{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2K4X3OL7HRW7AVHCF3W6XA5XFB","short_pith_number":"pith:2K4X3OL7","schema_version":"1.0","canonical_sha256":"d2b97db97f3c6df054e22eedeb83b7287441e1ae4ca4cf2601baae7c70d1767f","source":{"kind":"arxiv","id":"1007.4396","version":2},"attestation_state":"computed","paper":{"title":"Restricted $p$-isometry property and its application for nonconvex compressive sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Song Li, Yi Shen","submitted_at":"2010-07-26T08:25:15Z","abstract_excerpt":"Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \\cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers sparse signals from fewer linear measurements than does the $l_1$ minimization. They proved that $l_p$ minimization with $0<p<1$ recovers $S$-sparse signals $x\\in\\RN$ from fewer Gaussian random measurements for some smaller $p$ with probability exceeding $$1 - 1 / {N\\choose S}.$$ The first aim of this paper is to show that above result is right for the case of "},"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":"1007.4396","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-07-26T08:25:15Z","cross_cats_sorted":[],"title_canon_sha256":"f172bac3217d88d2c026ae37f4855723a6c875daa3be00410f21ad6759c8cbcc","abstract_canon_sha256":"4961dab36f095974d9b27c585a9e8acb0c7db0f97c3faecf42cdb1f2c76e3555"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:45.201984Z","signature_b64":"BWVIWo+iMN5+YuEfSq01Mg2huU+l6z3obR6rPRwQrSyi6TOLZ4Xj6ihhcmHQpDJ469R6arFDcHvOqoaTlnxIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2b97db97f3c6df054e22eedeb83b7287441e1ae4ca4cf2601baae7c70d1767f","last_reissued_at":"2026-05-18T04:27:45.201442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:45.201442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restricted $p$-isometry property and its application for nonconvex compressive sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Song Li, Yi Shen","submitted_at":"2010-07-26T08:25:15Z","abstract_excerpt":"Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \\cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers sparse signals from fewer linear measurements than does the $l_1$ minimization. They proved that $l_p$ minimization with $0<p<1$ recovers $S$-sparse signals $x\\in\\RN$ from fewer Gaussian random measurements for some smaller $p$ with probability exceeding $$1 - 1 / {N\\choose S}.$$ The first aim of this paper is to show that above result is right for the case of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4396","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":"1007.4396","created_at":"2026-05-18T04:27:45.201536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.4396v2","created_at":"2026-05-18T04:27:45.201536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4396","created_at":"2026-05-18T04:27:45.201536+00:00"},{"alias_kind":"pith_short_12","alias_value":"2K4X3OL7HRW7","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2K4X3OL7HRW7AVHC","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2K4X3OL7","created_at":"2026-05-18T12:26:03.138858+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/2K4X3OL7HRW7AVHCF3W6XA5XFB","json":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB.json","graph_json":"https://pith.science/api/pith-number/2K4X3OL7HRW7AVHCF3W6XA5XFB/graph.json","events_json":"https://pith.science/api/pith-number/2K4X3OL7HRW7AVHCF3W6XA5XFB/events.json","paper":"https://pith.science/paper/2K4X3OL7"},"agent_actions":{"view_html":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB","download_json":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB.json","view_paper":"https://pith.science/paper/2K4X3OL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.4396&json=true","fetch_graph":"https://pith.science/api/pith-number/2K4X3OL7HRW7AVHCF3W6XA5XFB/graph.json","fetch_events":"https://pith.science/api/pith-number/2K4X3OL7HRW7AVHCF3W6XA5XFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB/action/storage_attestation","attest_author":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB/action/author_attestation","sign_citation":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB/action/citation_signature","submit_replication":"https://pith.science/pith/2K4X3OL7HRW7AVHCF3W6XA5XFB/action/replication_record"}},"created_at":"2026-05-18T04:27:45.201536+00:00","updated_at":"2026-05-18T04:27:45.201536+00:00"}