{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:23CH3UD4T4HEWNKKS4O6S77YH3","short_pith_number":"pith:23CH3UD4","schema_version":"1.0","canonical_sha256":"d6c47dd07c9f0e4b354a971de97ff83eef570cbea88ac17a175b47c03d89cff8","source":{"kind":"arxiv","id":"1509.04376","version":1},"attestation_state":"computed","paper":{"title":"Precise Phase Transition of Total Variation Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Bingwen Zhang, Jian-Feng Cai, Lifeng Lai, Weiyu Xu","submitted_at":"2015-09-15T02:18:58Z","abstract_excerpt":"Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization"},"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":"1509.04376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-09-15T02:18:58Z","cross_cats_sorted":["cs.LG","math.IT","math.OC","stat.ML"],"title_canon_sha256":"825405d8748595b05770ac65c314ed1f3194cd212678b245312f5de6a84ff2e5","abstract_canon_sha256":"067a5c03b1029d009f0ec708c0a115a53d1dbc9742f6586e874eecea35dbd3c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:07.330090Z","signature_b64":"trpqYJT0yTcDahPrc77m9tOskHy8lTabm5K9EVswcZ4Dg+yE4omllJbQCcDf5of5x3l/WpGVCJEiBXaWujijAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6c47dd07c9f0e4b354a971de97ff83eef570cbea88ac17a175b47c03d89cff8","last_reissued_at":"2026-05-18T01:33:07.329690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:07.329690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precise Phase Transition of Total Variation Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","math.OC","stat.ML"],"primary_cat":"cs.IT","authors_text":"Bingwen Zhang, Jian-Feng Cai, Lifeng Lai, Weiyu Xu","submitted_at":"2015-09-15T02:18:58Z","abstract_excerpt":"Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04376","kind":"arxiv","version":1},"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":"1509.04376","created_at":"2026-05-18T01:33:07.329750+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.04376v1","created_at":"2026-05-18T01:33:07.329750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04376","created_at":"2026-05-18T01:33:07.329750+00:00"},{"alias_kind":"pith_short_12","alias_value":"23CH3UD4T4HE","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"23CH3UD4T4HEWNKK","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"23CH3UD4","created_at":"2026-05-18T12:28:59.999130+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/23CH3UD4T4HEWNKKS4O6S77YH3","json":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3.json","graph_json":"https://pith.science/api/pith-number/23CH3UD4T4HEWNKKS4O6S77YH3/graph.json","events_json":"https://pith.science/api/pith-number/23CH3UD4T4HEWNKKS4O6S77YH3/events.json","paper":"https://pith.science/paper/23CH3UD4"},"agent_actions":{"view_html":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3","download_json":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3.json","view_paper":"https://pith.science/paper/23CH3UD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.04376&json=true","fetch_graph":"https://pith.science/api/pith-number/23CH3UD4T4HEWNKKS4O6S77YH3/graph.json","fetch_events":"https://pith.science/api/pith-number/23CH3UD4T4HEWNKKS4O6S77YH3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3/action/storage_attestation","attest_author":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3/action/author_attestation","sign_citation":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3/action/citation_signature","submit_replication":"https://pith.science/pith/23CH3UD4T4HEWNKKS4O6S77YH3/action/replication_record"}},"created_at":"2026-05-18T01:33:07.329750+00:00","updated_at":"2026-05-18T01:33:07.329750+00:00"}