{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YYY4KIOVTXIFRFSFHQ2BKNGWSB","short_pith_number":"pith:YYY4KIOV","canonical_record":{"source":{"id":"1903.10857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-20T17:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"184d85b553792f66a744e4418f6b106bdf1bca1b44e5e8f6c415bfb556a47147","abstract_canon_sha256":"12b0e774dae5dd53b30e5114ec7a3363d34b26709f71e048feea56c735a3bcf4"},"schema_version":"1.0"},"canonical_sha256":"c631c521d59dd05896453c341534d690558dfa121a368ebcc78c7670d672539e","source":{"kind":"arxiv","id":"1903.10857","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10857","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10857v1","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10857","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"YYY4KIOVTXIF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YYY4KIOVTXIFRFSF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YYY4KIOV","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YYY4KIOVTXIFRFSFHQ2BKNGWSB","target":"record","payload":{"canonical_record":{"source":{"id":"1903.10857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-20T17:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"184d85b553792f66a744e4418f6b106bdf1bca1b44e5e8f6c415bfb556a47147","abstract_canon_sha256":"12b0e774dae5dd53b30e5114ec7a3363d34b26709f71e048feea56c735a3bcf4"},"schema_version":"1.0"},"canonical_sha256":"c631c521d59dd05896453c341534d690558dfa121a368ebcc78c7670d672539e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:17.512193Z","signature_b64":"sG1s1j6DuJRtY+3U4SMrOq7MFLNPUyECnPkJIZDrp6O2Q1owKII7dLPJrTIkanwDJuc/b7BHuF7g0gDoQ4jkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c631c521d59dd05896453c341534d690558dfa121a368ebcc78c7670d672539e","last_reissued_at":"2026-05-17T23:50:17.511510Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:17.511510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.10857","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":"2026-05-17T23:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1LXjWS1QQNt/HvNV8c/uy9ifr5J3RZP99au6pWoHvZP0l5w4aDzeDiCOVg+Hhmw/ne9/QwWyNm9AW8xsc6NDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:38:29.991804Z"},"content_sha256":"d73767f2cb0ce060332ced340a9b5141cd13d31ac9e7e3d254defb82aff37fc3","schema_version":"1.0","event_id":"sha256:d73767f2cb0ce060332ced340a9b5141cd13d31ac9e7e3d254defb82aff37fc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YYY4KIOVTXIFRFSFHQ2BKNGWSB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error Estimate of MacCormack Rapid Solver Method for 2D Incompressible Navier-Stokes Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric Ngondiep","submitted_at":"2019-03-20T17:02:04Z","abstract_excerpt":"The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis of the method. The theoretical result suggests that the rapid solver method is both convergent and second order accurate with respect to time step $\\Delta t.$ A wide set of numerical evidences confirm this theoretical analysis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10857","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":"2026-05-17T23:50:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1OZoAMTEWOByL3O0qipSQUWFr1kXrPqsbfxHDX0zL3CiTpbJ6xTvPMCddm1cmvucflHgvx42CZimTAsVJFMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:38:29.992159Z"},"content_sha256":"6d8d697c10f5663be90c3255b14e487cc9e47350d2b58d1819ac8683e13b27dc","schema_version":"1.0","event_id":"sha256:6d8d697c10f5663be90c3255b14e487cc9e47350d2b58d1819ac8683e13b27dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/bundle.json","state_url":"https://pith.science/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/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":"2026-06-02T21:38:29Z","links":{"resolver":"https://pith.science/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB","bundle":"https://pith.science/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/bundle.json","state":"https://pith.science/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYY4KIOVTXIFRFSFHQ2BKNGWSB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YYY4KIOVTXIFRFSFHQ2BKNGWSB","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":"12b0e774dae5dd53b30e5114ec7a3363d34b26709f71e048feea56c735a3bcf4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-20T17:02:04Z","title_canon_sha256":"184d85b553792f66a744e4418f6b106bdf1bca1b44e5e8f6c415bfb556a47147"},"schema_version":"1.0","source":{"id":"1903.10857","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10857","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10857v1","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10857","created_at":"2026-05-17T23:50:17Z"},{"alias_kind":"pith_short_12","alias_value":"YYY4KIOVTXIF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YYY4KIOVTXIFRFSF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YYY4KIOV","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:6d8d697c10f5663be90c3255b14e487cc9e47350d2b58d1819ac8683e13b27dc","target":"graph","created_at":"2026-05-17T23:50:17Z","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":"The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis of the method. The theoretical result suggests that the rapid solver method is both convergent and second order accurate with respect to time step $\\Delta t.$ A wide set of numerical evidences confirm this theoretical analysis.","authors_text":"Eric Ngondiep","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-20T17:02:04Z","title":"Error Estimate of MacCormack Rapid Solver Method for 2D Incompressible Navier-Stokes Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10857","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:d73767f2cb0ce060332ced340a9b5141cd13d31ac9e7e3d254defb82aff37fc3","target":"record","created_at":"2026-05-17T23:50:17Z","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":"12b0e774dae5dd53b30e5114ec7a3363d34b26709f71e048feea56c735a3bcf4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-20T17:02:04Z","title_canon_sha256":"184d85b553792f66a744e4418f6b106bdf1bca1b44e5e8f6c415bfb556a47147"},"schema_version":"1.0","source":{"id":"1903.10857","kind":"arxiv","version":1}},"canonical_sha256":"c631c521d59dd05896453c341534d690558dfa121a368ebcc78c7670d672539e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c631c521d59dd05896453c341534d690558dfa121a368ebcc78c7670d672539e","first_computed_at":"2026-05-17T23:50:17.511510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:17.511510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sG1s1j6DuJRtY+3U4SMrOq7MFLNPUyECnPkJIZDrp6O2Q1owKII7dLPJrTIkanwDJuc/b7BHuF7g0gDoQ4jkBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:17.512193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10857","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d73767f2cb0ce060332ced340a9b5141cd13d31ac9e7e3d254defb82aff37fc3","sha256:6d8d697c10f5663be90c3255b14e487cc9e47350d2b58d1819ac8683e13b27dc"],"state_sha256":"4f76561fb18d0fe73ac0927e7bca5d05c667d257318fbf5ae8a3ebe87ab989b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMMK/IEBH4D7nAWeWHipsykzXEvhmN+UWhu1LhOSu6fY/EN0jKzFynVuqMYoxPkZQLKzRFZXK/CfU76cs88zBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:38:29.994191Z","bundle_sha256":"67b94ba57d670c930f28f595e0e15c38cd94593329d0270b13d9f94c188ee5b8"}}