{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B6V3REUKNB5SZGFTH5SQFVUI32","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":"b16387d73a66801691abe4393d31b3f80b41944681331a6082db57a7b2260b7f","cross_cats_sorted":["cs.DC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-25T15:41:21Z","title_canon_sha256":"cf345c4ee9b556b9eea84233e1940298d26b4a45d2d1c67feac17a9ea195c15b"},"schema_version":"1.0","source":{"id":"1906.10613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10613","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10613v1","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10613","created_at":"2026-05-17T23:42:15Z"},{"alias_kind":"pith_short_12","alias_value":"B6V3REUKNB5S","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B6V3REUKNB5SZGFT","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B6V3REUK","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:14d192a8fd967ad4e381e8964ff8c72fdcbcbee02e114de72e5543b205749b98","target":"graph","created_at":"2026-05-17T23:42:15Z","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":"This paper studies a low-communication algorithm for solving elliptic partial differential equations (PDE's) on high-performance machines, the nested iteration with range decomposition algorithm (NIRD). Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accu","authors_text":"Tom Manteuffel, Wayne Mitchell","cross_cats":["cs.DC","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-25T15:41:21Z","title":"Advances in Implementation, Theoretical Motivation, and Numerical Results for the Nested Iteration with Range Decomposition Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10613","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:f2a93920f53e862c5ae8ee627f71c085e886d82f4bb278287f36af7933f74d5e","target":"record","created_at":"2026-05-17T23:42:15Z","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":"b16387d73a66801691abe4393d31b3f80b41944681331a6082db57a7b2260b7f","cross_cats_sorted":["cs.DC","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-06-25T15:41:21Z","title_canon_sha256":"cf345c4ee9b556b9eea84233e1940298d26b4a45d2d1c67feac17a9ea195c15b"},"schema_version":"1.0","source":{"id":"1906.10613","kind":"arxiv","version":1}},"canonical_sha256":"0fabb8928a687b2c98b33f6502d688dea953af55ff788b7785eb3eceeddd7c65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0fabb8928a687b2c98b33f6502d688dea953af55ff788b7785eb3eceeddd7c65","first_computed_at":"2026-05-17T23:42:15.804652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:15.804652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n5JpI5HMgfn6tNANKM4Chv5sdgl8dSVEev586gMdQdTPEQhxiqredo0ejHKb23DS/CRh7lNwr45iScSHIXK0BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:15.805375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2a93920f53e862c5ae8ee627f71c085e886d82f4bb278287f36af7933f74d5e","sha256:14d192a8fd967ad4e381e8964ff8c72fdcbcbee02e114de72e5543b205749b98"],"state_sha256":"e047672eed34d662cfc28bf2a55ea53dda5dcc10859a4c5f468da5feb0ed8162"}