{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:INLHBYHZTAVL5E3AYNROYGJQ6N","short_pith_number":"pith:INLHBYHZ","schema_version":"1.0","canonical_sha256":"435670e0f9982abe9360c362ec1930f363468386d79140eebef3d9a5d012b392","source":{"kind":"arxiv","id":"1209.4209","version":3},"attestation_state":"computed","paper":{"title":"Tight Sufficient Conditions on Exact Sparsity Pattern Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrooz Kamary Aliabadi, Sil\\`eye Ba","submitted_at":"2012-09-19T11:22:31Z","abstract_excerpt":"A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the information-theoretic constraints on exact support recovery of a sparse vector from the measurement vector and matrix. We compute a tight, sufficient condition that is applied to ergodic wide-sense stationary sparse vectors. We compare our results with the existing bounds and recovery conditions. Finally, we extend our results to approximately sparse signal"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.4209","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-09-19T11:22:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"06d577c4bb028074c4417ec617cd377f445caf2fdcde4aecdf579ce874da5ca4","abstract_canon_sha256":"ccaa9406d81cab667a27922b0a44065df92df958c495a4a668dfa94dc2767512"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:03.414807Z","signature_b64":"B+NsAt7VKYDlX6A2CY6NGsj/B5CGDJHtS64kz8SngcJ1VteItUzXKLySMd6+i2ZSY27vhvjyKVNHom0/pv/RBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"435670e0f9982abe9360c362ec1930f363468386d79140eebef3d9a5d012b392","last_reissued_at":"2026-05-18T02:49:03.414385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:03.414385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tight Sufficient Conditions on Exact Sparsity Pattern Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Behrooz Kamary Aliabadi, Sil\\`eye Ba","submitted_at":"2012-09-19T11:22:31Z","abstract_excerpt":"A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the information-theoretic constraints on exact support recovery of a sparse vector from the measurement vector and matrix. We compute a tight, sufficient condition that is applied to ergodic wide-sense stationary sparse vectors. We compare our results with the existing bounds and recovery conditions. Finally, we extend our results to approximately sparse signal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4209","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.4209","created_at":"2026-05-18T02:49:03.414446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.4209v3","created_at":"2026-05-18T02:49:03.414446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4209","created_at":"2026-05-18T02:49:03.414446+00:00"},{"alias_kind":"pith_short_12","alias_value":"INLHBYHZTAVL","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"INLHBYHZTAVL5E3A","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"INLHBYHZ","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N","json":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N.json","graph_json":"https://pith.science/api/pith-number/INLHBYHZTAVL5E3AYNROYGJQ6N/graph.json","events_json":"https://pith.science/api/pith-number/INLHBYHZTAVL5E3AYNROYGJQ6N/events.json","paper":"https://pith.science/paper/INLHBYHZ"},"agent_actions":{"view_html":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N","download_json":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N.json","view_paper":"https://pith.science/paper/INLHBYHZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.4209&json=true","fetch_graph":"https://pith.science/api/pith-number/INLHBYHZTAVL5E3AYNROYGJQ6N/graph.json","fetch_events":"https://pith.science/api/pith-number/INLHBYHZTAVL5E3AYNROYGJQ6N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N/action/storage_attestation","attest_author":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N/action/author_attestation","sign_citation":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N/action/citation_signature","submit_replication":"https://pith.science/pith/INLHBYHZTAVL5E3AYNROYGJQ6N/action/replication_record"}},"created_at":"2026-05-18T02:49:03.414446+00:00","updated_at":"2026-05-18T02:49:03.414446+00:00"}