{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KNR3P7L3CWKWYSRUAZHIMPDJJO","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":"eeeb04bff88da365fbd02cdf7abdfc0b300c02d50822f11f8dd4b1448a5dd965","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-27T14:03:15Z","title_canon_sha256":"846a0570075e14bdcd6ae237247e82b092bddce5f41f0e071e7d33ff699cd755"},"schema_version":"1.0","source":{"id":"0911.5267","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.5267","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"arxiv_version","alias_value":"0911.5267v5","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5267","created_at":"2026-05-18T02:30:48Z"},{"alias_kind":"pith_short_12","alias_value":"KNR3P7L3CWKW","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KNR3P7L3CWKWYSRU","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KNR3P7L3","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:978927a98b8062616341e02cff49b2788db93dfb7b5e8c9cc515e4dcb8eb047c","target":"graph","created_at":"2026-05-18T02:30:48Z","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 study operator log-convex functions on $(0,\\infty)$, and prove that a continuous nonnegative function on $(0,\\infty)$ is operator log-convex if and only if it is operator monotone decreasing. Several equivalent conditions related to operator means are given for such functions. Operator log-concave functions are also discussed.","authors_text":"Fumio Hiai, Tsuyoshi Ando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-27T14:03:15Z","title":"Operator log-convex functions and operator means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5267","kind":"arxiv","version":5},"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":"sha256:55514aada5dfb2bd1483c618103185e338c16eb7937e6ab895d0ffe53ae1c691","target":"record","created_at":"2026-05-18T02:30:48Z","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":"eeeb04bff88da365fbd02cdf7abdfc0b300c02d50822f11f8dd4b1448a5dd965","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-11-27T14:03:15Z","title_canon_sha256":"846a0570075e14bdcd6ae237247e82b092bddce5f41f0e071e7d33ff699cd755"},"schema_version":"1.0","source":{"id":"0911.5267","kind":"arxiv","version":5}},"canonical_sha256":"5363b7fd7b15956c4a34064e863c694ba06fff8b30aa1bb7269cae91476b9e6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5363b7fd7b15956c4a34064e863c694ba06fff8b30aa1bb7269cae91476b9e6a","first_computed_at":"2026-05-18T02:30:48.134840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:48.134840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jSGAsFYa7veZ/okFHxUVzXhmOhjR5A8cSR2lRBANU/U/MtRSp0sTsVE7qL8Xod1JcAm4prR3CmxnXgSNSzywDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:48.135300Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.5267","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55514aada5dfb2bd1483c618103185e338c16eb7937e6ab895d0ffe53ae1c691","sha256:978927a98b8062616341e02cff49b2788db93dfb7b5e8c9cc515e4dcb8eb047c"],"state_sha256":"16c4093202b7cf81678ff9b055df8860951833b6dfeeb8771c416427be95fa4e"}