{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AU7CPBPNDCSWACS7DRK425L3ZF","short_pith_number":"pith:AU7CPBPN","canonical_record":{"source":{"id":"1610.05355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T20:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"286f70dda54a3d8f158b6406d31201fe522f43737a60d6f2981e08f819842f09","abstract_canon_sha256":"94fbd5fdb89c7f9f919495549e23b41c458de8c858aed3e3e24dbe3fea766279"},"schema_version":"1.0"},"canonical_sha256":"053e2785ed18a5600a5f1c55cd757bc95f9c9e943a532ae6b3f2c4dceee48eb5","source":{"kind":"arxiv","id":"1610.05355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05355","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05355v1","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05355","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"AU7CPBPNDCSW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AU7CPBPNDCSWACS7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AU7CPBPN","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AU7CPBPNDCSWACS7DRK425L3ZF","target":"record","payload":{"canonical_record":{"source":{"id":"1610.05355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T20:59:38Z","cross_cats_sorted":[],"title_canon_sha256":"286f70dda54a3d8f158b6406d31201fe522f43737a60d6f2981e08f819842f09","abstract_canon_sha256":"94fbd5fdb89c7f9f919495549e23b41c458de8c858aed3e3e24dbe3fea766279"},"schema_version":"1.0"},"canonical_sha256":"053e2785ed18a5600a5f1c55cd757bc95f9c9e943a532ae6b3f2c4dceee48eb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:59.557116Z","signature_b64":"JHYOvfsKeIR2XUkOxnVpHEqTwfbfGJnjshJ13QHXa+vTArLtjZ4PuoQaa7HuzlpVsI7e/NaaCZ5Db5fz4KiNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053e2785ed18a5600a5f1c55cd757bc95f9c9e943a532ae6b3f2c4dceee48eb5","last_reissued_at":"2026-05-18T01:01:59.556445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:59.556445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.05355","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":"2026-05-18T01:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/b/ptBa+IVKY718vxkBRII0QxDth+yccui3wvYLY69aILgczTXjSdO8ohwcPlLGJsQ6lu3QVBqPPXg6hFJ3rBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:57:29.049443Z"},"content_sha256":"f38e6e5892ed6c3ee7b62a8c2dc50ef33d77810811280d5e846c09ea8ae7f739","schema_version":"1.0","event_id":"sha256:f38e6e5892ed6c3ee7b62a8c2dc50ef33d77810811280d5e846c09ea8ae7f739"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AU7CPBPNDCSWACS7DRK425L3ZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple finite element method for the Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lin Mu, Xiu Ye","submitted_at":"2016-10-17T20:59:38Z","abstract_excerpt":"The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05355","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":"2026-05-18T01:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oGonL2YZCjxXoW1xmn/j1wKrYFs0DKY24m+kVMwE3ac3HK42WSM+Grl0UqIW0+q0sUxH9t1GMm3xfmVp7PlgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:57:29.050139Z"},"content_sha256":"f2692575ae9aa85baedfe7d777cfcf911edc660ee3012fc5012cdd2d38e36b57","schema_version":"1.0","event_id":"sha256:f2692575ae9aa85baedfe7d777cfcf911edc660ee3012fc5012cdd2d38e36b57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU7CPBPNDCSWACS7DRK425L3ZF/bundle.json","state_url":"https://pith.science/pith/AU7CPBPNDCSWACS7DRK425L3ZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU7CPBPNDCSWACS7DRK425L3ZF/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":"2026-06-11T03:57:29Z","links":{"resolver":"https://pith.science/pith/AU7CPBPNDCSWACS7DRK425L3ZF","bundle":"https://pith.science/pith/AU7CPBPNDCSWACS7DRK425L3ZF/bundle.json","state":"https://pith.science/pith/AU7CPBPNDCSWACS7DRK425L3ZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU7CPBPNDCSWACS7DRK425L3ZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AU7CPBPNDCSWACS7DRK425L3ZF","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":"94fbd5fdb89c7f9f919495549e23b41c458de8c858aed3e3e24dbe3fea766279","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T20:59:38Z","title_canon_sha256":"286f70dda54a3d8f158b6406d31201fe522f43737a60d6f2981e08f819842f09"},"schema_version":"1.0","source":{"id":"1610.05355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05355","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05355v1","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05355","created_at":"2026-05-18T01:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"AU7CPBPNDCSW","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AU7CPBPNDCSWACS7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AU7CPBPN","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:f2692575ae9aa85baedfe7d777cfcf911edc660ee3012fc5012cdd2d38e36b57","target":"graph","created_at":"2026-05-18T01:01:59Z","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 goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are approximated by piecewise constant functions. Implementation issues as well as error analysis are investigated. A basis for a divergence free subspace of the velocity field is constructed so that the original saddle point problem can be reduced to a symmetric and positive definite system with much fewer unknowns. The numerical experiments indicate that the metho","authors_text":"Lin Mu, Xiu Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T20:59:38Z","title":"A simple finite element method for the Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05355","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:f38e6e5892ed6c3ee7b62a8c2dc50ef33d77810811280d5e846c09ea8ae7f739","target":"record","created_at":"2026-05-18T01:01:59Z","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":"94fbd5fdb89c7f9f919495549e23b41c458de8c858aed3e3e24dbe3fea766279","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T20:59:38Z","title_canon_sha256":"286f70dda54a3d8f158b6406d31201fe522f43737a60d6f2981e08f819842f09"},"schema_version":"1.0","source":{"id":"1610.05355","kind":"arxiv","version":1}},"canonical_sha256":"053e2785ed18a5600a5f1c55cd757bc95f9c9e943a532ae6b3f2c4dceee48eb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"053e2785ed18a5600a5f1c55cd757bc95f9c9e943a532ae6b3f2c4dceee48eb5","first_computed_at":"2026-05-18T01:01:59.556445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:59.556445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JHYOvfsKeIR2XUkOxnVpHEqTwfbfGJnjshJ13QHXa+vTArLtjZ4PuoQaa7HuzlpVsI7e/NaaCZ5Db5fz4KiNCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:59.557116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f38e6e5892ed6c3ee7b62a8c2dc50ef33d77810811280d5e846c09ea8ae7f739","sha256:f2692575ae9aa85baedfe7d777cfcf911edc660ee3012fc5012cdd2d38e36b57"],"state_sha256":"374c0e1742cd07e83b8001d81fb75a423209baa4bbdff9e32e2bd58653d73bb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wazzoJKJ+M3J0pPQWDC9AczNFdZWilpn9oQiy63NBTY8BzEX/mtJVgb1jfvgKFHZ6IINYk5QrsKcv2B7/MqQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:57:29.053805Z","bundle_sha256":"708c85731ec913642baf1a7cf6f063de9c4d1f434ba216a8aad281898d8b6f3c"}}