{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XR3BFGLXPXKL7WEXJ5D5VMGPIN","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":"bd31dbe3249e5b43bfb3ebfbe75c635457f447200515a32b1e680b5cddfe679f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-04T21:50:46Z","title_canon_sha256":"ee7db6fb1ce3bccbbd9fe4bb343a4c3541b1730691484ffcd0676d22d3d0756e"},"schema_version":"1.0","source":{"id":"1209.0807","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0807","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0807v1","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0807","created_at":"2026-05-18T03:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"XR3BFGLXPXKL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XR3BFGLXPXKL7WEX","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XR3BFGLX","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:c95a026f684a5200ce9b11da29e2ddecbc20f0a7b283793242e8f472a46b64f0","target":"graph","created_at":"2026-05-18T03:46:16Z","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":"Lagrangian submanifolds are becoming a very essential tool to generalize and geometrically understand results and procedures in the area of mathematical physics. Here we use general Lagrangian submanifolds to provide a geometric version of the Hamilton-Jacobi equation. This interpretation allows us to study some interesting applications of Hamilton-Jacobi equation in holonomic, nonholonomic and time-dependent dynamics from a geometrical point of view.","authors_text":"D. Mart\\'in de Diego, M. Barbero-Li\\~n\\'an, M. De Le\\'On","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-04T21:50:46Z","title":"Lagrangian submanifolds and Hamilton-Jacobi equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0807","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":"sha256:5d64482e8399aa159e7475445ca063c2681beaa596669795ab11088feac2fd15","target":"record","created_at":"2026-05-18T03:46:16Z","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":"bd31dbe3249e5b43bfb3ebfbe75c635457f447200515a32b1e680b5cddfe679f","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-09-04T21:50:46Z","title_canon_sha256":"ee7db6fb1ce3bccbbd9fe4bb343a4c3541b1730691484ffcd0676d22d3d0756e"},"schema_version":"1.0","source":{"id":"1209.0807","kind":"arxiv","version":1}},"canonical_sha256":"bc761299777dd4bfd8974f47dab0cf436b8632b4d9ff4dc9b7173bc4cda67192","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc761299777dd4bfd8974f47dab0cf436b8632b4d9ff4dc9b7173bc4cda67192","first_computed_at":"2026-05-18T03:46:16.172492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:16.172492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nvuMAneBuWU5ijvHd9WmopB1+JtOBN6bm0n3q0ZitpfE2fqgNOTdbVDQVu2S8eojmD91S1OCKlkefLeUUN/MAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:16.173179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0807","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d64482e8399aa159e7475445ca063c2681beaa596669795ab11088feac2fd15","sha256:c95a026f684a5200ce9b11da29e2ddecbc20f0a7b283793242e8f472a46b64f0"],"state_sha256":"38e841a402fc0dfaede72bdbf85626fb2f3d38a9de51c080983bb571493b2cdf"}