{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:H7WIPEH46R4LYXXEHPDJDC4625","short_pith_number":"pith:H7WIPEH4","schema_version":"1.0","canonical_sha256":"3fec8790fcf478bc5ee43bc6918b9ed7633123034c0909f4c14b3f9f309d78cd","source":{"kind":"arxiv","id":"1210.2922","version":2},"attestation_state":"computed","paper":{"title":"Decomposition and partial trace of positive matrices with Hermitian blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin","submitted_at":"2012-10-10T13:53:31Z","abstract_excerpt":"Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important inequalities in quantum information theory such as the Nielsen-Kempe separability criterion."},"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":"1210.2922","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-10-10T13:53:31Z","cross_cats_sorted":[],"title_canon_sha256":"5d189a7ec648a2e3bafc30acb189082643a842dc72ffacba79ad98baa173c54d","abstract_canon_sha256":"cf6a714519aaf5c9688282ab419aafaaf86c11ba3a72923b15cb064a051cd1c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:29.260741Z","signature_b64":"5Op96ybc63SbfzIiW9Il5/GugNpFSoTzS5OTlZ+6irQ8YbjhsnFC+oxbJFtouNvjYEOCwblckkarUPnjjUxZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fec8790fcf478bc5ee43bc6918b9ed7633123034c0909f4c14b3f9f309d78cd","last_reissued_at":"2026-05-18T03:43:29.259961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:29.259961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition and partial trace of positive matrices with Hermitian blocks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin","submitted_at":"2012-10-10T13:53:31Z","abstract_excerpt":"Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important inequalities in quantum information theory such as the Nielsen-Kempe separability criterion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2922","kind":"arxiv","version":2},"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":"1210.2922","created_at":"2026-05-18T03:43:29.260076+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2922v2","created_at":"2026-05-18T03:43:29.260076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2922","created_at":"2026-05-18T03:43:29.260076+00:00"},{"alias_kind":"pith_short_12","alias_value":"H7WIPEH46R4L","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"H7WIPEH46R4LYXXE","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"H7WIPEH4","created_at":"2026-05-18T12:27:06.952714+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/H7WIPEH46R4LYXXEHPDJDC4625","json":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625.json","graph_json":"https://pith.science/api/pith-number/H7WIPEH46R4LYXXEHPDJDC4625/graph.json","events_json":"https://pith.science/api/pith-number/H7WIPEH46R4LYXXEHPDJDC4625/events.json","paper":"https://pith.science/paper/H7WIPEH4"},"agent_actions":{"view_html":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625","download_json":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625.json","view_paper":"https://pith.science/paper/H7WIPEH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2922&json=true","fetch_graph":"https://pith.science/api/pith-number/H7WIPEH46R4LYXXEHPDJDC4625/graph.json","fetch_events":"https://pith.science/api/pith-number/H7WIPEH46R4LYXXEHPDJDC4625/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625/action/storage_attestation","attest_author":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625/action/author_attestation","sign_citation":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625/action/citation_signature","submit_replication":"https://pith.science/pith/H7WIPEH46R4LYXXEHPDJDC4625/action/replication_record"}},"created_at":"2026-05-18T03:43:29.260076+00:00","updated_at":"2026-05-18T03:43:29.260076+00:00"}