{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YTAYYFGI2IMR4OVDMT5ELXWWSC","short_pith_number":"pith:YTAYYFGI","schema_version":"1.0","canonical_sha256":"c4c18c14c8d2191e3aa364fa45ded6908309d2b106a1c0d2991eb370840c68c8","source":{"kind":"arxiv","id":"1208.6494","version":3},"attestation_state":"computed","paper":{"title":"Positive definite matrices with Hermitian blocks and their partial traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin, Minghua Lin","submitted_at":"2012-08-31T13:41:27Z","abstract_excerpt":"Let $H$ be a positive semi-definite matrix partitioned in $\\beta\\times \\beta$ Hermitian blocks,  $H=[A_{s,t}]$, $1\\le s,t,\\le \\beta$.  Then, for all symmetric  norms,\n{equation*}\n\\| H \\| \\le \\| \\sum_{s=1}^{\\beta} A_{s,s} \\|.\n{equation*}\nThe proof uses a nice decomposition   for positive   matrices   and unitary congruences with the generators of a Clifford algebra.   A few corollaries are given, in particular the partial trace operation increases norms of separable states on a real Hilbert space, leading to a  conjecture for  usual complex Hilbert spaces."},"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":"1208.6494","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-08-31T13:41:27Z","cross_cats_sorted":[],"title_canon_sha256":"d5ebe9a03de0277ca706002fb405a1f8fb2cbdb7b0c05ea07e0009bdb9600afc","abstract_canon_sha256":"4445f60741f31a5f264260082169009f6b7be7732603b805171ab715d9be374c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:54.913246Z","signature_b64":"DOYenn3QVMtGwAfy92NHWdi3nD7CMXJ8kcqQCnyqOTusSU77UPSFqVZN8p0mo9AGeBOTjli0CKyxqYgNLmYRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4c18c14c8d2191e3aa364fa45ded6908309d2b106a1c0d2991eb370840c68c8","last_reissued_at":"2026-05-18T03:45:54.912783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:54.912783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Positive definite matrices with Hermitian blocks and their partial traces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eun-Young Lee, Jean-Christophe Bourin, Minghua Lin","submitted_at":"2012-08-31T13:41:27Z","abstract_excerpt":"Let $H$ be a positive semi-definite matrix partitioned in $\\beta\\times \\beta$ Hermitian blocks,  $H=[A_{s,t}]$, $1\\le s,t,\\le \\beta$.  Then, for all symmetric  norms,\n{equation*}\n\\| H \\| \\le \\| \\sum_{s=1}^{\\beta} A_{s,s} \\|.\n{equation*}\nThe proof uses a nice decomposition   for positive   matrices   and unitary congruences with the generators of a Clifford algebra.   A few corollaries are given, in particular the partial trace operation increases norms of separable states on a real Hilbert space, leading to a  conjecture for  usual complex Hilbert spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6494","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":"1208.6494","created_at":"2026-05-18T03:45:54.912852+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.6494v3","created_at":"2026-05-18T03:45:54.912852+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6494","created_at":"2026-05-18T03:45:54.912852+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTAYYFGI2IMR","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTAYYFGI2IMR4OVD","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTAYYFGI","created_at":"2026-05-18T12:27:30.460161+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/YTAYYFGI2IMR4OVDMT5ELXWWSC","json":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC.json","graph_json":"https://pith.science/api/pith-number/YTAYYFGI2IMR4OVDMT5ELXWWSC/graph.json","events_json":"https://pith.science/api/pith-number/YTAYYFGI2IMR4OVDMT5ELXWWSC/events.json","paper":"https://pith.science/paper/YTAYYFGI"},"agent_actions":{"view_html":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC","download_json":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC.json","view_paper":"https://pith.science/paper/YTAYYFGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.6494&json=true","fetch_graph":"https://pith.science/api/pith-number/YTAYYFGI2IMR4OVDMT5ELXWWSC/graph.json","fetch_events":"https://pith.science/api/pith-number/YTAYYFGI2IMR4OVDMT5ELXWWSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC/action/storage_attestation","attest_author":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC/action/author_attestation","sign_citation":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC/action/citation_signature","submit_replication":"https://pith.science/pith/YTAYYFGI2IMR4OVDMT5ELXWWSC/action/replication_record"}},"created_at":"2026-05-18T03:45:54.912852+00:00","updated_at":"2026-05-18T03:45:54.912852+00:00"}