{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZYK2EGTSWELB6F37GMZOYGY545","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":"691ec0494abbc18ab35621d7c1d2755678b4c5f8aa6b3c05596d603b9a9a9e41","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-01T13:06:50Z","title_canon_sha256":"5e12c102e7ac7ca3d5c5925ed3ba04bb8b492ae004fb955567a08c9423bb4d74"},"schema_version":"1.0","source":{"id":"1009.0174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0174","created_at":"2026-05-18T02:05:38Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0174v2","created_at":"2026-05-18T02:05:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0174","created_at":"2026-05-18T02:05:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZYK2EGTSWELB","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZYK2EGTSWELB6F37","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZYK2EGTS","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:8eaa34c97352f005544721e84c8c7ec215716d423026d02737c96ff8a9e1b366","target":"graph","created_at":"2026-05-18T02:05:38Z","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":"A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism.","authors_text":"E. Guzm\\'an, J.C. Marrero","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-01T13:06:50Z","title":"Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0174","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":"sha256:57cc5f7703fbca50b27d0bfe6672497512f063b682fe8d4645652600d5dbe817","target":"record","created_at":"2026-05-18T02:05:38Z","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":"691ec0494abbc18ab35621d7c1d2755678b4c5f8aa6b3c05596d603b9a9a9e41","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-01T13:06:50Z","title_canon_sha256":"5e12c102e7ac7ca3d5c5925ed3ba04bb8b492ae004fb955567a08c9423bb4d74"},"schema_version":"1.0","source":{"id":"1009.0174","kind":"arxiv","version":2}},"canonical_sha256":"ce15a21a72b1161f177f3332ec1b1de7520c69f2b6a00cc4402c3588c370759d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce15a21a72b1161f177f3332ec1b1de7520c69f2b6a00cc4402c3588c370759d","first_computed_at":"2026-05-18T02:05:38.535282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:05:38.535282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rCFZgxDeyMmiZp6xV2XOjoOhZC+Hw50Qf2e3lkJwXbLIMCPKgq9SpS2EQnbaPPE9nw32K0S83NjHtfwx3PScDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:05:38.535980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57cc5f7703fbca50b27d0bfe6672497512f063b682fe8d4645652600d5dbe817","sha256:8eaa34c97352f005544721e84c8c7ec215716d423026d02737c96ff8a9e1b366"],"state_sha256":"b7757c4b924df5f893a40ea0b1c2eb93d563ba9f393073b858e022ee7ff91827"}