{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NQXQTL4YLAMFX5TME2QNA5RZPR","short_pith_number":"pith:NQXQTL4Y","canonical_record":{"source":{"id":"1908.08101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-21T20:06:43Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"031af82c0e8b85112c0fe7fd55e301d033b6560efa629c46db23dc98567b97ff","abstract_canon_sha256":"c24d007035a7464cc1d768d4b8b3857922aea47d9422372f9b8b41ad2e65d283"},"schema_version":"1.0"},"canonical_sha256":"6c2f09af9858185bf66c26a0d076397c4e9aed8b711d00e79e701a5c58f8e5ce","source":{"kind":"arxiv","id":"1908.08101","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NQXQTL4YLAMFX5TME2QNA5RZPR","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08101","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-08-21T20:06:43Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"031af82c0e8b85112c0fe7fd55e301d033b6560efa629c46db23dc98567b97ff","abstract_canon_sha256":"c24d007035a7464cc1d768d4b8b3857922aea47d9422372f9b8b41ad2e65d283"},"schema_version":"1.0"},"canonical_sha256":"6c2f09af9858185bf66c26a0d076397c4e9aed8b711d00e79e701a5c58f8e5ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:22:36.035303Z","signature_b64":"5wgnnPd2cM9dWwwiU0paRLaz6p8Q4WUyxxVK22q54WCmQluDR3Uhy2qVAkZ9jiPug0sBv3Ry6aQZejlGiVrIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c2f09af9858185bf66c26a0d076397c4e9aed8b711d00e79e701a5c58f8e5ce","last_reissued_at":"2026-07-05T01:22:36.034887Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:22:36.034887Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08101","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJCrRFfjzvZJfUqkAIW1nL7jPKY1ECOEOskERZGo8G5HjTT5AXjWrqeMPNOe86iOnpPeWJRPAaRe4+qniiHVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:03:19.530614Z"},"content_sha256":"d3ba0384367d61cfdf10b6b719231d184da317c99c6f127134a35c638199338e","schema_version":"1.0","event_id":"sha256:d3ba0384367d61cfdf10b6b719231d184da317c99c6f127134a35c638199338e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NQXQTL4YLAMFX5TME2QNA5RZPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbations of CUR Decompositions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Keaton Hamm, Longxiu Huang","submitted_at":"2019-08-21T20:06:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08101","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08101/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQyXv0/rIT9vrbWCATGndrWHSK1ls3E3usuVQJvlvJ6zCOLuVMVKn8nB85r0XduOI1j/HJBx6JgqfwlBRlNpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T20:03:19.531148Z"},"content_sha256":"e2833fcaead94ab09ea2bd5459df688b92e11d1befe21b3ec3adcdc142b77727","schema_version":"1.0","event_id":"sha256:e2833fcaead94ab09ea2bd5459df688b92e11d1befe21b3ec3adcdc142b77727"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/bundle.json","state_url":"https://pith.science/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/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":"2026-08-16T20:03:19Z","links":{"resolver":"https://pith.science/pith/NQXQTL4YLAMFX5TME2QNA5RZPR","bundle":"https://pith.science/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/bundle.json","state":"https://pith.science/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQXQTL4YLAMFX5TME2QNA5RZPR/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8o4vlLhPhVavtuvo1gxgR0IQ+jdcX36bzqf4MPorFhhnTV0gvCfchhTTg0oxgmKKjG2l7PTpTz4B7pG///1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T20:03:19.540687Z","bundle_sha256":"3e38a7ee2863ef2e6e2838fe9562a107f745a0b29a9d7a1e4ce2aa202d6b4c11"}}