{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:XZVR6YOKU47CZJZU7FGDKU4BO4","short_pith_number":"pith:XZVR6YOK","schema_version":"1.0","canonical_sha256":"be6b1f61caa73e2ca734f94c355381771eb0649bc6a854cff79d1838b57bab24","source":{"kind":"arxiv","id":"2007.09457","version":2},"attestation_state":"computed","paper":{"title":"Compressed sensing of low-rank plus sparse matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Jared Tanner, Simon Vary","submitted_at":"2020-07-18T15:36:11Z","abstract_excerpt":"Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing, matrix completion, and their variants (Eldar and Kutyniok, 2012; Foucart and Rauhut, 2013) have established that data satisfying low complexity models can be efficiently measured and recovered from a number of measurements proportional to the model complexity rather than the ambient dimension. This manuscript develops similar guarantees showing that $m\\times n$ m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2007.09457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-07-18T15:36:11Z","cross_cats_sorted":["cs.NA","stat.ML"],"title_canon_sha256":"854e53b0bfcb49f0a2c18d4911c93891a58664124697250f253fa99375500909","abstract_canon_sha256":"51e7db04e4fa8833d595c4d0246ae07eee958aadaf1452ae900b73d55e14e925"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:13.396957Z","signature_b64":"P+KX9+Barb444deDr83MyX2JvnF0PfmDYPv9n34LskWJEDRgAeKMgm7HthXS9/V57ThXwcNyWfCB/TmyPdwFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6b1f61caa73e2ca734f94c355381771eb0649bc6a854cff79d1838b57bab24","last_reissued_at":"2026-07-05T04:18:13.396443Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:13.396443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compressed sensing of low-rank plus sparse matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Jared Tanner, Simon Vary","submitted_at":"2020-07-18T15:36:11Z","abstract_excerpt":"Expressing a matrix as the sum of a low-rank matrix plus a sparse matrix is a flexible model capturing global and local features in data popularized as Robust PCA (Candes et al., 2011; Chandrasekaran et al., 2009). Compressed sensing, matrix completion, and their variants (Eldar and Kutyniok, 2012; Foucart and Rauhut, 2013) have established that data satisfying low complexity models can be efficiently measured and recovered from a number of measurements proportional to the model complexity rather than the ambient dimension. This manuscript develops similar guarantees showing that $m\\times n$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.09457","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/2007.09457/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2007.09457","created_at":"2026-07-05T04:18:13.396505+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.09457v2","created_at":"2026-07-05T04:18:13.396505+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.09457","created_at":"2026-07-05T04:18:13.396505+00:00"},{"alias_kind":"pith_short_12","alias_value":"XZVR6YOKU47C","created_at":"2026-07-05T04:18:13.396505+00:00"},{"alias_kind":"pith_short_16","alias_value":"XZVR6YOKU47CZJZU","created_at":"2026-07-05T04:18:13.396505+00:00"},{"alias_kind":"pith_short_8","alias_value":"XZVR6YOK","created_at":"2026-07-05T04:18:13.396505+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4","json":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4.json","graph_json":"https://pith.science/api/pith-number/XZVR6YOKU47CZJZU7FGDKU4BO4/graph.json","events_json":"https://pith.science/api/pith-number/XZVR6YOKU47CZJZU7FGDKU4BO4/events.json","paper":"https://pith.science/paper/XZVR6YOK"},"agent_actions":{"view_html":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4","download_json":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4.json","view_paper":"https://pith.science/paper/XZVR6YOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.09457&json=true","fetch_graph":"https://pith.science/api/pith-number/XZVR6YOKU47CZJZU7FGDKU4BO4/graph.json","fetch_events":"https://pith.science/api/pith-number/XZVR6YOKU47CZJZU7FGDKU4BO4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4/action/storage_attestation","attest_author":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4/action/author_attestation","sign_citation":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4/action/citation_signature","submit_replication":"https://pith.science/pith/XZVR6YOKU47CZJZU7FGDKU4BO4/action/replication_record"}},"created_at":"2026-07-05T04:18:13.396505+00:00","updated_at":"2026-07-05T04:18:13.396505+00:00"}