{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WK3NIYQXGFNCF6KRWKCGQ66FJQ","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":"3ec2d800db09655e698ee5aeb11a14d8a64a6798215a8ac2ae6e4b9be92ede1f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-18T09:08:06Z","title_canon_sha256":"eac7d2bde86b4f190fddef316c7ceb70650277a77d2540f353b5cd06ed2d92e1"},"schema_version":"1.0","source":{"id":"1806.06557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.06557","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1806.06557v1","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06557","created_at":"2026-05-17T23:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"WK3NIYQXGFNC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WK3NIYQXGFNCF6KR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WK3NIYQX","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:819dac0feeacff21e457641bfefcfd7f7c2417611e3941eb1e38c31ef9a9699b","target":"graph","created_at":"2026-05-17T23:50:13Z","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 paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\\Gamma\\subset\\R^3$. The method needs a shape regular tetrahedra mesh in $\\mathbb{R}^3$ to discretize equations on the surface, which can cut through this mesh in a fairly arbitrary way. Stability and error analysis of the fully discrete (in space and in time) scheme is given. The tangentiality condition for the velocity field on $\\Gamma$ is enforced weakly by a penalty term. The paper studies both theoretically and numerically the dependence of the error on the penalty parame","authors_text":"Maxim A. Olshanskii, Vladimir Yushutin","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-18T09:08:06Z","title":"A penalty finite element method for a fluid system posed on embedded surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06557","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":"sha256:7e7e535c1ea785a790de523709c87c7dca9ad35d164a324d554424cbc0987743","target":"record","created_at":"2026-05-17T23:50:13Z","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":"3ec2d800db09655e698ee5aeb11a14d8a64a6798215a8ac2ae6e4b9be92ede1f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-18T09:08:06Z","title_canon_sha256":"eac7d2bde86b4f190fddef316c7ceb70650277a77d2540f353b5cd06ed2d92e1"},"schema_version":"1.0","source":{"id":"1806.06557","kind":"arxiv","version":1}},"canonical_sha256":"b2b6d46217315a22f951b284687bc54c31841ad1a9283609156d4f080ef2102a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2b6d46217315a22f951b284687bc54c31841ad1a9283609156d4f080ef2102a","first_computed_at":"2026-05-17T23:50:13.372109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:13.372109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a4XVDL2RGnKD8Csaj4nVRfPKo3JWCb62lxH3otShqAYPgLYdknEHjZUQR5QfJ8vKhS5VVGtqFgM0EmL3eDO6Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:13.372753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.06557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e7e535c1ea785a790de523709c87c7dca9ad35d164a324d554424cbc0987743","sha256:819dac0feeacff21e457641bfefcfd7f7c2417611e3941eb1e38c31ef9a9699b"],"state_sha256":"3cff82e8ee5a7d4114a4acafd6eb6bf10c661caf27ba6cee7c4ecd573c5a4bc0"}