{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HKKYPH2BAPGUFNRYIXB32UZZ6K","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":"19d346c177493ece5937ff37295714ee861ff3d6816122f01e68a8d14f8b99c7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-09T14:16:18Z","title_canon_sha256":"01010740573246d6356972d8f4c580b53b897be160828d0da6fc570bbc7dc305"},"schema_version":"1.0","source":{"id":"1309.2166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2166","created_at":"2026-05-18T02:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2166v2","created_at":"2026-05-18T02:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2166","created_at":"2026-05-18T02:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"HKKYPH2BAPGU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HKKYPH2BAPGUFNRY","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HKKYPH2B","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:018250d878a84af0444d18f1c7fb9cb94c7b271fba0af9b8bc829ad514a81053","target":"graph","created_at":"2026-05-18T02:51:08Z","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":"The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi equations in these formalisms and apply our results to analyze some particular physical examples.","authors_text":"Leonardo Colombo, Manuel de Le\\'on, Narciso Rom\\'an-Roy, Pedro Daniel Prieto-Mart\\'inez","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-09T14:16:18Z","title":"Geometric Hamilton-Jacobi theory for higher-order autonomous systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2166","kind":"arxiv","version":2},"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":"sha256:1f86955bcb7481d93808ba5b77bb38252e8194478b19209bfe9c5dc449cf2e39","target":"record","created_at":"2026-05-18T02:51:08Z","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":"19d346c177493ece5937ff37295714ee861ff3d6816122f01e68a8d14f8b99c7","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-09T14:16:18Z","title_canon_sha256":"01010740573246d6356972d8f4c580b53b897be160828d0da6fc570bbc7dc305"},"schema_version":"1.0","source":{"id":"1309.2166","kind":"arxiv","version":2}},"canonical_sha256":"3a95879f4103cd42b63845c3bd5339f289ef10ee08f33a93df5aa32725c4f66b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a95879f4103cd42b63845c3bd5339f289ef10ee08f33a93df5aa32725c4f66b","first_computed_at":"2026-05-18T02:51:08.418947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:08.418947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sjsU5bGRe3xW/3Pzt04qhCqkk6COrfS8yucx/sd8SLaroTPyVVW3MHFTLqUNysbX1nuJwP//bygwrS+eqA7HDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:08.419358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f86955bcb7481d93808ba5b77bb38252e8194478b19209bfe9c5dc449cf2e39","sha256:018250d878a84af0444d18f1c7fb9cb94c7b271fba0af9b8bc829ad514a81053"],"state_sha256":"222b66b90157d939ab4907e4b0d1eef5725152c6723cd9226855aeaaeeec8c25"}