{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:533GAOA5EZCXN63YIMNJ7D6AWK","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":"5e2cf92d48bd0cf98b8d5d40a90cbe3ed053d76e777d49dbc610f4dbcef9e9c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-07T13:21:50Z","title_canon_sha256":"4fb30002ab8ff5b64ab945d9177b216f3d0bb13634c1873e95cc2a7c08ade1bc"},"schema_version":"1.0","source":{"id":"1610.02270","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02270","created_at":"2026-05-18T00:22:52Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02270v3","created_at":"2026-05-18T00:22:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02270","created_at":"2026-05-18T00:22:52Z"},{"alias_kind":"pith_short_12","alias_value":"533GAOA5EZCX","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"533GAOA5EZCXN63Y","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"533GAOA5","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a26db31be11004a8fd381ad77b2ca74684772c181d2f0e1dc1d1c9edf0dd7783","target":"graph","created_at":"2026-05-18T00:22:52Z","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":"Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave propagation problems, the Helmholtz equation. A specific class of these new preconditioners are considered here. They were developed by researchers with various backgrounds using formulations and notations that are very different, and all are among the most promising preconditioners for the Helmholtz equation.\n  The goal of the present manuscript is to show that","authors_text":"Hui Zhang, Martin J. Gander","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-07T13:21:50Z","title":"A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02270","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":"sha256:32bf4c7a03b68d435e97d70128a46bd1812ec61a7367bf41278a8875cf8896f0","target":"record","created_at":"2026-05-18T00:22:52Z","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":"5e2cf92d48bd0cf98b8d5d40a90cbe3ed053d76e777d49dbc610f4dbcef9e9c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-07T13:21:50Z","title_canon_sha256":"4fb30002ab8ff5b64ab945d9177b216f3d0bb13634c1873e95cc2a7c08ade1bc"},"schema_version":"1.0","source":{"id":"1610.02270","kind":"arxiv","version":3}},"canonical_sha256":"eef660381d264576fb78431a9f8fc0b2b1eb24ef8391008685167d81c7ed9a27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eef660381d264576fb78431a9f8fc0b2b1eb24ef8391008685167d81c7ed9a27","first_computed_at":"2026-05-18T00:22:52.980416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:52.980416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2mQ9A3UCwxjoX5GxnklVh7S4puVkEjGOFY2AQE6u6NeOo31dkONwIXZQ2fkR+7LmP7l0Cbe8b7YRQ+sQ2HSEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:52.980899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02270","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32bf4c7a03b68d435e97d70128a46bd1812ec61a7367bf41278a8875cf8896f0","sha256:a26db31be11004a8fd381ad77b2ca74684772c181d2f0e1dc1d1c9edf0dd7783"],"state_sha256":"cb7fdaf3fd72d6e625f53ea18d692eed0f4438895fca9006cd71d3bd40e6d6aa"}