{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RTMB24YLW6PTCAQMN6XKLHNUZH","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":"b016e27c07f42843bfc03a8e58dc4a7089a832702bdd8bd8d2a6f1802b80ad7a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-29T17:39:17Z","title_canon_sha256":"c25f1b4cec1dd6b6976411c89648abd3fd15c17509293368aec839d55929d0f5"},"schema_version":"1.0","source":{"id":"2411.19877","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.19877","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"arxiv_version","alias_value":"2411.19877v3","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19877","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_12","alias_value":"RTMB24YLW6PT","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_16","alias_value":"RTMB24YLW6PTCAQM","created_at":"2026-07-05T10:46:59Z"},{"alias_kind":"pith_short_8","alias_value":"RTMB24YL","created_at":"2026-07-05T10:46:59Z"}],"graph_snapshots":[{"event_id":"sha256:504f950ab76a5cdc9e730b63cafd84a3593baa43f192397c400a98a5b4f30485","target":"graph","created_at":"2026-07-05T10:46:59Z","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/2411.19877/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The randomized Kaczmarz (RK) method is a well-known approach for solving linear least-squares problems with a large number of rows. RK accesses and processes just one row at a time, leading to exponentially fast convergence for consistent linear systems. However, RK fails to converge to the least-squares solution for inconsistent systems. This work presents a simple fix: average the RK iterates produced in the tail part of the algorithm. The proposed tail-averaged randomized Kaczmarz (TARK) converges for both consistent and inconsistent least-squares problems at a polynomial rate, which is kno","authors_text":"Ethan N. Epperly, Gil Goldshlager, Robert J. Webber","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-29T17:39:17Z","title":"Randomized Kaczmarz with tail averaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19877","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":"sha256:282f2e2334fb8f612586dc8bd44d1c225b4baa5e655bba4fdc610455177ddc65","target":"record","created_at":"2026-07-05T10:46:59Z","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":"b016e27c07f42843bfc03a8e58dc4a7089a832702bdd8bd8d2a6f1802b80ad7a","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-29T17:39:17Z","title_canon_sha256":"c25f1b4cec1dd6b6976411c89648abd3fd15c17509293368aec839d55929d0f5"},"schema_version":"1.0","source":{"id":"2411.19877","kind":"arxiv","version":3}},"canonical_sha256":"8cd81d730bb79f31020c6faea59db4c9f67ee3bc5475ab4ea2dbcb025001bc2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cd81d730bb79f31020c6faea59db4c9f67ee3bc5475ab4ea2dbcb025001bc2a","first_computed_at":"2026-07-05T10:46:59.045490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:46:59.045490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/Zm2PuTVplmTKCwzbYMPiYDg+mZFay2yWAQmxg215A1PRkDjDet9C/j+x/wNYaTFR181RA6Jwq5VB6WAzsiAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:46:59.046087Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.19877","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:282f2e2334fb8f612586dc8bd44d1c225b4baa5e655bba4fdc610455177ddc65","sha256:504f950ab76a5cdc9e730b63cafd84a3593baa43f192397c400a98a5b4f30485"],"state_sha256":"c5f7d6f616f3f1cd8b50b03fe0f400829d93c72ee36636f44f755b8ac937a5f8"}