{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NQXQTL4YLAMFX5TME2QNA5RZPR","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":"c24d007035a7464cc1d768d4b8b3857922aea47d9422372f9b8b41ad2e65d283","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-21T20:06:43Z","title_canon_sha256":"031af82c0e8b85112c0fe7fd55e301d033b6560efa629c46db23dc98567b97ff"},"schema_version":"1.0","source":{"id":"1908.08101","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08101","created_at":"2026-07-05T01:22:36Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08101v2","created_at":"2026-07-05T01:22:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08101","created_at":"2026-07-05T01:22:36Z"},{"alias_kind":"pith_short_12","alias_value":"NQXQTL4YLAMF","created_at":"2026-07-05T01:22:36Z"},{"alias_kind":"pith_short_16","alias_value":"NQXQTL4YLAMFX5TM","created_at":"2026-07-05T01:22:36Z"},{"alias_kind":"pith_short_8","alias_value":"NQXQTL4Y","created_at":"2026-07-05T01:22:36Z"}],"graph_snapshots":[{"event_id":"sha256:e2833fcaead94ab09ea2bd5459df688b92e11d1befe21b3ec3adcdc142b77727","target":"graph","created_at":"2026-07-05T01:22:36Z","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/1908.08101/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The CUR decomposition is a factorization of a low-rank matrix obtained by selecting certain column and row submatrices of it. We perform a thorough investigation of what happens to such decompositions in the presence of noise. Since CUR decompositions are non-uniquely formed, we investigate several variants and give perturbation estimates for each in terms of the magnitude of the noise matrix in a broad class of norms which includes all Schatten $p$--norms. The estimates given here are qualitative and illustrate how the choice of columns and rows affects the quality of the approximation, and a","authors_text":"Keaton Hamm, Longxiu Huang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-21T20:06:43Z","title":"Perturbations of CUR Decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08101","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:d3ba0384367d61cfdf10b6b719231d184da317c99c6f127134a35c638199338e","target":"record","created_at":"2026-07-05T01:22:36Z","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":"c24d007035a7464cc1d768d4b8b3857922aea47d9422372f9b8b41ad2e65d283","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-21T20:06:43Z","title_canon_sha256":"031af82c0e8b85112c0fe7fd55e301d033b6560efa629c46db23dc98567b97ff"},"schema_version":"1.0","source":{"id":"1908.08101","kind":"arxiv","version":2}},"canonical_sha256":"6c2f09af9858185bf66c26a0d076397c4e9aed8b711d00e79e701a5c58f8e5ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c2f09af9858185bf66c26a0d076397c4e9aed8b711d00e79e701a5c58f8e5ce","first_computed_at":"2026-07-05T01:22:36.034887Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:22:36.034887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wgnnPd2cM9dWwwiU0paRLaz6p8Q4WUyxxVK22q54WCmQluDR3Uhy2qVAkZ9jiPug0sBv3Ry6aQZejlGiVrIDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:22:36.035303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08101","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3ba0384367d61cfdf10b6b719231d184da317c99c6f127134a35c638199338e","sha256:e2833fcaead94ab09ea2bd5459df688b92e11d1befe21b3ec3adcdc142b77727"],"state_sha256":"4887987b3ad685bd3d40c3d2ddc5cdebd4ada425d057cef1cd712bfde790a60d"}