{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UYBUEOTHYL6SXQCTIPZRAUC47L","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":"794ca1889a0f7b0f794fbec77b3a6adfc6a1766835758a7d05752fc74d5e443f","cross_cats_sorted":["math.IT","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-12-02T22:07:05Z","title_canon_sha256":"519e2b047bc5ef1bc7dd433bad7890f53573355c0f1b60df19cdd58311769071"},"schema_version":"1.0","source":{"id":"1312.0641","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0641","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0641v2","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0641","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"UYBUEOTHYL6S","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UYBUEOTHYL6SXQCT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UYBUEOTH","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:fb6c2d0d3e9ef29209955d304c8ebfafafd09d860e6e9ed935f67075f243e3b9","target":"graph","created_at":"2026-05-18T03:05:27Z","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":"This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\\cdot)$ that exploits the structure of the signal. For example, $\\ell_1$ norm can be used for sparse signals. To carry out the estimation, we consider two well-known convex programs: 1) Second order cone program (SOCP), and, 2) Lasso. Assuming Gaussian measurements, we show that, if precise information about the value $f(x)$ or the $\\ell_2$-norm of the noise is available, one can do a ","authors_text":"Babak Hassibi, Christos Thrampoulidis, Samet Oymak","cross_cats":["math.IT","math.OC","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-12-02T22:07:05Z","title":"Simple Bounds for Noisy Linear Inverse Problems with Exact Side Information"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0641","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":"sha256:722924eeb6e98dc8f9eeb937c28e50f8960e7fb562e30b2bdd1aab98d6fbcd1f","target":"record","created_at":"2026-05-18T03:05:27Z","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":"794ca1889a0f7b0f794fbec77b3a6adfc6a1766835758a7d05752fc74d5e443f","cross_cats_sorted":["math.IT","math.OC","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-12-02T22:07:05Z","title_canon_sha256":"519e2b047bc5ef1bc7dd433bad7890f53573355c0f1b60df19cdd58311769071"},"schema_version":"1.0","source":{"id":"1312.0641","kind":"arxiv","version":2}},"canonical_sha256":"a603423a67c2fd2bc05343f310505cfaef981a0bc6abc75cf63da017e78ab68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a603423a67c2fd2bc05343f310505cfaef981a0bc6abc75cf63da017e78ab68a","first_computed_at":"2026-05-18T03:05:27.643084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:27.643084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fR5lCc2AeesUujwRplcL9x/fjeYvwqH3FJZqxxS0LP3fSINiK9+Y9bF+Cuq5aaO2le7O2xGBIphGOkCklrUYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:27.643667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0641","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722924eeb6e98dc8f9eeb937c28e50f8960e7fb562e30b2bdd1aab98d6fbcd1f","sha256:fb6c2d0d3e9ef29209955d304c8ebfafafd09d860e6e9ed935f67075f243e3b9"],"state_sha256":"3bbe8dc5147cd54f13570e732298726d7414fa7479b77ecfa5bd3d9784845060"}