{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YU6LTRW74EPEZR4YQE6CDJQHOH","short_pith_number":"pith:YU6LTRW7","canonical_record":{"source":{"id":"1803.00120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T22:33:01Z","cross_cats_sorted":[],"title_canon_sha256":"eece3e7c70e3b8ae5e07018a2b63eebfe2794a0f22ad749bb5d8762680d21015","abstract_canon_sha256":"c2117dcebc5873eda5d9675b0ac4fc014c2943585ef2bcc8e586e062bb34eefa"},"schema_version":"1.0"},"canonical_sha256":"c53cb9c6dfe11e4cc798813c21a60771ce368fc2d73c50f540064d55da8df315","source":{"kind":"arxiv","id":"1803.00120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00120","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00120v2","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00120","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"YU6LTRW74EPE","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YU6LTRW74EPEZR4Y","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YU6LTRW7","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YU6LTRW74EPEZR4YQE6CDJQHOH","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T22:33:01Z","cross_cats_sorted":[],"title_canon_sha256":"eece3e7c70e3b8ae5e07018a2b63eebfe2794a0f22ad749bb5d8762680d21015","abstract_canon_sha256":"c2117dcebc5873eda5d9675b0ac4fc014c2943585ef2bcc8e586e062bb34eefa"},"schema_version":"1.0"},"canonical_sha256":"c53cb9c6dfe11e4cc798813c21a60771ce368fc2d73c50f540064d55da8df315","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:09.557563Z","signature_b64":"npmUBh2OSIqN66F3Olq6S3XJi8dGylslkTKN0u1GuIKskHrFrlOJz7NRmYnKgUn6AIiPyDG13ZK3TewjDPrdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c53cb9c6dfe11e4cc798813c21a60771ce368fc2d73c50f540064d55da8df315","last_reissued_at":"2026-05-18T00:09:09.556777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:09.556777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00120","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":"2026-05-18T00:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5ybq7RzaBXR78Vw9yqXiPZfuZbxAH3nPKKAWq2J54Sy/zghg9jfDkxz6A8AYlq4T3UBH4Lc0Tmyk6M4l5apDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:04:34.270846Z"},"content_sha256":"958a3dd9292f24cc90594804d28b40157287d2174648fc8239e0e83cf4463ab6","schema_version":"1.0","event_id":"sha256:958a3dd9292f24cc90594804d28b40157287d2174648fc8239e0e83cf4463ab6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YU6LTRW74EPEZR4YQE6CDJQHOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplified Weak Galerkin and New Finite Difference Schemes for the Stokes Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Junping Wang, Yujie Liu","submitted_at":"2018-02-28T22:33:01Z","abstract_excerpt":"This article presents a simplified formulation for the weak Galerkin finite element method for the Stokes equation without using the degrees of freedom associated with the unknowns in the interior of each element as formulated in the original weak Galerkin algorithm. The simplified formulation preserves the important mass conservation property locally on each element and allows the use of general polygonal partitions. A particular application of the simplified weak Galerkin on rectangular partitions yields a new class of 5- and 7-point finite difference schemes for the Stokes equation. An expl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00120","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":"2026-05-18T00:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LwOHUO9IO7D498FO+0croxuzuuHzsYP1zT04XWBb8Yjj3GTlRg5Mtvbl0vwMCg9XLulYKXoo5HsaQdr+c0tUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:04:34.271542Z"},"content_sha256":"6323305c2bb4221f102e2e3201f6ebbb715abafd5577e9d023618f5feced6e8a","schema_version":"1.0","event_id":"sha256:6323305c2bb4221f102e2e3201f6ebbb715abafd5577e9d023618f5feced6e8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/bundle.json","state_url":"https://pith.science/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/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":"2026-06-10T12:04:34Z","links":{"resolver":"https://pith.science/pith/YU6LTRW74EPEZR4YQE6CDJQHOH","bundle":"https://pith.science/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/bundle.json","state":"https://pith.science/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YU6LTRW74EPEZR4YQE6CDJQHOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YU6LTRW74EPEZR4YQE6CDJQHOH","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":"c2117dcebc5873eda5d9675b0ac4fc014c2943585ef2bcc8e586e062bb34eefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T22:33:01Z","title_canon_sha256":"eece3e7c70e3b8ae5e07018a2b63eebfe2794a0f22ad749bb5d8762680d21015"},"schema_version":"1.0","source":{"id":"1803.00120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00120","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00120v2","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00120","created_at":"2026-05-18T00:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"YU6LTRW74EPE","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YU6LTRW74EPEZR4Y","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YU6LTRW7","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:6323305c2bb4221f102e2e3201f6ebbb715abafd5577e9d023618f5feced6e8a","target":"graph","created_at":"2026-05-18T00:09:09Z","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":"This article presents a simplified formulation for the weak Galerkin finite element method for the Stokes equation without using the degrees of freedom associated with the unknowns in the interior of each element as formulated in the original weak Galerkin algorithm. The simplified formulation preserves the important mass conservation property locally on each element and allows the use of general polygonal partitions. A particular application of the simplified weak Galerkin on rectangular partitions yields a new class of 5- and 7-point finite difference schemes for the Stokes equation. An expl","authors_text":"Junping Wang, Yujie Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T22:33:01Z","title":"Simplified Weak Galerkin and New Finite Difference Schemes for the Stokes Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00120","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":"sha256:958a3dd9292f24cc90594804d28b40157287d2174648fc8239e0e83cf4463ab6","target":"record","created_at":"2026-05-18T00:09:09Z","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":"c2117dcebc5873eda5d9675b0ac4fc014c2943585ef2bcc8e586e062bb34eefa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-02-28T22:33:01Z","title_canon_sha256":"eece3e7c70e3b8ae5e07018a2b63eebfe2794a0f22ad749bb5d8762680d21015"},"schema_version":"1.0","source":{"id":"1803.00120","kind":"arxiv","version":2}},"canonical_sha256":"c53cb9c6dfe11e4cc798813c21a60771ce368fc2d73c50f540064d55da8df315","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c53cb9c6dfe11e4cc798813c21a60771ce368fc2d73c50f540064d55da8df315","first_computed_at":"2026-05-18T00:09:09.556777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:09.556777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"npmUBh2OSIqN66F3Olq6S3XJi8dGylslkTKN0u1GuIKskHrFrlOJz7NRmYnKgUn6AIiPyDG13ZK3TewjDPrdCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:09.557563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:958a3dd9292f24cc90594804d28b40157287d2174648fc8239e0e83cf4463ab6","sha256:6323305c2bb4221f102e2e3201f6ebbb715abafd5577e9d023618f5feced6e8a"],"state_sha256":"82d87868c7841b52d12ede1fb77fafd2afac6b37ae553e4dd01b396dc2ddf304"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRNXujQQ3ljxUYa4sX8DpP3JqD76go9EtxCpSq7tzwFbk8ufsTduaB/FIE06cRq+G5SZFiX6PXqPW/Tq45H+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:04:34.275763Z","bundle_sha256":"367b0fda24f75acd3c06ccbfb6372883bbb8773d57ad89802a8d4aba7ad6d316"}}