{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XSMBBLH6NAQYYRIS4KERZ57TJ7","short_pith_number":"pith:XSMBBLH6","canonical_record":{"source":{"id":"1405.4688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-19T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3113cf1ac6dcf07907edee19b340736351ec106d821a98c04a468e7ccea812a7","abstract_canon_sha256":"16c1ec170f0c2b70bc90cec98cfc811c6c4fd1babcfaa6e1490ac6aae6840f23"},"schema_version":"1.0"},"canonical_sha256":"bc9810acfe68218c4512e2891cf7f34feacc7fbac2b1960386b980ea9fcd02ad","source":{"kind":"arxiv","id":"1405.4688","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4688","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4688v2","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4688","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"XSMBBLH6NAQY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XSMBBLH6NAQYYRIS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XSMBBLH6","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XSMBBLH6NAQYYRIS4KERZ57TJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4688","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-19T12:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"3113cf1ac6dcf07907edee19b340736351ec106d821a98c04a468e7ccea812a7","abstract_canon_sha256":"16c1ec170f0c2b70bc90cec98cfc811c6c4fd1babcfaa6e1490ac6aae6840f23"},"schema_version":"1.0"},"canonical_sha256":"bc9810acfe68218c4512e2891cf7f34feacc7fbac2b1960386b980ea9fcd02ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:22.498597Z","signature_b64":"DJO0JGwkCCtGb6CLy2dBLuHbUJdzmc1zCSKr2urbxq8TQE/Uhege28oD3Fi5Ag9LOFUN9f67HG9tQmcaWaxIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc9810acfe68218c4512e2891cf7f34feacc7fbac2b1960386b980ea9fcd02ad","last_reissued_at":"2026-05-18T02:50:22.497980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:22.497980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4688","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/WiqHOM3IoK+zlimrfyN2XQR4mQ3eHi55h9/NPpFx8ntTWSa0dFUM438pCvoXkukeoT5sA7PmOmQ1cu4NSfzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:09:06.928542Z"},"content_sha256":"7885053fac97f7ddfcb50cbf33af0da04f8b82f901fb7477d271377d07d73c0e","schema_version":"1.0","event_id":"sha256:7885053fac97f7ddfcb50cbf33af0da04f8b82f901fb7477d271377d07d73c0e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XSMBBLH6NAQYYRIS4KERZ57TJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some operator convex functions of several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Zhihua Zhang","submitted_at":"2014-05-19T12:00:00Z","abstract_excerpt":"We obtain operator concavity (convexity) of some functions of two or three variables by using perspectives of regular operator mappings of one or several variables. As an application, we obtain, for $ 0<p < 1,$ concavity, respectively convexity, of the Frech\\'{e}t differential mapping associated with the functions $t \\to t^{1+p} $ and $t \\to t^{1-p}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4688","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:50:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbAHpuhHOIv8vWIRVHl2kDyN5v2G9E1E0EKSnjLtNrhC0SXsfkYnjVDnSLsU9cW+z67smPunsfocLlNlE0vqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:09:06.929177Z"},"content_sha256":"7bd6ad43922979aadfc6ddbbb936794887095411259d24e1ee84017ac4f8b420","schema_version":"1.0","event_id":"sha256:7bd6ad43922979aadfc6ddbbb936794887095411259d24e1ee84017ac4f8b420"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/bundle.json","state_url":"https://pith.science/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-12T00:09:06Z","links":{"resolver":"https://pith.science/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7","bundle":"https://pith.science/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/bundle.json","state":"https://pith.science/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSMBBLH6NAQYYRIS4KERZ57TJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XSMBBLH6NAQYYRIS4KERZ57TJ7","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":"16c1ec170f0c2b70bc90cec98cfc811c6c4fd1babcfaa6e1490ac6aae6840f23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-19T12:00:00Z","title_canon_sha256":"3113cf1ac6dcf07907edee19b340736351ec106d821a98c04a468e7ccea812a7"},"schema_version":"1.0","source":{"id":"1405.4688","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4688","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4688v2","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4688","created_at":"2026-05-18T02:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"XSMBBLH6NAQY","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XSMBBLH6NAQYYRIS","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XSMBBLH6","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:7bd6ad43922979aadfc6ddbbb936794887095411259d24e1ee84017ac4f8b420","target":"graph","created_at":"2026-05-18T02:50:22Z","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 obtain operator concavity (convexity) of some functions of two or three variables by using perspectives of regular operator mappings of one or several variables. As an application, we obtain, for $ 0<p < 1,$ concavity, respectively convexity, of the Frech\\'{e}t differential mapping associated with the functions $t \\to t^{1+p} $ and $t \\to t^{1-p}.$","authors_text":"Zhihua Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-19T12:00:00Z","title":"Some operator convex functions of several variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4688","kind":"arxiv","version":2},"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":"sha256:7885053fac97f7ddfcb50cbf33af0da04f8b82f901fb7477d271377d07d73c0e","target":"record","created_at":"2026-05-18T02:50:22Z","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":"16c1ec170f0c2b70bc90cec98cfc811c6c4fd1babcfaa6e1490ac6aae6840f23","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-05-19T12:00:00Z","title_canon_sha256":"3113cf1ac6dcf07907edee19b340736351ec106d821a98c04a468e7ccea812a7"},"schema_version":"1.0","source":{"id":"1405.4688","kind":"arxiv","version":2}},"canonical_sha256":"bc9810acfe68218c4512e2891cf7f34feacc7fbac2b1960386b980ea9fcd02ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc9810acfe68218c4512e2891cf7f34feacc7fbac2b1960386b980ea9fcd02ad","first_computed_at":"2026-05-18T02:50:22.497980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:22.497980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJO0JGwkCCtGb6CLy2dBLuHbUJdzmc1zCSKr2urbxq8TQE/Uhege28oD3Fi5Ag9LOFUN9f67HG9tQmcaWaxIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:22.498597Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4688","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7885053fac97f7ddfcb50cbf33af0da04f8b82f901fb7477d271377d07d73c0e","sha256:7bd6ad43922979aadfc6ddbbb936794887095411259d24e1ee84017ac4f8b420"],"state_sha256":"331249a8ed9f5392b5f6377985761cb92dfd6df7491e2ded15412043e173d57c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nphYicziPdJ4tbUWCnXxYaRlS15BvGhsm6jPZC6u7+HxYm8XcwXHXdupxZ3FpWE+AChhOcftfI6cc1Kfu7dYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:09:06.932570Z","bundle_sha256":"df70a71d7f54e1f707f01a81a1d99e97e2963c3d2f5d691d34be49ab78ae7120"}}