{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VLRQK255CWVXSNCMCYHL4XGCT2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"86ff03f1f83b6d0a871c150824696fcdb4128c175ee232f9f1e1e83712cb0e47","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-04-08T00:04:52Z","title_canon_sha256":"c3dad1405c68ff38708bc64ecd6d14425127ef866e4821de59c13a925367106a"},"schema_version":"1.0","source":{"id":"1604.04141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.04141","created_at":"2026-05-18T01:17:06Z"},{"alias_kind":"arxiv_version","alias_value":"1604.04141v1","created_at":"2026-05-18T01:17:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.04141","created_at":"2026-05-18T01:17:06Z"},{"alias_kind":"pith_short_12","alias_value":"VLRQK255CWVX","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VLRQK255CWVXSNCM","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VLRQK255","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:e1bcc30f6ea24fe6168a394d7df688232367ee3c77203aad3e8e1772b7d292a1","target":"graph","created_at":"2026-05-18T01:17:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In comparing geodesics induced by different metrics, Audenaert formulated the following determinantal inequality\n  $$\\det(A^2+|BA|)\\le \\det(A^2+AB),$$ where $A, B$ are $n\\times n$ positive semidefinite matrices. We complement his result by proving\n  $$\\det(A^2+|AB|)\\ge \\det(A^2+AB).$$ Our proofs feature the fruitful interplay between determinantal inequalities and majorization relations. Some related questions are mentioned.","authors_text":"Minghua Lin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-04-08T00:04:52Z","title":"On a determinantal inequality arising from diffusion tensor imaging"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04141","kind":"arxiv","version":1},"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":"sha256:0ce6405449087bc3217ba03276e13266220ea8b0234f29193b6d489f85c20f75","target":"record","created_at":"2026-05-18T01:17:06Z","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":"86ff03f1f83b6d0a871c150824696fcdb4128c175ee232f9f1e1e83712cb0e47","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-04-08T00:04:52Z","title_canon_sha256":"c3dad1405c68ff38708bc64ecd6d14425127ef866e4821de59c13a925367106a"},"schema_version":"1.0","source":{"id":"1604.04141","kind":"arxiv","version":1}},"canonical_sha256":"aae3056bbd15ab79344c160ebe5cc29e828745e4aef2f5724c7610eba9cbc838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aae3056bbd15ab79344c160ebe5cc29e828745e4aef2f5724c7610eba9cbc838","first_computed_at":"2026-05-18T01:17:06.512160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:06.512160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZCALgrS1oE/kM2KXBFe4lBoUfnfFIWZiXmmsoIW4irU4K85+INQvrQPW1AMQOUkB4n/siyRT0BNhv2gQkvXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:06.512863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.04141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ce6405449087bc3217ba03276e13266220ea8b0234f29193b6d489f85c20f75","sha256:e1bcc30f6ea24fe6168a394d7df688232367ee3c77203aad3e8e1772b7d292a1"],"state_sha256":"393223bdde586b03242c49e98a1b35553144acff56b90aab08919364c9c2130c"}