{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BHZT6XIBU6XU3YR5XEP66QSZDV","short_pith_number":"pith:BHZT6XIB","canonical_record":{"source":{"id":"1611.03189","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-10T05:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"c06f75af17424a2391bdc1131039f4b5774f0a99fb5a682f569cfdfbc619c99d","abstract_canon_sha256":"a2b264ef2d1c3e775d29a34569fdd460f4cd825934af8f4f86ac8975db486d1b"},"schema_version":"1.0"},"canonical_sha256":"09f33f5d01a7af4de23db91fef42591d487d2a97b7cd413a4036228fdd5f1e08","source":{"kind":"arxiv","id":"1611.03189","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03189","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03189v2","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03189","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"BHZT6XIBU6XU","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BHZT6XIBU6XU3YR5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BHZT6XIB","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BHZT6XIBU6XU3YR5XEP66QSZDV","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03189","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-10T05:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"c06f75af17424a2391bdc1131039f4b5774f0a99fb5a682f569cfdfbc619c99d","abstract_canon_sha256":"a2b264ef2d1c3e775d29a34569fdd460f4cd825934af8f4f86ac8975db486d1b"},"schema_version":"1.0"},"canonical_sha256":"09f33f5d01a7af4de23db91fef42591d487d2a97b7cd413a4036228fdd5f1e08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:53.727776Z","signature_b64":"0i1LmfXyyGOm79/vGOTsRqX53VOkWHseha1YP5/KNKlIyhh40a2R+0H62W+RRkhxmQdk94htHmTc1G/B1EZYBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09f33f5d01a7af4de23db91fef42591d487d2a97b7cd413a4036228fdd5f1e08","last_reissued_at":"2026-05-18T00:48:53.727131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:53.727131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03189","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NhTZBOznm4gu0yOzT3iuesytBvsh8sc7cPhUUQDw+ftU7nj7VO3c3nvem2GVSsfV8VftY/tyKD7qFWup0seVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:13:54.517655Z"},"content_sha256":"3162e226e1f268912dda8c537eb887d8cb3bcc74b5c8fc1ab9ee7ada66e6f2da","schema_version":"1.0","event_id":"sha256:3162e226e1f268912dda8c537eb887d8cb3bcc74b5c8fc1ab9ee7ada66e6f2da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BHZT6XIBU6XU3YR5XEP66QSZDV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Hierarchical Solvers with Guaranteed Convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric Darve, Hadi Pouransari, Kai Yang","submitted_at":"2016-11-10T05:42:17Z","abstract_excerpt":"Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners, such as incomplete LU factorization, provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low-frequency errors, we propose a novel hierarchical sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03189","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkhOT8wGaN8LX5F99C//dtNYKaVxZX4DvniLvCDldNX/rC2dO8vwA2uW9I2rPjq3FCtEcrjl60Bma287QPaPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:13:54.517990Z"},"content_sha256":"21ffb8087b33ace5dc22299126d431c5653540f745c9b2cc77534beb94e0a633","schema_version":"1.0","event_id":"sha256:21ffb8087b33ace5dc22299126d431c5653540f745c9b2cc77534beb94e0a633"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/bundle.json","state_url":"https://pith.science/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T16:13:54Z","links":{"resolver":"https://pith.science/pith/BHZT6XIBU6XU3YR5XEP66QSZDV","bundle":"https://pith.science/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/bundle.json","state":"https://pith.science/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BHZT6XIBU6XU3YR5XEP66QSZDV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BHZT6XIBU6XU3YR5XEP66QSZDV","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":"a2b264ef2d1c3e775d29a34569fdd460f4cd825934af8f4f86ac8975db486d1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-10T05:42:17Z","title_canon_sha256":"c06f75af17424a2391bdc1131039f4b5774f0a99fb5a682f569cfdfbc619c99d"},"schema_version":"1.0","source":{"id":"1611.03189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03189","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03189v2","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03189","created_at":"2026-05-18T00:48:53Z"},{"alias_kind":"pith_short_12","alias_value":"BHZT6XIBU6XU","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BHZT6XIBU6XU3YR5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BHZT6XIB","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:21ffb8087b33ace5dc22299126d431c5653540f745c9b2cc77534beb94e0a633","target":"graph","created_at":"2026-05-18T00:48:53Z","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 sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners, such as incomplete LU factorization, provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low-frequency errors, we propose a novel hierarchical sol","authors_text":"Eric Darve, Hadi Pouransari, Kai Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-10T05:42:17Z","title":"Sparse Hierarchical Solvers with Guaranteed Convergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03189","kind":"arxiv","version":2},"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":"sha256:3162e226e1f268912dda8c537eb887d8cb3bcc74b5c8fc1ab9ee7ada66e6f2da","target":"record","created_at":"2026-05-18T00:48:53Z","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":"a2b264ef2d1c3e775d29a34569fdd460f4cd825934af8f4f86ac8975db486d1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-10T05:42:17Z","title_canon_sha256":"c06f75af17424a2391bdc1131039f4b5774f0a99fb5a682f569cfdfbc619c99d"},"schema_version":"1.0","source":{"id":"1611.03189","kind":"arxiv","version":2}},"canonical_sha256":"09f33f5d01a7af4de23db91fef42591d487d2a97b7cd413a4036228fdd5f1e08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09f33f5d01a7af4de23db91fef42591d487d2a97b7cd413a4036228fdd5f1e08","first_computed_at":"2026-05-18T00:48:53.727131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:53.727131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0i1LmfXyyGOm79/vGOTsRqX53VOkWHseha1YP5/KNKlIyhh40a2R+0H62W+RRkhxmQdk94htHmTc1G/B1EZYBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:53.727776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3162e226e1f268912dda8c537eb887d8cb3bcc74b5c8fc1ab9ee7ada66e6f2da","sha256:21ffb8087b33ace5dc22299126d431c5653540f745c9b2cc77534beb94e0a633"],"state_sha256":"8c88c8d8b910fb18814f99233e4e714d10518eade38b615a41143d1585cfc08c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9XEFsZ5eNK/2XHPKB4M4t4nEq6p5WQiuEbiXeWNEjWIGva9j10gHSRErZ+7WgFVxptUXXtxwHKGb3ytk3Ya9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:13:54.519838Z","bundle_sha256":"be098cb7c412c3edc6163c5c7cc0ce2f95648416e0d0cb45b0b63323d8aea1c3"}}