{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JJ3Q6H7W7UF3BVCJHTYJEC7QDC","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":"5a21933e9d7970fd7e7bd0c5bd63b128afeecba7d2909c7c8467a600a3fde21f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-10-28T21:48:59Z","title_canon_sha256":"3aed5c1374e9f9aa8ac994b26c0d0503fdc3f534fa9d3a7c2080de058858c91d"},"schema_version":"1.0","source":{"id":"1410.7825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7825","created_at":"2026-05-18T02:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7825v1","created_at":"2026-05-18T02:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7825","created_at":"2026-05-18T02:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"JJ3Q6H7W7UF3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JJ3Q6H7W7UF3BVCJ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JJ3Q6H7W","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:e84b05dbcb493b16002ebfb4b2403541ed85f479fd7af9b16faeeb732655c04f","target":"graph","created_at":"2026-05-18T02:39:08Z","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":"In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian function/density, or a Hamiltonian that admits Lagrangian counterpart. These geometric frameworks are used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems ","authors_text":"Pedro D. Prieto-Mart\\'inez","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-10-28T21:48:59Z","title":"Geometrical structures of higher-order dynamical systems and field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7825","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":"sha256:18053683e85ebf91bdefe6c5749c1345efc15a35d0d3ce8f8227e32a17b6805b","target":"record","created_at":"2026-05-18T02:39:08Z","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":"5a21933e9d7970fd7e7bd0c5bd63b128afeecba7d2909c7c8467a600a3fde21f","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-10-28T21:48:59Z","title_canon_sha256":"3aed5c1374e9f9aa8ac994b26c0d0503fdc3f534fa9d3a7c2080de058858c91d"},"schema_version":"1.0","source":{"id":"1410.7825","kind":"arxiv","version":1}},"canonical_sha256":"4a770f1ff6fd0bb0d4493cf0920bf018af4cb9679c5f2a21f0f86931661d2276","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a770f1ff6fd0bb0d4493cf0920bf018af4cb9679c5f2a21f0f86931661d2276","first_computed_at":"2026-05-18T02:39:08.119083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:08.119083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cscjoy7aIAZEBS0PCsdOZSt2HswaIoYhfuvAdA6ipGwpivUORo6dBdnC+nujfPyGdl687jTOWB1FL/NChkY4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:08.119562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18053683e85ebf91bdefe6c5749c1345efc15a35d0d3ce8f8227e32a17b6805b","sha256:e84b05dbcb493b16002ebfb4b2403541ed85f479fd7af9b16faeeb732655c04f"],"state_sha256":"b01b4cc65a3dbfdb95d0edff1f66b7ef5ebdb931a712245a24dc69ebb6716e53"}