{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:66VFHHRFGCMNLQRWQX3EAA6NAY","short_pith_number":"pith:66VFHHRF","canonical_record":{"source":{"id":"1410.4419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-16T13:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"4364ac214332c4da6a38a59f92133a1ed0e76119e4c237910cf8ee2f9ad7cb7f","abstract_canon_sha256":"03d1635692e2a8908d2d0047573f3be5adfd532289cd8b88a40e63332248e698"},"schema_version":"1.0"},"canonical_sha256":"f7aa539e253098d5c23685f64003cd060e5ff59022e80fe9c4903e377e69e9aa","source":{"kind":"arxiv","id":"1410.4419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4419","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4419v1","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4419","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"66VFHHRFGCMN","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"66VFHHRFGCMNLQRW","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"66VFHHRF","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:66VFHHRFGCMNLQRWQX3EAA6NAY","target":"record","payload":{"canonical_record":{"source":{"id":"1410.4419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-16T13:44:21Z","cross_cats_sorted":[],"title_canon_sha256":"4364ac214332c4da6a38a59f92133a1ed0e76119e4c237910cf8ee2f9ad7cb7f","abstract_canon_sha256":"03d1635692e2a8908d2d0047573f3be5adfd532289cd8b88a40e63332248e698"},"schema_version":"1.0"},"canonical_sha256":"f7aa539e253098d5c23685f64003cd060e5ff59022e80fe9c4903e377e69e9aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:56.181806Z","signature_b64":"Y6jDB8wzGG2++nE4ekWVhtmlAJSQaOI+77nx89KqRQPAjS74m7fDrb0jekksiIo+YSUq1NjaEHGdrOoZ/dWaBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7aa539e253098d5c23685f64003cd060e5ff59022e80fe9c4903e377e69e9aa","last_reissued_at":"2026-05-18T02:39:56.181415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:56.181415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.4419","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqpczXkHmLZhEKJnVj4sN5vckAR45ZcfOKtqvmuXukL96G4o9dC1p/KS6I6VasFi5uM7KjYyKReC/0hFzxcIAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:10:22.288403Z"},"content_sha256":"a16c68bdb225ce0616ec32113dd127a2231b621dd4842cbb03b95fe6e46afade","schema_version":"1.0","event_id":"sha256:a16c68bdb225ce0616ec32113dd127a2231b621dd4842cbb03b95fe6e46afade"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:66VFHHRFGCMNLQRWQX3EAA6NAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical solution of the Burgers' equation with high order splitting methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Muaz Seydao\\u{g}lu, Turgut \\\"Ozi\\c{s}, Utku Erdo\\u{g}an","submitted_at":"2014-10-16T13:44:21Z","abstract_excerpt":"In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and can not be used for time-irreversible systems, such as Burgers equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we conside"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4419","kind":"arxiv","version":1},"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":"2026-05-18T02:39:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Duea9HhPDGT9+aN/5J7vJknoJEysMynhsiMh6AmD+sRt4AQWTTEsGAG485Ux3zLW/fukFjvRE0PAWzMX+/ODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:10:22.288964Z"},"content_sha256":"90d7317c6ab0e7c4b4a92a68a9441b0b5f9fa9ed0dfd822e2d7bde4c19047319","schema_version":"1.0","event_id":"sha256:90d7317c6ab0e7c4b4a92a68a9441b0b5f9fa9ed0dfd822e2d7bde4c19047319"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/bundle.json","state_url":"https://pith.science/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/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":"2026-06-22T12:10:22Z","links":{"resolver":"https://pith.science/pith/66VFHHRFGCMNLQRWQX3EAA6NAY","bundle":"https://pith.science/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/bundle.json","state":"https://pith.science/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/66VFHHRFGCMNLQRWQX3EAA6NAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:66VFHHRFGCMNLQRWQX3EAA6NAY","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":"03d1635692e2a8908d2d0047573f3be5adfd532289cd8b88a40e63332248e698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-16T13:44:21Z","title_canon_sha256":"4364ac214332c4da6a38a59f92133a1ed0e76119e4c237910cf8ee2f9ad7cb7f"},"schema_version":"1.0","source":{"id":"1410.4419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4419","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4419v1","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4419","created_at":"2026-05-18T02:39:56Z"},{"alias_kind":"pith_short_12","alias_value":"66VFHHRFGCMN","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"66VFHHRFGCMNLQRW","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"66VFHHRF","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:90d7317c6ab0e7c4b4a92a68a9441b0b5f9fa9ed0dfd822e2d7bde4c19047319","target":"graph","created_at":"2026-05-18T02:39:56Z","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, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and can not be used for time-irreversible systems, such as Burgers equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we conside","authors_text":"Muaz Seydao\\u{g}lu, Turgut \\\"Ozi\\c{s}, Utku Erdo\\u{g}an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-16T13:44:21Z","title":"Numerical solution of the Burgers' equation with high order splitting methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4419","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:a16c68bdb225ce0616ec32113dd127a2231b621dd4842cbb03b95fe6e46afade","target":"record","created_at":"2026-05-18T02:39:56Z","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":"03d1635692e2a8908d2d0047573f3be5adfd532289cd8b88a40e63332248e698","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-10-16T13:44:21Z","title_canon_sha256":"4364ac214332c4da6a38a59f92133a1ed0e76119e4c237910cf8ee2f9ad7cb7f"},"schema_version":"1.0","source":{"id":"1410.4419","kind":"arxiv","version":1}},"canonical_sha256":"f7aa539e253098d5c23685f64003cd060e5ff59022e80fe9c4903e377e69e9aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7aa539e253098d5c23685f64003cd060e5ff59022e80fe9c4903e377e69e9aa","first_computed_at":"2026-05-18T02:39:56.181415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:56.181415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y6jDB8wzGG2++nE4ekWVhtmlAJSQaOI+77nx89KqRQPAjS74m7fDrb0jekksiIo+YSUq1NjaEHGdrOoZ/dWaBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:56.181806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a16c68bdb225ce0616ec32113dd127a2231b621dd4842cbb03b95fe6e46afade","sha256:90d7317c6ab0e7c4b4a92a68a9441b0b5f9fa9ed0dfd822e2d7bde4c19047319"],"state_sha256":"6e90a72809934c2926dd751bd9d7faa47f78d8cac974d9fde73f798793aa3d95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvnwIA7zi7vIjRSYIoRwLvH7eism8cZ9V+NGQDEdcwwioTPygv+TdbAK5vilLRc6zm70LskCFURgxKUCblDfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:10:22.291610Z","bundle_sha256":"73018031932ceeae51e2cca7837e18cf22ba891c41d98064f48472feab7c372c"}}