{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:37LHOZT53M7XRR644SNLAGTPM6","short_pith_number":"pith:37LHOZT5","schema_version":"1.0","canonical_sha256":"dfd677667ddb3f78c7dce49ab01a6f67ad1548109048c14c3e2a535a4c423856","source":{"kind":"arxiv","id":"1603.03534","version":1},"attestation_state":"computed","paper":{"title":"All 2-positive linear maps from M3 to M3 are decomposable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Denny H. Leung, Waishing Tang, Yu Yang","submitted_at":"2016-03-11T06:29:40Z","abstract_excerpt":"Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k<min{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every 2-positive linear map from M3 to M3 is decomposable."},"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":"1603.03534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-03-11T06:29:40Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"3ff8bd534be1d4c9199fdcd73a9264cf7bc2c3004cca3cb36d13f6b0e80884b5","abstract_canon_sha256":"3e3d2ed982a63f0efa6f751780599123fbcf1f6c4a8ec7c9351a0f93e51e9a40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:15.391584Z","signature_b64":"iYcVXxgpL7BNq5T8SSzgqZ+4MYGBh5PADHsWCql9txXGGaDCuisgE4QvWEO/MtA2tbIF2RyVlfRRp1aJgc28DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfd677667ddb3f78c7dce49ab01a6f67ad1548109048c14c3e2a535a4c423856","last_reissued_at":"2026-05-18T01:19:15.391014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:15.391014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All 2-positive linear maps from M3 to M3 are decomposable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Denny H. Leung, Waishing Tang, Yu Yang","submitted_at":"2016-03-11T06:29:40Z","abstract_excerpt":"Following an idea of Choi, we obtain a decomposition theorem for k-positive linear maps from Mm to Mn, where 2<=k<min{m,n}. As a consequence, we give an affirmative answer to Kye's conjecture (also solved independently by Choi) that every 2-positive linear map from M3 to M3 is decomposable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03534","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":"1603.03534","created_at":"2026-05-18T01:19:15.391094+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03534v1","created_at":"2026-05-18T01:19:15.391094+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03534","created_at":"2026-05-18T01:19:15.391094+00:00"},{"alias_kind":"pith_short_12","alias_value":"37LHOZT53M7X","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"37LHOZT53M7XRR64","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"37LHOZT5","created_at":"2026-05-18T12:29:55.572404+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/37LHOZT53M7XRR644SNLAGTPM6","json":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6.json","graph_json":"https://pith.science/api/pith-number/37LHOZT53M7XRR644SNLAGTPM6/graph.json","events_json":"https://pith.science/api/pith-number/37LHOZT53M7XRR644SNLAGTPM6/events.json","paper":"https://pith.science/paper/37LHOZT5"},"agent_actions":{"view_html":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6","download_json":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6.json","view_paper":"https://pith.science/paper/37LHOZT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03534&json=true","fetch_graph":"https://pith.science/api/pith-number/37LHOZT53M7XRR644SNLAGTPM6/graph.json","fetch_events":"https://pith.science/api/pith-number/37LHOZT53M7XRR644SNLAGTPM6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6/action/storage_attestation","attest_author":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6/action/author_attestation","sign_citation":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6/action/citation_signature","submit_replication":"https://pith.science/pith/37LHOZT53M7XRR644SNLAGTPM6/action/replication_record"}},"created_at":"2026-05-18T01:19:15.391094+00:00","updated_at":"2026-05-18T01:19:15.391094+00:00"}