{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FSPW7LCQESWWGXAB4BROVDNWDW","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":"ccfeca19d003efddd66ffccc873eb647541830347d58e3a62a4062345dbabe5e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-05T20:43:13Z","title_canon_sha256":"11cb2ca84c42dda4ae997092cfe49c5805b0d5dabfd784f8da8fbb86584476b4"},"schema_version":"1.0","source":{"id":"1712.01915","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.01915","created_at":"2026-05-18T00:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1712.01915v2","created_at":"2026-05-18T00:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.01915","created_at":"2026-05-18T00:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"FSPW7LCQESWW","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FSPW7LCQESWWGXAB","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FSPW7LCQ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:fab93ea1f0fad16104b1e36f800d44f9a3342313bf3fcbbec25807ccbe600122","target":"graph","created_at":"2026-05-18T00:27:17Z","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":"Tremendous efforts have been made to study the theoretical and algorithmic aspects of sparse recovery and low-rank matrix recovery. This paper fills a theoretical gap in matrix recovery: the optimal sample complexity for stable recovery without constants or log factors. We treat sparsity, low-rankness, and potentially other parsimonious structures within the same framework: constraint sets that have small covering numbers or Minkowski dimensions. We consider three types of random measurement matrices (unstructured, rank-1, and symmetric rank-1 matrices), following probability distributions tha","authors_text":"Kiryung Lee, Yanjun Li, Yoram Bresler","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-05T20:43:13Z","title":"Optimal Sample Complexity for Stable Matrix Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.01915","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":"sha256:4af86051d0d05b6aa9ac897b7b172f1a2a0e3368afebc8ec05572584021b30e0","target":"record","created_at":"2026-05-18T00:27:17Z","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":"ccfeca19d003efddd66ffccc873eb647541830347d58e3a62a4062345dbabe5e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-12-05T20:43:13Z","title_canon_sha256":"11cb2ca84c42dda4ae997092cfe49c5805b0d5dabfd784f8da8fbb86584476b4"},"schema_version":"1.0","source":{"id":"1712.01915","kind":"arxiv","version":2}},"canonical_sha256":"2c9f6fac5024ad635c01e062ea8db61daebd31570ff8eed2ee0f6621e1286777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c9f6fac5024ad635c01e062ea8db61daebd31570ff8eed2ee0f6621e1286777","first_computed_at":"2026-05-18T00:27:17.461566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:17.461566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gIGBhTOFY6irs+YNnABtg6NMGqM1opMQpWrFLjwspISeyeYsRKOMdbfA38Nypp491qb5JEtEbWg3aNwvROL3DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:17.462292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.01915","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4af86051d0d05b6aa9ac897b7b172f1a2a0e3368afebc8ec05572584021b30e0","sha256:fab93ea1f0fad16104b1e36f800d44f9a3342313bf3fcbbec25807ccbe600122"],"state_sha256":"5d71db5c5d2eef3a2b0c1ccf4546e4c0166b8dcd668eac0e6b913a53ff6d21fb"}