{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YE5QC3RWEEVXLPIEG3LQVUKTWJ","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":"4c4cee42773fa102e98838fc7f7a54ea9d3df1778d464bb21cad84692a4854ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-23T11:00:45Z","title_canon_sha256":"8e76a63b45cd4d1a0d74313b1fa292e0f4fcae8fcd25770ecc3792d40533e52f"},"schema_version":"1.0","source":{"id":"1304.6232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6232","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6232v1","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6232","created_at":"2026-05-18T03:27:22Z"},{"alias_kind":"pith_short_12","alias_value":"YE5QC3RWEEVX","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YE5QC3RWEEVXLPIE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YE5QC3RW","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f1c0b2d58b2bcb1837932b8c4d295fbf3a5eeda8b84c75d48e84c908714d0891","target":"graph","created_at":"2026-05-18T03:27:22Z","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":"In this paper, we consider the \"foreach\" sparse recovery problem with failure probability $p$. The goal of which is to design a distribution over $m \\times N$ matrices $\\Phi$ and a decoding algorithm $\\algo$ such that for every $\\vx\\in\\R^N$, we have the following error guarantee with probability at least $1-p$ \\[\\|\\vx-\\algo(\\Phi\\vx)\\|_2\\le C\\|\\vx-\\vx_k\\|_2,\\] where $C$ is a constant (ideally arbitrarily close to 1) and $\\vx_k$ is the best $k$-sparse approximation of $\\vx$.\n  Much of the sparse recovery or compressive sensing literature has focused on the case of either $p = 0$ or $p = \\Omega(1","authors_text":"Anna C. Gilbert, Atri Rudra, Ely Porat, Hung Q. Ngo, Martin J. Strauss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-23T11:00:45Z","title":"L2/L2-foreach sparse recovery with low risk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6232","kind":"arxiv","version":1},"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:b9e7fd6fbd67636a148e534d206bc1a520105eb8dabc704edf3e0aa1bd0b8784","target":"record","created_at":"2026-05-18T03:27:22Z","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":"4c4cee42773fa102e98838fc7f7a54ea9d3df1778d464bb21cad84692a4854ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-04-23T11:00:45Z","title_canon_sha256":"8e76a63b45cd4d1a0d74313b1fa292e0f4fcae8fcd25770ecc3792d40533e52f"},"schema_version":"1.0","source":{"id":"1304.6232","kind":"arxiv","version":1}},"canonical_sha256":"c13b016e36212b75bd0436d70ad153b2747f9c341fd2a2c3eecd601f01e05d19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c13b016e36212b75bd0436d70ad153b2747f9c341fd2a2c3eecd601f01e05d19","first_computed_at":"2026-05-18T03:27:22.027444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:22.027444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6/dn8dWcVA8aAt/N8iSXY+gmIDEWSi6Xk2zjR4D/jMhbidJXOZCuME5wNfz/oj9/CeFfqqxp57Q5kPr6F8U4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:22.028136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9e7fd6fbd67636a148e534d206bc1a520105eb8dabc704edf3e0aa1bd0b8784","sha256:f1c0b2d58b2bcb1837932b8c4d295fbf3a5eeda8b84c75d48e84c908714d0891"],"state_sha256":"67e4d8a85fd606b990302dfa3cb80f7a7408b7ce9fc3355d3477c605f36d6810"}