{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4GQ6RWM3MMGRPNJAUVA56UOY7Z","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":"0a80abd5f5dfc577628b0bb9fb4349abf645f899afa87be14db9e04d9540f611","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-04T16:54:11Z","title_canon_sha256":"42e128eab8d37c6efd93105c8f45b2296b3e59b8e6f08bf93f672d4c9bfffcbc"},"schema_version":"1.0","source":{"id":"1708.01586","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01586","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01586v1","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01586","created_at":"2026-05-18T00:21:13Z"},{"alias_kind":"pith_short_12","alias_value":"4GQ6RWM3MMGR","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"4GQ6RWM3MMGRPNJA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"4GQ6RWM3","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:842a89ed2e0e9bb9a4ed88c6c16b5354d8d657db3b7419d5d717ac08106aadb9","target":"graph","created_at":"2026-05-18T00:21:13Z","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 paper, we propose a geometric Hamilton-Jacobi theory for systems of implicit differential equations. In particular, we are interested in implicit Hamiltonian systems, described in terms of Lagrangian submanifolds of $TT^*Q$ generated by Morse families.\n  The implicit character implies the nonexistence of a Hamiltonian function describing the dynamics. This fact is here amended by a generating family of Morse functions which plays the role of a Hamiltonian. A Hamilton--Jacobi equation is obtained with the aid of this generating family of functions.\n  To conclude, we apply our results to","authors_text":"C. Sard\\'on, M. De Le\\'On, O. Esen","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-04T16:54:11Z","title":"A Hamilton-Jacobi theory for implicit differential systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01586","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":"sha256:11bfa36b6e750edfd3ec1a5fa09530e693b3822f41c5bbce9cf92cabfabfddb6","target":"record","created_at":"2026-05-18T00:21:13Z","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":"0a80abd5f5dfc577628b0bb9fb4349abf645f899afa87be14db9e04d9540f611","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-04T16:54:11Z","title_canon_sha256":"42e128eab8d37c6efd93105c8f45b2296b3e59b8e6f08bf93f672d4c9bfffcbc"},"schema_version":"1.0","source":{"id":"1708.01586","kind":"arxiv","version":1}},"canonical_sha256":"e1a1e8d99b630d17b520a541df51d8fe5765e5415c0376f5547179500e3c797b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1a1e8d99b630d17b520a541df51d8fe5765e5415c0376f5547179500e3c797b","first_computed_at":"2026-05-18T00:21:13.180855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:13.180855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a3I0ZrJoWBi0U9U7PdXelMI1Zejc7fCXq60kcjesxucPcetEdW4Eodq/TL3RDXYaEL25+HAlHqEXhno2WrYrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:13.181488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01586","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11bfa36b6e750edfd3ec1a5fa09530e693b3822f41c5bbce9cf92cabfabfddb6","sha256:842a89ed2e0e9bb9a4ed88c6c16b5354d8d657db3b7419d5d717ac08106aadb9"],"state_sha256":"1c67a4945001c07f40bca0d622c22b40c2382699b486825363f9076e640e2697"}