{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:OYKG2O7C6D2SGPP4LHMCD5ZTHO","short_pith_number":"pith:OYKG2O7C","schema_version":"1.0","canonical_sha256":"76146d3be2f0f5233dfc59d821f7333b8bdc1d04f22c8f8967ac7ce6a01171dc","source":{"kind":"arxiv","id":"1306.2665","version":3},"attestation_state":"computed","paper":{"title":"Precisely Verifying the Null Space Conditions in Compressed Sensing: A Sandwiching Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Myung Cho, Weiyu Xu","submitted_at":"2013-06-11T21:57:47Z","abstract_excerpt":"In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an $(n-m) \\times n$ ($m>0$) CS matrix $A$ and a positive $k$, we are interested in computing $\\displaystyle \\alpha_k = \\max_{\\{z: Az=0,z\\neq 0\\}}\\max_{\\{K: |K|\\leq k\\}}$ ${\\|z_K \\|_{1}}{\\|z\\|_{1}}$, where $K$ represents subsets of $\\{1,2,...,n\\}$, and $|K|$ is the cardinality of $K$. In particular, we are interested in finding the maximum $k$ such that $\\alpha_k < {1}{2}$. However, computing $\\alpha_k$ is known to be extremely challenging. In this paper, we first propose a se"},"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":"1306.2665","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-06-11T21:57:47Z","cross_cats_sorted":["cs.LG","cs.SY","math.IT","math.OC","stat.ML"],"title_canon_sha256":"e1623fe939cc20aa7bb69aed60c3c866cbd8e229e6d16fd0c027440f360cb679","abstract_canon_sha256":"dc1daf10d1de4b3358d2ce844903fb7a5961767ab53dc55db30cd958751cab26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:16.296829Z","signature_b64":"3gfGQrOwmQMWEw4TIsSJEHJ8ebt9nTgYTcrg+t1MbA7Nt8CSHf3zl8n50mkRTZFmcUH0mOm8wTXKH/23QIwhAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76146d3be2f0f5233dfc59d821f7333b8bdc1d04f22c8f8967ac7ce6a01171dc","last_reissued_at":"2026-05-18T03:16:16.296080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:16.296080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precisely Verifying the Null Space Conditions in Compressed Sensing: A Sandwiching Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.SY","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Myung Cho, Weiyu Xu","submitted_at":"2013-06-11T21:57:47Z","abstract_excerpt":"In this paper, we propose new efficient algorithms to verify the null space condition in compressed sensing (CS). Given an $(n-m) \\times n$ ($m>0$) CS matrix $A$ and a positive $k$, we are interested in computing $\\displaystyle \\alpha_k = \\max_{\\{z: Az=0,z\\neq 0\\}}\\max_{\\{K: |K|\\leq k\\}}$ ${\\|z_K \\|_{1}}{\\|z\\|_{1}}$, where $K$ represents subsets of $\\{1,2,...,n\\}$, and $|K|$ is the cardinality of $K$. In particular, we are interested in finding the maximum $k$ such that $\\alpha_k < {1}{2}$. However, computing $\\alpha_k$ is known to be extremely challenging. In this paper, we first propose a se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2665","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":"1306.2665","created_at":"2026-05-18T03:16:16.296206+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.2665v3","created_at":"2026-05-18T03:16:16.296206+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2665","created_at":"2026-05-18T03:16:16.296206+00:00"},{"alias_kind":"pith_short_12","alias_value":"OYKG2O7C6D2S","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"OYKG2O7C6D2SGPP4","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"OYKG2O7C","created_at":"2026-05-18T12:27:54.935989+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/OYKG2O7C6D2SGPP4LHMCD5ZTHO","json":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO.json","graph_json":"https://pith.science/api/pith-number/OYKG2O7C6D2SGPP4LHMCD5ZTHO/graph.json","events_json":"https://pith.science/api/pith-number/OYKG2O7C6D2SGPP4LHMCD5ZTHO/events.json","paper":"https://pith.science/paper/OYKG2O7C"},"agent_actions":{"view_html":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO","download_json":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO.json","view_paper":"https://pith.science/paper/OYKG2O7C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.2665&json=true","fetch_graph":"https://pith.science/api/pith-number/OYKG2O7C6D2SGPP4LHMCD5ZTHO/graph.json","fetch_events":"https://pith.science/api/pith-number/OYKG2O7C6D2SGPP4LHMCD5ZTHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO/action/storage_attestation","attest_author":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO/action/author_attestation","sign_citation":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO/action/citation_signature","submit_replication":"https://pith.science/pith/OYKG2O7C6D2SGPP4LHMCD5ZTHO/action/replication_record"}},"created_at":"2026-05-18T03:16:16.296206+00:00","updated_at":"2026-05-18T03:16:16.296206+00:00"}