{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:YJSA5SKMKYOET7FHO3QUAWIOCZ","short_pith_number":"pith:YJSA5SKM","schema_version":"1.0","canonical_sha256":"c2640ec94c561c49fca776e140590e1653d0522cff7ad575a038f7c067790792","source":{"kind":"arxiv","id":"1106.1474","version":2},"attestation_state":"computed","paper":{"title":"Simple Bounds for Recovering Low-complexity Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Benjamin Recht, Emmanuel Candes","submitted_at":"2011-06-07T23:24:36Z","abstract_excerpt":"This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n measurements with high probability and a rank r, n by n matrix can be efficiently recovered from r(6n-5r) with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches the best known bounds. We present a parallel analysis for block sparse vectors obtaining similarly tight bounds."},"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":"1106.1474","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-06-07T23:24:36Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ca1502ab8a16f5b219c69e0d6f4dcc54ae2b921f1f3bed03ea031b2eee8cb9e2","abstract_canon_sha256":"453600f452837dd146877a49f7f3cb631e34476b5d0a6173283539fef77eda2d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:01:13.190136Z","signature_b64":"uatt44zMctKU6MVEpISvxn3ciR9EZKPpA7WG3+QLBSsvRST+NEiG+C9vlOf6dr1aNY+NyPqZB7oN76vROaZ5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2640ec94c561c49fca776e140590e1653d0522cff7ad575a038f7c067790792","last_reissued_at":"2026-05-18T04:01:13.189448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:01:13.189448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple Bounds for Recovering Low-complexity Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Benjamin Recht, Emmanuel Candes","submitted_at":"2011-06-07T23:24:36Z","abstract_excerpt":"This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n measurements with high probability and a rank r, n by n matrix can be efficiently recovered from r(6n-5r) with high probability. For sparse vectors, this is within an additive factor of the best known nonasymptotic bounds. For low-rank matrices, this matches the best known bounds. We present a parallel analysis for block sparse vectors obtaining similarly tight bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1474","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":""},"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":"1106.1474","created_at":"2026-05-18T04:01:13.189565+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1474v2","created_at":"2026-05-18T04:01:13.189565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1474","created_at":"2026-05-18T04:01:13.189565+00:00"},{"alias_kind":"pith_short_12","alias_value":"YJSA5SKMKYOE","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_16","alias_value":"YJSA5SKMKYOET7FH","created_at":"2026-05-18T12:26:47.523578+00:00"},{"alias_kind":"pith_short_8","alias_value":"YJSA5SKM","created_at":"2026-05-18T12:26:47.523578+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/YJSA5SKMKYOET7FHO3QUAWIOCZ","json":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ.json","graph_json":"https://pith.science/api/pith-number/YJSA5SKMKYOET7FHO3QUAWIOCZ/graph.json","events_json":"https://pith.science/api/pith-number/YJSA5SKMKYOET7FHO3QUAWIOCZ/events.json","paper":"https://pith.science/paper/YJSA5SKM"},"agent_actions":{"view_html":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ","download_json":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ.json","view_paper":"https://pith.science/paper/YJSA5SKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1474&json=true","fetch_graph":"https://pith.science/api/pith-number/YJSA5SKMKYOET7FHO3QUAWIOCZ/graph.json","fetch_events":"https://pith.science/api/pith-number/YJSA5SKMKYOET7FHO3QUAWIOCZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ/action/storage_attestation","attest_author":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ/action/author_attestation","sign_citation":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ/action/citation_signature","submit_replication":"https://pith.science/pith/YJSA5SKMKYOET7FHO3QUAWIOCZ/action/replication_record"}},"created_at":"2026-05-18T04:01:13.189565+00:00","updated_at":"2026-05-18T04:01:13.189565+00:00"}