06B0eD43QC7WomAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e650d7d80aebbdec111c8ad9c08f1d1b08045c52d423feca0cc68c10c5e1197","last_reissued_at":"2026-05-18T02:44:41.876276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:41.876276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifted tensors and Hamilton-Jacobi separability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"G. Waeyaert, W. Sarlet","submitted_at":"2014-07-18T12:17:35Z","abstract_excerpt":"Starting from a bundle E over R, the dual of the first jet bundle, which is a co-dimension 1 sub-bundle of the cotangent bundle of E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. Based on previous work, we recall properties of the complete lifts of a type (1,1) tensor R on E to both of these manifolds. We discuss how an interplay between these lifted tensors leads to the identification of related distributions on both manifolds. The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4968","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":"1407.4968","created_at":"2026-05-18T02:44:41.876350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.4968v1","created_at":"2026-05-18T02:44:41.876350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.4968","created_at":"2026-05-18T02:44:41.876350+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZSQ27MAV255","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZSQ27MAV2555QIR","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZSQ27MA","created_at":"2026-05-18T12:28:33.132498+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/HZSQ27MAV2555QIRZCWZYCHR2G","json":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G.json","graph_json":"https://pith.science/api/pith-number/HZSQ27MAV2555QIRZCWZYCHR2G/graph.json","events_json":"https://pith.science/api/pith-number/HZSQ27MAV2555QIRZCWZYCHR2G/events.json","paper":"https://pith.science/paper/HZSQ27MA"},"agent_actions":{"view_html":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G","download_json":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G.json","view_paper":"https://pith.science/paper/HZSQ27MA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.4968&json=true","fetch_graph":"https://pith.science/api/pith-number/HZSQ27MAV2555QIRZCWZYCHR2G/graph.json","fetch_events":"https://pith.science/api/pith-number/HZSQ27MAV2555QIRZCWZYCHR2G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G/action/storage_attestation","attest_author":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G/action/author_attestation","sign_citation":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G/action/citation_signature","submit_replication":"https://pith.science/pith/HZSQ27MAV2555QIRZCWZYCHR2G/action/replication_record"}},"created_at":"2026-05-18T02:44:41.876350+00:00","updated_at":"2026-05-18T02:44:41.876350+00:00"}