{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:UG4GMBZHSMIREORXDAHH72TK26","short_pith_number":"pith:UG4GMBZH","schema_version":"1.0","canonical_sha256":"a1b86607279311123a37180e7fea6ad7b51dccf7d3df36d84fbb2e7a43d833f5","source":{"kind":"arxiv","id":"math-ph/0403041","version":1},"attestation_state":"computed","paper":{"title":"Lagrangian Description of the Variational Equations","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. L. Salas-Brito, C. M. Arizmendi, H. N. N\\'u\\~nez-Y\\'epez, J. Delgado","submitted_at":"2004-03-21T15:57:49Z","abstract_excerpt":"A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter d"},"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":"math-ph/0403041","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-03-21T15:57:49Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1364be85afc0c554dec5b883605740fe396199cf06babbb56a454b2f8e784aac","abstract_canon_sha256":"4cc4663908ab5326eba56ed9e93abb43d94308973c8950fba22ee5f5d77e4684"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:09.790841Z","signature_b64":"ezxZAFvRiIfOWiamMl7z07PTq9274VWeNQB/vMVnDPzfkQXnVH9JT5T1pkc+FxV4gULXOUzOBF7TCA7Z/QJXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1b86607279311123a37180e7fea6ad7b51dccf7d3df36d84fbb2e7a43d833f5","last_reissued_at":"2026-05-18T01:04:09.790336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:09.790336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangian Description of the Variational Equations","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. L. Salas-Brito, C. M. Arizmendi, H. N. N\\'u\\~nez-Y\\'epez, J. Delgado","submitted_at":"2004-03-21T15:57:49Z","abstract_excerpt":"A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0403041","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":"math-ph/0403041","created_at":"2026-05-18T01:04:09.790420+00:00"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0403041v1","created_at":"2026-05-18T01:04:09.790420+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0403041","created_at":"2026-05-18T01:04:09.790420+00:00"},{"alias_kind":"pith_short_12","alias_value":"UG4GMBZHSMIR","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"UG4GMBZHSMIREORX","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"UG4GMBZH","created_at":"2026-05-18T12:25:52.687210+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/UG4GMBZHSMIREORXDAHH72TK26","json":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26.json","graph_json":"https://pith.science/api/pith-number/UG4GMBZHSMIREORXDAHH72TK26/graph.json","events_json":"https://pith.science/api/pith-number/UG4GMBZHSMIREORXDAHH72TK26/events.json","paper":"https://pith.science/paper/UG4GMBZH"},"agent_actions":{"view_html":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26","download_json":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26.json","view_paper":"https://pith.science/paper/UG4GMBZH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math-ph/0403041&json=true","fetch_graph":"https://pith.science/api/pith-number/UG4GMBZHSMIREORXDAHH72TK26/graph.json","fetch_events":"https://pith.science/api/pith-number/UG4GMBZHSMIREORXDAHH72TK26/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26/action/storage_attestation","attest_author":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26/action/author_attestation","sign_citation":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26/action/citation_signature","submit_replication":"https://pith.science/pith/UG4GMBZHSMIREORXDAHH72TK26/action/replication_record"}},"created_at":"2026-05-18T01:04:09.790420+00:00","updated_at":"2026-05-18T01:04:09.790420+00:00"}