{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VSGRCCY72ARN3S2GMBOL5TMN4M","short_pith_number":"pith:VSGRCCY7","schema_version":"1.0","canonical_sha256":"ac8d110b1fd022ddcb46605cbecd8de3015780ccf1b0141ddb4ce1fd76c8a931","source":{"kind":"arxiv","id":"1106.0365","version":2},"attestation_state":"computed","paper":{"title":"Lower Bounds for Sparse Recovery","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Eric Price, Khanh Do Ba, Piotr Indyk","submitted_at":"2011-06-02T05:20:14Z","abstract_excerpt":"We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying\n  ||x-x'||_1 <= C min_{k-sparse} x\"} ||x-x\"||_1.\n  It is known that there exist matrices A with this property that have only O(k log (n/k)) rows.\n  In this paper we show that this bound is tight. Our bound holds even for the more general /randomized/ version of the problem, where A is a random variable and the recovery algorithm is required to work for any fixed x with constant probability (over A)."},"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":"1106.0365","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2011-06-02T05:20:14Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"ef55706dcab07ee2a24c128da6b8e6db24f3ce4e0b33b29d7f328ed358c57140","abstract_canon_sha256":"76137c575e51c36fc42b9729a5982203a255af36e67ebc0c1b413f287a4cba3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:49.348080Z","signature_b64":"5DQygTs/A5ANqNiv+9mqUQFUIKurwaFW8GaKdcU3vaD5YLgY7cUE3kz41KaNKoKNGNTw8sKmWBADxA4DtIn+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8d110b1fd022ddcb46605cbecd8de3015780ccf1b0141ddb4ce1fd76c8a931","last_reissued_at":"2026-05-18T04:20:49.347500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:49.347500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower Bounds for Sparse Recovery","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Eric Price, Khanh Do Ba, Piotr Indyk","submitted_at":"2011-06-02T05:20:14Z","abstract_excerpt":"We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying\n  ||x-x'||_1 <= C min_{k-sparse} x\"} ||x-x\"||_1.\n  It is known that there exist matrices A with this property that have only O(k log (n/k)) rows.\n  In this paper we show that this bound is tight. Our bound holds even for the more general /randomized/ version of the problem, where A is a random variable and the recovery algorithm is required to work for any fixed x with constant probability (over A)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0365","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":"1106.0365","created_at":"2026-05-18T04:20:49.347591+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.0365v2","created_at":"2026-05-18T04:20:49.347591+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0365","created_at":"2026-05-18T04:20:49.347591+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSGRCCY72ARN","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSGRCCY72ARN3S2G","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSGRCCY7","created_at":"2026-05-18T12:26:44.992195+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/VSGRCCY72ARN3S2GMBOL5TMN4M","json":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M.json","graph_json":"https://pith.science/api/pith-number/VSGRCCY72ARN3S2GMBOL5TMN4M/graph.json","events_json":"https://pith.science/api/pith-number/VSGRCCY72ARN3S2GMBOL5TMN4M/events.json","paper":"https://pith.science/paper/VSGRCCY7"},"agent_actions":{"view_html":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M","download_json":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M.json","view_paper":"https://pith.science/paper/VSGRCCY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.0365&json=true","fetch_graph":"https://pith.science/api/pith-number/VSGRCCY72ARN3S2GMBOL5TMN4M/graph.json","fetch_events":"https://pith.science/api/pith-number/VSGRCCY72ARN3S2GMBOL5TMN4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M/action/storage_attestation","attest_author":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M/action/author_attestation","sign_citation":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M/action/citation_signature","submit_replication":"https://pith.science/pith/VSGRCCY72ARN3S2GMBOL5TMN4M/action/replication_record"}},"created_at":"2026-05-18T04:20:49.347591+00:00","updated_at":"2026-05-18T04:20:49.347591+00:00"}