{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ESMJLLLQM7K4YKKOQS7NHSLMHZ","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":"6252bb0369d17a4079b9342fc0c3419aac77e57081eb0a516f52254f246b11dd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-22T20:26:03Z","title_canon_sha256":"d472cbc7c9955c09db68b5159b07d1346068a9625c9a28efc097550d981fbce2"},"schema_version":"1.0","source":{"id":"1903.09698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09698","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09698v2","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09698","created_at":"2026-05-17T23:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"ESMJLLLQM7K4","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESMJLLLQM7K4YKKO","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESMJLLLQ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:cf316aa5591e1e1be84ab96973d7df863234081d6405edc845eaa3f80c3aa3e1","target":"graph","created_at":"2026-05-17T23:49:28Z","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":"This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in this is a new characterization of exact CUR decompositions. A novel perturbation analysis is performed on CUR approximations of noisy versions of low-rank matrices, which compares them with the putative CUR decomposition of the underlying low-rank part. Additionally, we give new column and row sampling results which allow one to conclude that a CUR decompos","authors_text":"Keaton Hamm, Longxiu Huang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-22T20:26:03Z","title":"CUR Decompositions, Approximations, and Perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09698","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":"sha256:78fedcdfe53eb0c80c5665f49eca803d056b29aee4c0f0bd4340f40dfc0ef1c6","target":"record","created_at":"2026-05-17T23:49:28Z","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":"6252bb0369d17a4079b9342fc0c3419aac77e57081eb0a516f52254f246b11dd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-22T20:26:03Z","title_canon_sha256":"d472cbc7c9955c09db68b5159b07d1346068a9625c9a28efc097550d981fbce2"},"schema_version":"1.0","source":{"id":"1903.09698","kind":"arxiv","version":2}},"canonical_sha256":"249895ad7067d5cc294e84bed3c96c3e41730e832ddbd01f46315a9d05dcdbb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"249895ad7067d5cc294e84bed3c96c3e41730e832ddbd01f46315a9d05dcdbb8","first_computed_at":"2026-05-17T23:49:28.624575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:28.624575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AVTyTX5p1hiHs+iQ9LArlY5EqTgPcmiqzT/grwT7mumrrGb2X0U59wJ2jls6jJciaPeYQ1eh7MjmzVHXzfwDDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:28.625195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78fedcdfe53eb0c80c5665f49eca803d056b29aee4c0f0bd4340f40dfc0ef1c6","sha256:cf316aa5591e1e1be84ab96973d7df863234081d6405edc845eaa3f80c3aa3e1"],"state_sha256":"df955dd198b7eff4b5e173e72d3a6c365f0f91638a99aaaa8bb755549510346b"}