{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KAIYVJS3Y6V4TDDGYV5MJBHYPU","short_pith_number":"pith:KAIYVJS3","schema_version":"1.0","canonical_sha256":"50118aa65bc7abc98c66c57ac484f87d35a9ea137ed8845d67ffaac47841e818","source":{"kind":"arxiv","id":"1810.02971","version":2},"attestation_state":"computed","paper":{"title":"$2\\odot 2=4$: Temporal-Spatial Coupling and Beyond in Computational Fluid Dynamics (CFD)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jiequan Li","submitted_at":"2018-10-06T10:01:43Z","abstract_excerpt":"With increasing engineering demands, there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct \"physics\". There are two families of high order methods: One is the method of line, relying on the Runge-Kutta (R-K) time-stepping. The building block is the Riemann solution labeled as the solution element \"1\". Each step in R-K just has first order accuracy. In order to derive a fourth order accuracy scheme in time, one needs four stages labeled as \"$1\\odot 1\\odot 1\\odot 1=4$\". The other is the "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1810.02971","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-06T10:01:43Z","cross_cats_sorted":[],"title_canon_sha256":"a3f78427a7c2ed67d509360a6dd5cb3fb506ce7e858c03ac616d33c6180e021b","abstract_canon_sha256":"db84b45151cdffa4c05d35b3f8e24a064ae7aa2727450636929274d13bbdeb9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:01.827903Z","signature_b64":"JDg/Z0brGG74acKIuVvtzKWdGQtK+3DxUUO6/5IPjnJUOlREZbR4DJbMFQJ6lt10Bvc1V0LGviAYvtfMZHObCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50118aa65bc7abc98c66c57ac484f87d35a9ea137ed8845d67ffaac47841e818","last_reissued_at":"2026-05-18T00:00:01.827462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:01.827462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$2\\odot 2=4$: Temporal-Spatial Coupling and Beyond in Computational Fluid Dynamics (CFD)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jiequan Li","submitted_at":"2018-10-06T10:01:43Z","abstract_excerpt":"With increasing engineering demands, there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct \"physics\". There are two families of high order methods: One is the method of line, relying on the Runge-Kutta (R-K) time-stepping. The building block is the Riemann solution labeled as the solution element \"1\". Each step in R-K just has first order accuracy. In order to derive a fourth order accuracy scheme in time, one needs four stages labeled as \"$1\\odot 1\\odot 1\\odot 1=4$\". The other is the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02971","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.02971","created_at":"2026-05-18T00:00:01.827527+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.02971v2","created_at":"2026-05-18T00:00:01.827527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02971","created_at":"2026-05-18T00:00:01.827527+00:00"},{"alias_kind":"pith_short_12","alias_value":"KAIYVJS3Y6V4","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KAIYVJS3Y6V4TDDG","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KAIYVJS3","created_at":"2026-05-18T12:32:33.847187+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU","json":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU.json","graph_json":"https://pith.science/api/pith-number/KAIYVJS3Y6V4TDDGYV5MJBHYPU/graph.json","events_json":"https://pith.science/api/pith-number/KAIYVJS3Y6V4TDDGYV5MJBHYPU/events.json","paper":"https://pith.science/paper/KAIYVJS3"},"agent_actions":{"view_html":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU","download_json":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU.json","view_paper":"https://pith.science/paper/KAIYVJS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.02971&json=true","fetch_graph":"https://pith.science/api/pith-number/KAIYVJS3Y6V4TDDGYV5MJBHYPU/graph.json","fetch_events":"https://pith.science/api/pith-number/KAIYVJS3Y6V4TDDGYV5MJBHYPU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU/action/storage_attestation","attest_author":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU/action/author_attestation","sign_citation":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU/action/citation_signature","submit_replication":"https://pith.science/pith/KAIYVJS3Y6V4TDDGYV5MJBHYPU/action/replication_record"}},"created_at":"2026-05-18T00:00:01.827527+00:00","updated_at":"2026-05-18T00:00:01.827527+00:00"}