{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:A6XXAXFMZG75KUTKO5X2MTYET2","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":"323ca7843952438378b5e299f3f0c7f655d0a0db0a474620a1dee5f8dde2bc44","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-01T05:31:18Z","title_canon_sha256":"ac957d40797138110b4e5d04eae9c06db9b9ddbf40b7a225256787252dc5b08d"},"schema_version":"1.0","source":{"id":"2401.00672","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.00672","created_at":"2026-07-05T11:25:00Z"},{"alias_kind":"arxiv_version","alias_value":"2401.00672v4","created_at":"2026-07-05T11:25:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.00672","created_at":"2026-07-05T11:25:00Z"},{"alias_kind":"pith_short_12","alias_value":"A6XXAXFMZG75","created_at":"2026-07-05T11:25:00Z"},{"alias_kind":"pith_short_16","alias_value":"A6XXAXFMZG75KUTK","created_at":"2026-07-05T11:25:00Z"},{"alias_kind":"pith_short_8","alias_value":"A6XXAXFM","created_at":"2026-07-05T11:25:00Z"}],"graph_snapshots":[{"event_id":"sha256:93903a07e25727545c01b9bbdf1dc49fb6a7f8ddc2230995c7d5bfa7d1bcb71d","target":"graph","created_at":"2026-07-05T11:25:00Z","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/2401.00672/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Existing block Kaczmarz methods face challenges in balancing computational efficiency and convergence for large sparse linear systems with scattered nonzero patterns, due to costly partitioning strategies and non-orthogonal projections. In this paper, we propose the orthogonal block Kaczmarz (OBK-RCM) algorithm with the Reverse Cuthill-McKee (RCM), which integrates the RCM reordering with a novel orthogonal block partitioning strategy. RCM transforms sparse matrices into banded structures to enhance inter-block orthogonality, while dynamic grouping of mutually orthogonal blocks based on angle ","authors_text":"Hou-Biao Li, Yu-Fang Liang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-01T05:31:18Z","title":"OBK-RCM: Accelerated Orthogonal Block Kaczmarz Algorithm via RCM Reordering and Dynamic Grouping for Sparse Linear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.00672","kind":"arxiv","version":4},"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":"sha256:5f96049246acca9df99fb6ddb41d1f499075ece62a4875e1af295af3feb12ec3","target":"record","created_at":"2026-07-05T11:25:00Z","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":"323ca7843952438378b5e299f3f0c7f655d0a0db0a474620a1dee5f8dde2bc44","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-01-01T05:31:18Z","title_canon_sha256":"ac957d40797138110b4e5d04eae9c06db9b9ddbf40b7a225256787252dc5b08d"},"schema_version":"1.0","source":{"id":"2401.00672","kind":"arxiv","version":4}},"canonical_sha256":"07af705cacc9bfd5526a776fa64f049e8359353ea691f4f3df45defb8b551a02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07af705cacc9bfd5526a776fa64f049e8359353ea691f4f3df45defb8b551a02","first_computed_at":"2026-07-05T11:25:00.176741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:00.176741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MnRikjbxkMmVE2w6SA2urbutQSa9WAKBOh1UtjwfX0O2tWns7DoKa/UHWMvHcOWZEKqFQ8HOFMuZq3NhwI0ACw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:00.177173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.00672","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f96049246acca9df99fb6ddb41d1f499075ece62a4875e1af295af3feb12ec3","sha256:93903a07e25727545c01b9bbdf1dc49fb6a7f8ddc2230995c7d5bfa7d1bcb71d"],"state_sha256":"b63fd1f564b950e404fe9562aac3257a58cc2dfc3111da23a07dcb2f310d9ee5"}