{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JVVVUAQNKHHFXCNUH42YCSDXEJ","short_pith_number":"pith:JVVVUAQN","canonical_record":{"source":{"id":"1902.09946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T14:14:20Z","cross_cats_sorted":[],"title_canon_sha256":"4cb53590e016b63322eb79299b296c5ccfe7c7ed2e644e1146c6d1fc03ff0252","abstract_canon_sha256":"fce730d660e513616f0fc09264a0da1d1e678a4d5f39dc34fd4502324e5358f6"},"schema_version":"1.0"},"canonical_sha256":"4d6b5a020d51ce5b89b43f358148772259583ef9a62e8b0851684211fe1a8db4","source":{"kind":"arxiv","id":"1902.09946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09946","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09946v1","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09946","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"JVVVUAQNKHHF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JVVVUAQNKHHFXCNU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JVVVUAQN","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JVVVUAQNKHHFXCNUH42YCSDXEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1902.09946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T14:14:20Z","cross_cats_sorted":[],"title_canon_sha256":"4cb53590e016b63322eb79299b296c5ccfe7c7ed2e644e1146c6d1fc03ff0252","abstract_canon_sha256":"fce730d660e513616f0fc09264a0da1d1e678a4d5f39dc34fd4502324e5358f6"},"schema_version":"1.0"},"canonical_sha256":"4d6b5a020d51ce5b89b43f358148772259583ef9a62e8b0851684211fe1a8db4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:34.988444Z","signature_b64":"xwrTs5FVD7hoWOes54yxqbKEAo6Jws8YpKBjyZL/vw5b0jdaF4WwDe8YBnN4uTufWqdxqgvP+aoeWpOb9Z07Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d6b5a020d51ce5b89b43f358148772259583ef9a62e8b0851684211fe1a8db4","last_reissued_at":"2026-05-17T23:52:34.987988Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:34.987988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.09946","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlMPC3vv/1SntxyemevzuOGyHCXqSpgm0gPC/e6KbjBgMUeqtOPrwxf+uCP14Y2etg3Ir7oYgjLXtVBZ4xLPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:15:22.199511Z"},"content_sha256":"9e17614acc974806f077b64cf0e38f93c6517717be381d4996e2963a83eec410","schema_version":"1.0","event_id":"sha256:9e17614acc974806f077b64cf0e38f93c6517717be381d4996e2963a83eec410"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JVVVUAQNKHHFXCNUH42YCSDXEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Faster randomized block Kaczmarz algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ion Necoara","submitted_at":"2019-02-26T14:14:20Z","abstract_excerpt":"The Kaczmarz algorithm is a simple iterative scheme for solving consistent linear systems. At each step, the method projects the current iterate onto the solution space of a single constraint. Hence, it requires very low cost per iteration and storage, and it has a linear rate of convergence. Distributed implementations of Kaczmarz have become, in recent years, the de facto architectural choice for large-scale linear systems. Therefore, in this paper we develop a family of randomized block Kaczmarz algorithms that uses at each step a subset of the constraints and extrapolated stepsizes, and ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09946","kind":"arxiv","version":1},"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":"2026-05-17T23:52:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KeoiyoK/NmpdFLXUfR0+VR0JkEhxiJuyJCyTuUzJwizID7r8JqJEDeAT1cWr8HcviDeO0j4sBgcwK4Ymwp+IBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:15:22.199867Z"},"content_sha256":"e2c3381d98ae951dfaad923c90c13b10cff3b5a2a0526f474bba64fac8a19e75","schema_version":"1.0","event_id":"sha256:e2c3381d98ae951dfaad923c90c13b10cff3b5a2a0526f474bba64fac8a19e75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/bundle.json","state_url":"https://pith.science/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/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":"2026-06-02T20:15:22Z","links":{"resolver":"https://pith.science/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ","bundle":"https://pith.science/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/bundle.json","state":"https://pith.science/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVVVUAQNKHHFXCNUH42YCSDXEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JVVVUAQNKHHFXCNUH42YCSDXEJ","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":"fce730d660e513616f0fc09264a0da1d1e678a4d5f39dc34fd4502324e5358f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T14:14:20Z","title_canon_sha256":"4cb53590e016b63322eb79299b296c5ccfe7c7ed2e644e1146c6d1fc03ff0252"},"schema_version":"1.0","source":{"id":"1902.09946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.09946","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"arxiv_version","alias_value":"1902.09946v1","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.09946","created_at":"2026-05-17T23:52:34Z"},{"alias_kind":"pith_short_12","alias_value":"JVVVUAQNKHHF","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JVVVUAQNKHHFXCNU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JVVVUAQN","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:e2c3381d98ae951dfaad923c90c13b10cff3b5a2a0526f474bba64fac8a19e75","target":"graph","created_at":"2026-05-17T23:52:34Z","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":"The Kaczmarz algorithm is a simple iterative scheme for solving consistent linear systems. At each step, the method projects the current iterate onto the solution space of a single constraint. Hence, it requires very low cost per iteration and storage, and it has a linear rate of convergence. Distributed implementations of Kaczmarz have become, in recent years, the de facto architectural choice for large-scale linear systems. Therefore, in this paper we develop a family of randomized block Kaczmarz algorithms that uses at each step a subset of the constraints and extrapolated stepsizes, and ca","authors_text":"Ion Necoara","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T14:14:20Z","title":"Faster randomized block Kaczmarz algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09946","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":"sha256:9e17614acc974806f077b64cf0e38f93c6517717be381d4996e2963a83eec410","target":"record","created_at":"2026-05-17T23:52:34Z","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":"fce730d660e513616f0fc09264a0da1d1e678a4d5f39dc34fd4502324e5358f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-26T14:14:20Z","title_canon_sha256":"4cb53590e016b63322eb79299b296c5ccfe7c7ed2e644e1146c6d1fc03ff0252"},"schema_version":"1.0","source":{"id":"1902.09946","kind":"arxiv","version":1}},"canonical_sha256":"4d6b5a020d51ce5b89b43f358148772259583ef9a62e8b0851684211fe1a8db4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d6b5a020d51ce5b89b43f358148772259583ef9a62e8b0851684211fe1a8db4","first_computed_at":"2026-05-17T23:52:34.987988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:34.987988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xwrTs5FVD7hoWOes54yxqbKEAo6Jws8YpKBjyZL/vw5b0jdaF4WwDe8YBnN4uTufWqdxqgvP+aoeWpOb9Z07Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:34.988444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.09946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e17614acc974806f077b64cf0e38f93c6517717be381d4996e2963a83eec410","sha256:e2c3381d98ae951dfaad923c90c13b10cff3b5a2a0526f474bba64fac8a19e75"],"state_sha256":"c656e236fb79f17376ea7a0127dc09ab201ac3a5a4d9900c1f2d72ef72dc7496"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7QC7aFpBltZS4z+WaEdwLFuL+IrOTwUd90CrXMHXGV19x5Ze+Ao3BRbm5e0EW8i86DXn2YwloGboSEJnmpDABw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:15:22.203538Z","bundle_sha256":"5583f020af6a60edf644f654b3448e902f1a6405c8006bd8a9cee65bcf608b9a"}}