{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:5AWQSD3ZKOZO3OGZ2BOMHUXKX6","short_pith_number":"pith:5AWQSD3Z","canonical_record":{"source":{"id":"2007.00789","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-01T22:12:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"580c29fcd710e7e602fcbf3a999ac1d1f4ee295c32e78905296f8da4891c5f3b","abstract_canon_sha256":"2909cca1eced7b891f2314321a810bab68bb7c3d21cf24067242413835e15363"},"schema_version":"1.0"},"canonical_sha256":"e82d090f7953b2edb8d9d05cc3d2eabf8e06cba747fb0db3b63f2f0f26e55d60","source":{"kind":"arxiv","id":"2007.00789","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.00789","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"arxiv_version","alias_value":"2007.00789v3","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.00789","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_12","alias_value":"5AWQSD3ZKOZO","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_16","alias_value":"5AWQSD3ZKOZO3OGZ","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_8","alias_value":"5AWQSD3Z","created_at":"2026-07-05T01:24:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:5AWQSD3ZKOZO3OGZ2BOMHUXKX6","target":"record","payload":{"canonical_record":{"source":{"id":"2007.00789","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-01T22:12:22Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"580c29fcd710e7e602fcbf3a999ac1d1f4ee295c32e78905296f8da4891c5f3b","abstract_canon_sha256":"2909cca1eced7b891f2314321a810bab68bb7c3d21cf24067242413835e15363"},"schema_version":"1.0"},"canonical_sha256":"e82d090f7953b2edb8d9d05cc3d2eabf8e06cba747fb0db3b63f2f0f26e55d60","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:24:16.793260Z","signature_b64":"XcznNdoG9QDFPlI5fO6KYHgtftmlEgDSGotX6AJTkzS79k/DyhjnIf5YdlC0Ar8vXPGXOUqK3feHIXUkXP0QBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e82d090f7953b2edb8d9d05cc3d2eabf8e06cba747fb0db3b63f2f0f26e55d60","last_reissued_at":"2026-07-05T01:24:16.792763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:24:16.792763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.00789","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:24:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2a02DrsNhJCI9mb/SuVVBUANJMAuUFOIO9IXQIvR7mmeUBSBKjVODqeO/OMJBMNF8fZ5MfkRxUJvtQHZZ4aiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:50:04.238860Z"},"content_sha256":"ef62fa7dfd7868a46730473f21b8e2b7bfb8ca76d5038caa173bb91dd7748f65","schema_version":"1.0","event_id":"sha256:ef62fa7dfd7868a46730473f21b8e2b7bfb8ca76d5038caa173bb91dd7748f65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:5AWQSD3ZKOZO3OGZ2BOMHUXKX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Second Order Accurate Hierarchical Approximate Factorization of Sparse SPD Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Bazyli Klockiewicz, Eric Darve, Hamdi Tchelepi, L\\'eopold Cambier, Ryan Humble","submitted_at":"2020-07-01T22:12:22Z","abstract_excerpt":"We describe a second-order accurate approach to sparsifying the off-diagonal blocks in the hierarchical approximate factorizations of sparse symmetric positive definite matrices. The norm of the error made by the new approach depends quadratically, not linearly, on the error in the low-rank approximation of the given block. The analysis of the resulting two-level preconditioner shows that the preconditioner is second-order accurate as well. We incorporate the new approach into the recent Sparsified Nested Dissection algorithm [SIAM J. Matrix Anal. Appl., 41 (2020), pp. 715-746], and test it on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.00789","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.00789/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:24:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVJlcyXXWKorQwBoM7bROzD+rJQrHUr9igkL2qEeI37VBGgUcOvoqgFvUe2AbIOnh8G51tBNGjE6kGfXG0L+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T22:50:04.239261Z"},"content_sha256":"f3d9c3b8c682799fa9a211193f7b57eea627e98ae50dcd2893ea56306257d2f8","schema_version":"1.0","event_id":"sha256:f3d9c3b8c682799fa9a211193f7b57eea627e98ae50dcd2893ea56306257d2f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/bundle.json","state_url":"https://pith.science/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/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":"2026-08-23T22:50:04Z","links":{"resolver":"https://pith.science/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6","bundle":"https://pith.science/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/bundle.json","state":"https://pith.science/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AWQSD3ZKOZO3OGZ2BOMHUXKX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5AWQSD3ZKOZO3OGZ2BOMHUXKX6","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":"2909cca1eced7b891f2314321a810bab68bb7c3d21cf24067242413835e15363","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-01T22:12:22Z","title_canon_sha256":"580c29fcd710e7e602fcbf3a999ac1d1f4ee295c32e78905296f8da4891c5f3b"},"schema_version":"1.0","source":{"id":"2007.00789","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.00789","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"arxiv_version","alias_value":"2007.00789v3","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.00789","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_12","alias_value":"5AWQSD3ZKOZO","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_16","alias_value":"5AWQSD3ZKOZO3OGZ","created_at":"2026-07-05T01:24:16Z"},{"alias_kind":"pith_short_8","alias_value":"5AWQSD3Z","created_at":"2026-07-05T01:24:16Z"}],"graph_snapshots":[{"event_id":"sha256:f3d9c3b8c682799fa9a211193f7b57eea627e98ae50dcd2893ea56306257d2f8","target":"graph","created_at":"2026-07-05T01:24:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.00789/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe a second-order accurate approach to sparsifying the off-diagonal blocks in the hierarchical approximate factorizations of sparse symmetric positive definite matrices. The norm of the error made by the new approach depends quadratically, not linearly, on the error in the low-rank approximation of the given block. The analysis of the resulting two-level preconditioner shows that the preconditioner is second-order accurate as well. We incorporate the new approach into the recent Sparsified Nested Dissection algorithm [SIAM J. Matrix Anal. Appl., 41 (2020), pp. 715-746], and test it on","authors_text":"Bazyli Klockiewicz, Eric Darve, Hamdi Tchelepi, L\\'eopold Cambier, Ryan Humble","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-01T22:12:22Z","title":"Second Order Accurate Hierarchical Approximate Factorization of Sparse SPD Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.00789","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:ef62fa7dfd7868a46730473f21b8e2b7bfb8ca76d5038caa173bb91dd7748f65","target":"record","created_at":"2026-07-05T01:24:16Z","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":"2909cca1eced7b891f2314321a810bab68bb7c3d21cf24067242413835e15363","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-01T22:12:22Z","title_canon_sha256":"580c29fcd710e7e602fcbf3a999ac1d1f4ee295c32e78905296f8da4891c5f3b"},"schema_version":"1.0","source":{"id":"2007.00789","kind":"arxiv","version":3}},"canonical_sha256":"e82d090f7953b2edb8d9d05cc3d2eabf8e06cba747fb0db3b63f2f0f26e55d60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e82d090f7953b2edb8d9d05cc3d2eabf8e06cba747fb0db3b63f2f0f26e55d60","first_computed_at":"2026-07-05T01:24:16.792763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:24:16.792763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XcznNdoG9QDFPlI5fO6KYHgtftmlEgDSGotX6AJTkzS79k/DyhjnIf5YdlC0Ar8vXPGXOUqK3feHIXUkXP0QBg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:24:16.793260Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.00789","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef62fa7dfd7868a46730473f21b8e2b7bfb8ca76d5038caa173bb91dd7748f65","sha256:f3d9c3b8c682799fa9a211193f7b57eea627e98ae50dcd2893ea56306257d2f8"],"state_sha256":"dd26fabd2c85fa14056ad13d0d7ee19c2a8e13b81bf5abf6631c43de9736e36e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MkNyv8E9WYszR3l/MP2rKwXn3lZsreRmNbNf3ExmGBcJkvSP4SNXkQ0lLbe1tjR9P/scjYGc9eZG7Z0yIjDXAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T22:50:04.243119Z","bundle_sha256":"8b315ad91e1ce98f79daaee1cb2570a0c788efbd1fd45180691b80ca22a1e16d"}}