{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IUDTYIRKPHHHGPD5I4YJ6O7RTA","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":"2cf536a299229aa4ee17a5bcd123d335221e4c9bbaa2e6ed0da2219e49788ddb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-21T18:02:53Z","title_canon_sha256":"a5386973cd1a27dfc5c2348da585feefd4fb1842f396962cfb62a7795194b9a7"},"schema_version":"1.0","source":{"id":"1410.5766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5766","created_at":"2026-05-18T02:38:28Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5766v2","created_at":"2026-05-18T02:38:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5766","created_at":"2026-05-18T02:38:28Z"},{"alias_kind":"pith_short_12","alias_value":"IUDTYIRKPHHH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IUDTYIRKPHHHGPD5","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IUDTYIRK","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:7f8230d0f15405c8c646296d2dc4a3fbcbb993f9e08780b8e42688186e452e65","target":"graph","created_at":"2026-05-18T02:38:28Z","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":"Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for higher-order Lagrangian systems. Given a regular higher-order Lagrangian $L\\colon T^{(k)}Q\\to\\mathbb{R}$ with $k\\geq 1$, the resulting discrete equations define a generally implicit numerical integrator algorithm on $T^{(k-1)}Q\\times T^{(k-1)}Q$ that approximates the flow of the higher-order Euler--Lagrange equations for $L$. The algorithm equations are called hig","authors_text":"David Mart\\'in de Diego, Leonardo Colombo, Sebasti\\'an Ferraro","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-21T18:02:53Z","title":"Geometric integrators for higher-order variational systems and their application to optimal control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5766","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":"sha256:4703be5adfe6d16331a9efaffa5561a22c7257741f43f45422ddb4fafce8981f","target":"record","created_at":"2026-05-18T02:38:28Z","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":"2cf536a299229aa4ee17a5bcd123d335221e4c9bbaa2e6ed0da2219e49788ddb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-21T18:02:53Z","title_canon_sha256":"a5386973cd1a27dfc5c2348da585feefd4fb1842f396962cfb62a7795194b9a7"},"schema_version":"1.0","source":{"id":"1410.5766","kind":"arxiv","version":2}},"canonical_sha256":"45073c222a79ce733c7d47309f3bf19829e7debd399f4970a4addcec69ecd374","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45073c222a79ce733c7d47309f3bf19829e7debd399f4970a4addcec69ecd374","first_computed_at":"2026-05-18T02:38:28.183536Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:28.183536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNAxl9g0GHAdNGqgpMT9OBgj9X/sCqhD2K4+QfHffhhRnnE+d29BCY4k29lSKb2+cUR4DSdynb0+i1V6Br5ACg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:28.184112Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4703be5adfe6d16331a9efaffa5561a22c7257741f43f45422ddb4fafce8981f","sha256:7f8230d0f15405c8c646296d2dc4a3fbcbb993f9e08780b8e42688186e452e65"],"state_sha256":"622e7c4f7b7e349db5d6815d415e2ad5a01a16ad0dd4e41035ccd8de5df9106b"}