{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FLLYEEJKQRAE7LIRSRCRLTNGIO","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":"07b9197b902ce41485cced136ab207e48157a795c0eccb6846c154e96e5085b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-23T09:30:23Z","title_canon_sha256":"04053c988c6e34cd3b5056268a5b71d86b027bcb51b9fa86faaf1414aa9cb05c"},"schema_version":"1.0","source":{"id":"1506.06922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.06922","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1506.06922v1","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.06922","created_at":"2026-05-18T01:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"FLLYEEJKQRAE","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FLLYEEJKQRAE7LIR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FLLYEEJK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:7326fda846f9003be2c33a2107ba973acdca9f19de44428c7c9c7dfaac3b0921","target":"graph","created_at":"2026-05-18T01:40:55Z","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 prove that a continuous function $f:(0,\\infty) \\to (0,\\infty)$ is operator monotone increasing if and only if $f(A \\: !_t \\: B) \\leqs f(A) \\: !_t \\: f(B)$ for any positive operators $A,B$ and scalar $t \\in [0,1]$. Here, $!_t$ denotes the $t$-weighted harmonic mean. As a counterpart, $f$ is operator monotone decreasing if and only if the reverse of preceding inequality holds. Moreover, we obtain many characterizations of operator-monotone increasingness/decreasingness in terms of operator means. These characterizations lead to many operator inequalities involving means.","authors_text":"Pattrawut Chansangiam","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-23T09:30:23Z","title":"Characterizations of Operator Monotonicity via Operator Means and Applications to Operator Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06922","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:d2583a3b7ea65e8dec271f4904899dc903d058985c10e6deb61c5816e3cbc8f5","target":"record","created_at":"2026-05-18T01:40:55Z","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":"07b9197b902ce41485cced136ab207e48157a795c0eccb6846c154e96e5085b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-23T09:30:23Z","title_canon_sha256":"04053c988c6e34cd3b5056268a5b71d86b027bcb51b9fa86faaf1414aa9cb05c"},"schema_version":"1.0","source":{"id":"1506.06922","kind":"arxiv","version":1}},"canonical_sha256":"2ad782112a84404fad11944515cda6438e9189030f79c5e3c15a3c15cafabed9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ad782112a84404fad11944515cda6438e9189030f79c5e3c15a3c15cafabed9","first_computed_at":"2026-05-18T01:40:55.570847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:55.570847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8U/V+pH/7K0XgypYcRvuA2lTQEfiJ0x5dX5CFSoJBBbKSZLzQy0kppelT8m5bTubmdZZFDHkxAIUgU4fJzzTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:55.571505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.06922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2583a3b7ea65e8dec271f4904899dc903d058985c10e6deb61c5816e3cbc8f5","sha256:7326fda846f9003be2c33a2107ba973acdca9f19de44428c7c9c7dfaac3b0921"],"state_sha256":"9a1d1dc2949a825c5d2f85adaa2960cab1478226f11c149b479e04b0cc672d6c"}