{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:JATKFLWSKFILUA6XBEVI4BFKA2","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":"a7ee7fbcd00bfd2c7694de7f75ed3f47e5a2f65c50d41bfff79e10e1fddac230","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-03-03T19:36:54Z","title_canon_sha256":"c2bbbf9a093638e202ad49976f7d2757cb1c1b9bfd3031784838fd3d18fc9d58"},"schema_version":"1.0","source":{"id":"math/0503066","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503066","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503066v2","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503066","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"JATKFLWSKFIL","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"JATKFLWSKFILUA6X","created_at":"2026-06-03T22:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"JATKFLWS","created_at":"2026-06-03T22:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:43159d260125e6531145116486b12a939b8ac764a24823ac6b330862cd94811b","target":"graph","created_at":"2026-06-03T22:06:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0503066/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an error term. Is it possible to recover x_0 accurately based on the data y?\n  To recover x_0, we consider the solution x* to the l1-regularization problem min \\|x\\|_1 subject to \\|Ax-y\\|_2 <= epsilon, where epsilon is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unit-normed columns) and if the vector x_0 is sufficient","authors_text":"Emmanuel Candes, Justin Romberg, Terence Tao","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2005-03-03T19:36:54Z","title":"Stable Signal Recovery from Incomplete and Inaccurate Measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503066","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":"sha256:152b0f4b2c4647c69cfcb0a47bff352d07a9b751a98d5fac38d94d4c83d6d3e5","target":"record","created_at":"2026-06-03T22:06:16Z","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":"a7ee7fbcd00bfd2c7694de7f75ed3f47e5a2f65c50d41bfff79e10e1fddac230","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2005-03-03T19:36:54Z","title_canon_sha256":"c2bbbf9a093638e202ad49976f7d2757cb1c1b9bfd3031784838fd3d18fc9d58"},"schema_version":"1.0","source":{"id":"math/0503066","kind":"arxiv","version":2}},"canonical_sha256":"4826a2aed25150ba03d7092a8e04aa06a8c4e40d514cbc472963a5d7815b3f09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4826a2aed25150ba03d7092a8e04aa06a8c4e40d514cbc472963a5d7815b3f09","first_computed_at":"2026-06-03T22:06:16.540574Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:16.540574Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L33kMSQ3kBBhlxCR4H+Apx+Bbkp4koeU1WL5lkg8ExG7XMmtZq/D3iw89Un0IQ2eUMoKZudlis/iLpvHl1jNAQ==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:16.540983Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0503066","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:152b0f4b2c4647c69cfcb0a47bff352d07a9b751a98d5fac38d94d4c83d6d3e5","sha256:43159d260125e6531145116486b12a939b8ac764a24823ac6b330862cd94811b"],"state_sha256":"2e377014ed6de278b845b78a6febc9d325a6c0ab071d1b245cc256f1a3a7bfe6"}