{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IK44Z6UTYA2WCMFLNPORODB477","short_pith_number":"pith:IK44Z6UT","canonical_record":{"source":{"id":"1304.1398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-04T15:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"80a9fa052e3d070e7961193807c239b86aff9ceb4ea3180f8f34b57c39f0d4f8","abstract_canon_sha256":"b71bdfddddc319e5c9a290fab8670b4b74e8271c965c1643be125a0183fa12bc"},"schema_version":"1.0"},"canonical_sha256":"42b9ccfa93c0356130ab6bdd170c3cffdeb9666b465b7cd7a73923f16c30ef0b","source":{"kind":"arxiv","id":"1304.1398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1398","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1398v2","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1398","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"IK44Z6UTYA2W","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IK44Z6UTYA2WCMFL","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IK44Z6UT","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IK44Z6UTYA2WCMFLNPORODB477","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-04T15:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"80a9fa052e3d070e7961193807c239b86aff9ceb4ea3180f8f34b57c39f0d4f8","abstract_canon_sha256":"b71bdfddddc319e5c9a290fab8670b4b74e8271c965c1643be125a0183fa12bc"},"schema_version":"1.0"},"canonical_sha256":"42b9ccfa93c0356130ab6bdd170c3cffdeb9666b465b7cd7a73923f16c30ef0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:47.096006Z","signature_b64":"u8EO9tNcglvbesJB5/AopPXHuWPa+4Y0FH8f/iY2xd/TT1MwQkzmc0lCnPMH4Zbwjdx5zyDuvEu9f33uXXBaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42b9ccfa93c0356130ab6bdd170c3cffdeb9666b465b7cd7a73923f16c30ef0b","last_reissued_at":"2026-05-18T02:54:47.095635Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:47.095635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1398","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/9KDyttXFWdnsst8L1WKo0DdM1amIFE7MuSlA9HBrrIGroMRXEQeunYSXrVdcXEFrIyJh1GlKt+xWl+hH/5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:42:36.592284Z"},"content_sha256":"3463fc43640793af5f94d78ff64341276f4e4c397c97cbf2a775bafb1a716af2","schema_version":"1.0","event_id":"sha256:3463fc43640793af5f94d78ff64341276f4e4c397c97cbf2a775bafb1a716af2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IK44Z6UTYA2WCMFLNPORODB477","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction and analysis of higher order Galerkin variational integrators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Nils Saake, Sina Ober-Bl\\\"obaum","submitted_at":"2013-04-04T15:27:38Z","abstract_excerpt":"In this work we derive and analyze variational integrators of higher order for the structure-preserving simulation of mechanical systems. The construction is based on a space of polynomials together with Gauss and Lobatto quadrature rules to approximate the relevant integrals in the variational principle. The use of higher order schemes increases the accuracy of the discrete solution and thereby decrease the computational cost while the preservation properties of the scheme are still guaranteed. The order of convergence of the resulting variational integrators are investigated numerically and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1398","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmqwGWM55aTnb9Ve4fRLqRbiPGH+J0Amj1H9ekmFyR2ygN1H3Dia34YmVUNCG90z3cw0Gv2uTJa5QS8H6IANCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:42:36.592646Z"},"content_sha256":"9c6850af76802ad6b759cbdff4c5354c8a7a476505b3e66277eacafd1b1908a1","schema_version":"1.0","event_id":"sha256:9c6850af76802ad6b759cbdff4c5354c8a7a476505b3e66277eacafd1b1908a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IK44Z6UTYA2WCMFLNPORODB477/bundle.json","state_url":"https://pith.science/pith/IK44Z6UTYA2WCMFLNPORODB477/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IK44Z6UTYA2WCMFLNPORODB477/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T02:42:36Z","links":{"resolver":"https://pith.science/pith/IK44Z6UTYA2WCMFLNPORODB477","bundle":"https://pith.science/pith/IK44Z6UTYA2WCMFLNPORODB477/bundle.json","state":"https://pith.science/pith/IK44Z6UTYA2WCMFLNPORODB477/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IK44Z6UTYA2WCMFLNPORODB477/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IK44Z6UTYA2WCMFLNPORODB477","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":"b71bdfddddc319e5c9a290fab8670b4b74e8271c965c1643be125a0183fa12bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-04T15:27:38Z","title_canon_sha256":"80a9fa052e3d070e7961193807c239b86aff9ceb4ea3180f8f34b57c39f0d4f8"},"schema_version":"1.0","source":{"id":"1304.1398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1398","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1398v2","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1398","created_at":"2026-05-18T02:54:47Z"},{"alias_kind":"pith_short_12","alias_value":"IK44Z6UTYA2W","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"IK44Z6UTYA2WCMFL","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"IK44Z6UT","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:9c6850af76802ad6b759cbdff4c5354c8a7a476505b3e66277eacafd1b1908a1","target":"graph","created_at":"2026-05-18T02:54:47Z","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 work we derive and analyze variational integrators of higher order for the structure-preserving simulation of mechanical systems. The construction is based on a space of polynomials together with Gauss and Lobatto quadrature rules to approximate the relevant integrals in the variational principle. The use of higher order schemes increases the accuracy of the discrete solution and thereby decrease the computational cost while the preservation properties of the scheme are still guaranteed. The order of convergence of the resulting variational integrators are investigated numerically and ","authors_text":"Nils Saake, Sina Ober-Bl\\\"obaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-04T15:27:38Z","title":"Construction and analysis of higher order Galerkin variational integrators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1398","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":"sha256:3463fc43640793af5f94d78ff64341276f4e4c397c97cbf2a775bafb1a716af2","target":"record","created_at":"2026-05-18T02:54:47Z","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":"b71bdfddddc319e5c9a290fab8670b4b74e8271c965c1643be125a0183fa12bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-04T15:27:38Z","title_canon_sha256":"80a9fa052e3d070e7961193807c239b86aff9ceb4ea3180f8f34b57c39f0d4f8"},"schema_version":"1.0","source":{"id":"1304.1398","kind":"arxiv","version":2}},"canonical_sha256":"42b9ccfa93c0356130ab6bdd170c3cffdeb9666b465b7cd7a73923f16c30ef0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42b9ccfa93c0356130ab6bdd170c3cffdeb9666b465b7cd7a73923f16c30ef0b","first_computed_at":"2026-05-18T02:54:47.095635Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:47.095635Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u8EO9tNcglvbesJB5/AopPXHuWPa+4Y0FH8f/iY2xd/TT1MwQkzmc0lCnPMH4Zbwjdx5zyDuvEu9f33uXXBaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:47.096006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3463fc43640793af5f94d78ff64341276f4e4c397c97cbf2a775bafb1a716af2","sha256:9c6850af76802ad6b759cbdff4c5354c8a7a476505b3e66277eacafd1b1908a1"],"state_sha256":"0d584aa889ce33cc2985622f4d6df6cd48a15341d6c724032d7c3d1cd32c7d71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+/L+86bYpUayuuoQF2BfRaUuzMM6CQZPJsggcu57Ca7g5FqXCZOPrZBUXWnv/AFtbrAeHrR8BQgf8J4a8XkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:42:36.594597Z","bundle_sha256":"9359f95d4ddb7a9cf9d29df14312954fce2f683c338ec870f4f8306c0d105e26"}}