{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OZ7CZFE7NLE7LGCALPTDOG52JB","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":"ba3cafefa47ca61472ac112e94c1034a35aba9457342edf3aeca3be02e14467e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-28T15:50:36Z","title_canon_sha256":"9f4866f3e90998dc51cc1a76ced0272a5a87a516b58ba1e9d21f967703be9815"},"schema_version":"1.0","source":{"id":"1311.7343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7343","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7343v1","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7343","created_at":"2026-05-18T03:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"OZ7CZFE7NLE7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OZ7CZFE7NLE7LGCA","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OZ7CZFE7","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:600026322d4e088355b27bfe0c49b3a0e04880e7ea3ea1b9aa1c380a50815ba3","target":"graph","created_at":"2026-05-18T03:05:56Z","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":"We give two different definitions of what it means for a matrix-valued function to be log concave, guided by similar notions in complex differential geometry. After discussing a few simple examples, we proceed to develop some of the basic properties associated with these new concepts. Finally, we prove a matrix-valued Pr\\'ekopa theorem using a weighted, vector-valued Paley-Wiener theorem, and positivity properties of direct image bundles.","authors_text":"Hossein Raufi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-28T15:50:36Z","title":"Log concavity for matrix-valued functions and a matrix-valued Pr\\'ekopa theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7343","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":"sha256:2847f8b955c1675307aa5b4232ce3ac78c11b56b7ff0421d6839a88541af469c","target":"record","created_at":"2026-05-18T03:05:56Z","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":"ba3cafefa47ca61472ac112e94c1034a35aba9457342edf3aeca3be02e14467e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-11-28T15:50:36Z","title_canon_sha256":"9f4866f3e90998dc51cc1a76ced0272a5a87a516b58ba1e9d21f967703be9815"},"schema_version":"1.0","source":{"id":"1311.7343","kind":"arxiv","version":1}},"canonical_sha256":"767e2c949f6ac9f598405be6371bba484b4146f12bd94fbec21a2ea0991e37c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"767e2c949f6ac9f598405be6371bba484b4146f12bd94fbec21a2ea0991e37c8","first_computed_at":"2026-05-18T03:05:56.557004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:56.557004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9iPPzgbWPGR9e7oehs3O0GskEiC6HirFpPSoEX8SerJXiAHIAUhQwU23gjZlMbcv0vdw81XFYoEsZ0jcp2LaDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:56.557568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2847f8b955c1675307aa5b4232ce3ac78c11b56b7ff0421d6839a88541af469c","sha256:600026322d4e088355b27bfe0c49b3a0e04880e7ea3ea1b9aa1c380a50815ba3"],"state_sha256":"ecc4625164837912830a17305192f06bae6c41e02ec2991377397bbe2f235b80"}