{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VNUCI4L4PKY3ZMFOHFTIKJSE52","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":"a4292b7513571afc42dd2fcd187e16937bde7f0afabc7bf3081308092df4fceb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-20T02:48:24Z","title_canon_sha256":"8b0a4cdb7eb217a4d8329a02e5e2edcc02f66b540c7943536651b49d43ac5bb8"},"schema_version":"1.0","source":{"id":"1410.5143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5143","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5143v1","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5143","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"pith_short_12","alias_value":"VNUCI4L4PKY3","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VNUCI4L4PKY3ZMFO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VNUCI4L4","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:ad5d5b2c1d9a5c3796cea162ad5afe305df674fcf3b1b2928cfc55fb0c09aab2","target":"graph","created_at":"2026-05-18T02:39:46Z","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":"Let $T=\\begin{bmatrix} X &Y\\\\ 0 & Z\\end{bmatrix}$ be an $n$-square matrix, where $X, Z$ are $r$-square and $(n-r)$-square, respectively. Among other determinantal inequalities, it is proved $\\det(I_n+T^*T)\\ge \\det(I_r+X^*X)\\cdot \\det(I_{n-r}+Z^*Z)$ with equality holds if and only if $Y=0$.","authors_text":"Minghua Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-20T02:48:24Z","title":"Determinantal inequalities for block triangular matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5143","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":"sha256:8b0455796fe8c46ea02da8c7c0d7af681a9d230f4f04204a64d1bbf24ccf60c3","target":"record","created_at":"2026-05-18T02:39:46Z","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":"a4292b7513571afc42dd2fcd187e16937bde7f0afabc7bf3081308092df4fceb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-20T02:48:24Z","title_canon_sha256":"8b0a4cdb7eb217a4d8329a02e5e2edcc02f66b540c7943536651b49d43ac5bb8"},"schema_version":"1.0","source":{"id":"1410.5143","kind":"arxiv","version":1}},"canonical_sha256":"ab6824717c7ab1bcb0ae3966852644ee93862876aec92509c51905656b8087b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab6824717c7ab1bcb0ae3966852644ee93862876aec92509c51905656b8087b4","first_computed_at":"2026-05-18T02:39:46.769827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:46.769827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ngtRVHXfGe1WJYcvMSUq8U/4Uf4GoVWfWMwgxLXqCKtI2H5ce6uqG/79om3rdZISJ717vtDn9vUB1l7vFdoTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:46.770436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b0455796fe8c46ea02da8c7c0d7af681a9d230f4f04204a64d1bbf24ccf60c3","sha256:ad5d5b2c1d9a5c3796cea162ad5afe305df674fcf3b1b2928cfc55fb0c09aab2"],"state_sha256":"45cdf7729b6efe70ff7613f6ce1322766d9093d6e8eccd5568277770b313898a"}