{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BMOZC2QRMXU2RA6RK5UJU5OMNJ","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":"8cd5421458db6a83323aaa1975ba46de80b415f3ead2c435e45260bf6e7d2078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-28T13:49:30Z","title_canon_sha256":"41596119cf8e13fadf50289d67730c0bacaa832dc0db13d503d5524c62cca880"},"schema_version":"1.0","source":{"id":"1205.6113","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6113","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6113v3","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6113","created_at":"2026-05-18T03:33:37Z"},{"alias_kind":"pith_short_12","alias_value":"BMOZC2QRMXU2","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BMOZC2QRMXU2RA6R","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BMOZC2QR","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:a49fda54ea0e0aa3c1368ed4329ebb7fca20c0e4f6a2a3462a1ca56d644dad1d","target":"graph","created_at":"2026-05-18T03:33:37Z","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":"We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner. The resulting preconditioner, which we refer to as a combined preconditioner, is much more robust and efficient than the iterative method and preconditioner when used in Krylov subspace methods. We prove that the combined preconditioner is positive definite and show estimates on the condition number of the preconditioned system. We combine an algebraic mult","authors_text":"Chen-Song Zhang, Jinchao Xu, Ludmil Zikatanov, Shiquan Zhang, Shuhong Wu, Xiao-Hui Wu, Xiaozhe Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-28T13:49:30Z","title":"Combined Preconditioning with Applications in Reservoir Simulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6113","kind":"arxiv","version":3},"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":"sha256:30657bc141b7552a86eddd1092bb0808a1d4f07aa591bfeebf851ef6ffc79171","target":"record","created_at":"2026-05-18T03:33:37Z","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":"8cd5421458db6a83323aaa1975ba46de80b415f3ead2c435e45260bf6e7d2078","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-28T13:49:30Z","title_canon_sha256":"41596119cf8e13fadf50289d67730c0bacaa832dc0db13d503d5524c62cca880"},"schema_version":"1.0","source":{"id":"1205.6113","kind":"arxiv","version":3}},"canonical_sha256":"0b1d916a1165e9a883d157689a75cc6a704fc096e8dcbbc12e3046b115535018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b1d916a1165e9a883d157689a75cc6a704fc096e8dcbbc12e3046b115535018","first_computed_at":"2026-05-18T03:33:37.781011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:37.781011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4rH4Ar3jHvbxD5HxdKdI9C0ZJpdgV93kHBLZNTGSNXVA/2NwLaGE7RKTW7zFVwvosAKjiiiF7keScYVnTWnGDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:37.781863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6113","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30657bc141b7552a86eddd1092bb0808a1d4f07aa591bfeebf851ef6ffc79171","sha256:a49fda54ea0e0aa3c1368ed4329ebb7fca20c0e4f6a2a3462a1ca56d644dad1d"],"state_sha256":"aaf9be8b99d10bd4f11b905f6c0acf49d60b8817d9c1cde4551fa9f9b7859345"}