{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RUKERETHDEVBU5RZO2DCXCKNA2","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":"ca54712d47343bf04809e6bf5f9272402d812f6a7df38624b22679367e88e8f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-19T17:32:01Z","title_canon_sha256":"475632760ad310d5406775917bbb09ef1bfff264547df344409bace7deeb788e"},"schema_version":"1.0","source":{"id":"1312.5653","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5653","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5653v1","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5653","created_at":"2026-05-18T03:04:14Z"},{"alias_kind":"pith_short_12","alias_value":"RUKERETHDEVB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RUKERETHDEVBU5RZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RUKERETH","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:d3d297500be45803c9b2f8301ce787f7fca5f8284e29fe4d7c9b85ae69a6a995","target":"graph","created_at":"2026-05-18T03:04:14Z","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 distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution of which is crucial. A new factorization of the Schur complement for such a system is proposed and its characteristics discussed. The factorization introduces two complex factors that are complex conjugate to each other. The proposed solution methodology involves the application of a parallel linear domain decomposition solver---FETI-DPH---for the solution of","authors_text":"Charbel Farhat, Michael Saunders, Walter Murray, Youngsoo Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-19T17:32:01Z","title":"A practical factorization of a Schur complement for PDE-constrained Distributed Optimal Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5653","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":"sha256:13db720295aaf3150b770e8a07e81be923c43fea92fd2007ebb41432e22a62f0","target":"record","created_at":"2026-05-18T03:04:14Z","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":"ca54712d47343bf04809e6bf5f9272402d812f6a7df38624b22679367e88e8f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-19T17:32:01Z","title_canon_sha256":"475632760ad310d5406775917bbb09ef1bfff264547df344409bace7deeb788e"},"schema_version":"1.0","source":{"id":"1312.5653","kind":"arxiv","version":1}},"canonical_sha256":"8d14489267192a1a763976862b894d06b707a0a025bcccf361b0675b2179ecbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d14489267192a1a763976862b894d06b707a0a025bcccf361b0675b2179ecbe","first_computed_at":"2026-05-18T03:04:14.359963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:14.359963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PNJKkN8CNoy7Hb/2qqrXHvSdW6KxuftNUso/rtmAX6DgOxQTYL7FTTP5OMTgtkB4Y/nQqTKPTTR0yjP8cptBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:14.360696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5653","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13db720295aaf3150b770e8a07e81be923c43fea92fd2007ebb41432e22a62f0","sha256:d3d297500be45803c9b2f8301ce787f7fca5f8284e29fe4d7c9b85ae69a6a995"],"state_sha256":"ac23d8e076420c8bc89015101e32323bfadd59923084df396556e5326967802d"}