{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4A2OP255OI3AXQ6ZWNRGFJUT6Y","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":"4839dec3feddd1fce5693d6e40415c2aa81c5cceb1c7dd276df65bbf66581e59","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-14T15:19:46Z","title_canon_sha256":"10b6b171baef62f782cb8076b3e1dbf0d2b02ccab01045a183a70ffeab6a7e99"},"schema_version":"1.0","source":{"id":"1007.2354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2354","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2354v2","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2354","created_at":"2026-05-18T04:15:28Z"},{"alias_kind":"pith_short_12","alias_value":"4A2OP255OI3A","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4A2OP255OI3AXQ6Z","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4A2OP255","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:4483487e59246bd03611d018e77262d5467d75d2433ba317c5397d40147f7d65","target":"graph","created_at":"2026-05-18T04:15:28Z","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"},"paper":{"abstract_excerpt":"Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\\ell_1$-minimization find the sparsest solution to certain systems of equations. Random matrices have become a popular choice for the measurement matrix. Indeed, near-optimal uniform recovery results have been shown for such matrices. In this note we focus on nonuniform recovery using Gaussian random matrices and $\\ell_1$-minimization. We provide a condition on the number of samples in terms of the sparsity and the signal length which guarantees","authors_text":"Holger Rauhut, Ula\\c{s} Ayaz","cross_cats":["math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-14T15:19:46Z","title":"Nonuniform Sparse Recovery with Subgaussian Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2354","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":"sha256:6987f34c3ae6ed815737363a15a2a84e9e082cf7327936aaf8383713efb6211a","target":"record","created_at":"2026-05-18T04:15:28Z","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":"4839dec3feddd1fce5693d6e40415c2aa81c5cceb1c7dd276df65bbf66581e59","cross_cats_sorted":["math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-14T15:19:46Z","title_canon_sha256":"10b6b171baef62f782cb8076b3e1dbf0d2b02ccab01045a183a70ffeab6a7e99"},"schema_version":"1.0","source":{"id":"1007.2354","kind":"arxiv","version":2}},"canonical_sha256":"e034e7ebbd72360bc3d9b36262a693f61305a0293485062a63742daec12ed5e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e034e7ebbd72360bc3d9b36262a693f61305a0293485062a63742daec12ed5e3","first_computed_at":"2026-05-18T04:15:28.484415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:15:28.484415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynDA6hduYdtqxhyqaW7F0R8jXsQH+T5YO3xSwNCpwJFTy9tTO03zALxM+wWBwfJTWloteOUQEARsFW6j24JUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:15:28.484873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6987f34c3ae6ed815737363a15a2a84e9e082cf7327936aaf8383713efb6211a","sha256:4483487e59246bd03611d018e77262d5467d75d2433ba317c5397d40147f7d65"],"state_sha256":"a30890af7b2fe006004282987702129d0672aebf66c255c40710af0fa21ff5cf"}