{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:H7UH546A6AHU263QT7F4VCNLSL","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":"ad8c5987738725eb9664cb59df16420c0b6e461bf861d636563d5d9c5c66e31f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T20:44:57Z","title_canon_sha256":"c1161f5b6c0f3c951c210ce7d7387e6660aa2230f477820628c3fa6742336b2d"},"schema_version":"1.0","source":{"id":"1208.1781","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1781","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1781v1","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1781","created_at":"2026-05-18T03:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"H7UH546A6AHU","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"H7UH546A6AHU263Q","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"H7UH546A","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:bbb72b8c8fbed7795969c44c17fe2d0e560331282398d972f0d8014a601237f1","target":"graph","created_at":"2026-05-18T03:48:35Z","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":"A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equations. A distinctive feature of this framework is that it allows using both continuous and discontinuous pressures in the algorithm, while previous FETI-DP methods only apply to discontinuous pressures. A preconditioned conjugate gradient method is used in the algorithm with either a lumped or a Dirichlet preconditioner, and scalable convergence rates are proved. This framework is also used to describe several previous","authors_text":"Jing Li, Xuemin Tu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T20:44:57Z","title":"A unified FETI-DP approach for incompressible Stokes equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1781","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":"sha256:2799b574f320949e04d4d830583f5a86ca830f0628580762aaf11363e0595e95","target":"record","created_at":"2026-05-18T03:48:35Z","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":"ad8c5987738725eb9664cb59df16420c0b6e461bf861d636563d5d9c5c66e31f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NA","submitted_at":"2012-08-08T20:44:57Z","title_canon_sha256":"c1161f5b6c0f3c951c210ce7d7387e6660aa2230f477820628c3fa6742336b2d"},"schema_version":"1.0","source":{"id":"1208.1781","kind":"arxiv","version":1}},"canonical_sha256":"3fe87ef3c0f00f4d7b709fcbca89ab92f009c482a427d1ff8b0d5a7bc9c2b9de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fe87ef3c0f00f4d7b709fcbca89ab92f009c482a427d1ff8b0d5a7bc9c2b9de","first_computed_at":"2026-05-18T03:48:35.775563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:35.775563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AW0P6qoalqmJi6fHxT9TrGpXVdyKAvtLrjRelHimGHuP+673aqpoU1JuQB90h7sDsgRVgNKaEPOB4ivKmoC/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:35.775989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1781","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2799b574f320949e04d4d830583f5a86ca830f0628580762aaf11363e0595e95","sha256:bbb72b8c8fbed7795969c44c17fe2d0e560331282398d972f0d8014a601237f1"],"state_sha256":"0c1fc76363f9770ee003554cf2341983274070bc222a80d7c4971a2fbd58a5c6"}