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For example, for any real number $r \\in \\{1\\} \\cup [2, \\infty)$, positive semi-definite matrices $A_i,\\ B_i,\\ C_i\\in M_{n_i}$, $i=1,2$, and generalized matrix functions $d_\\chi, d_\\xi$ such as the determinant and permanent, etc., we have \\begin{eqnarray*}&&\\left(d_\\chi(A_1+B_1+C_1)d_\\xi(A_2+B_2+C_2)\\right)^r \\\\ &&\\hskip 1in\n  + \\left(d_\\chi(A_1)d_\\xi(A_2)\\right)^r\n  + \\left(d_\\chi(B_1)d_\\xi(B_2)\\right)^r + \\left(d_\\chi(C_1)d_\\xi(C_2)\\right)^r \\\\ & \\ge &\\left(","authors_text":"Chi-Kwong Li, Qing-Wen Wang, Shaowu Huang, Yiu-Tung Poon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:54:08Z","title":"Inequalities on generalized matrix functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06984","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:577cd8be91b2ed0b065ea2ba3289a113fae86216f6860ea0263f9cc19ef5398c","target":"record","created_at":"2026-05-18T01:06:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"94cee0f279af4cb88aa15431bf443b19691e3a4157968cb75e93bc303ca231f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-05-23T11:54:08Z","title_canon_sha256":"2a7a05f8646891d642c11904ca656681789f30b9b37940195e09d878a732ac86"},"schema_version":"1.0","source":{"id":"1605.06984","kind":"arxiv","version":2}},"canonical_sha256":"5e0993b2bd98561ee47ac5bb0605e4024f7019abffe829211ef2c26cc7ad76fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e0993b2bd98561ee47ac5bb0605e4024f7019abffe829211ef2c26cc7ad76fb","first_computed_at":"2026-05-18T01:06:40.614762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:40.614762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EdUANYzP4k0WTF+ARriyjFGug5vPGa0wsd7BtQnyF5EOvvXN9236rWoC34UaFhzKmA6Vmc/pNwItVflrtH+PCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:40.615392Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:577cd8be91b2ed0b065ea2ba3289a113fae86216f6860ea0263f9cc19ef5398c","sha256:60c80bfa8040dd49fb196bcfc48d142d898a028921210930e95e23c24bba70cf"],"state_sha256":"1ff6029f3a2f61dec4be8a4efa7214e4dd7eb1c12e35086f490d96d8411b211f"}