{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BQFOELW7ALX7HZRBDKXBETHSCE","short_pith_number":"pith:BQFOELW7","canonical_record":{"source":{"id":"1211.2337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-10T17:47:23Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"8e1823863cbb7ada60ba1487a294ac1de1f7d502f96593f026a318f892a41988","abstract_canon_sha256":"777da2f40c652e02d421cbcc5b0dfbe25390f87dc475a9a4660aed7c508be174"},"schema_version":"1.0"},"canonical_sha256":"0c0ae22edf02eff3e6211aae124cf21139399876685813c3320ea79b9edb8e7b","source":{"kind":"arxiv","id":"1211.2337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2337","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2337v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2337","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"BQFOELW7ALX7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BQFOELW7ALX7HZRB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BQFOELW7","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BQFOELW7ALX7HZRBDKXBETHSCE","target":"record","payload":{"canonical_record":{"source":{"id":"1211.2337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-10T17:47:23Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"8e1823863cbb7ada60ba1487a294ac1de1f7d502f96593f026a318f892a41988","abstract_canon_sha256":"777da2f40c652e02d421cbcc5b0dfbe25390f87dc475a9a4660aed7c508be174"},"schema_version":"1.0"},"canonical_sha256":"0c0ae22edf02eff3e6211aae124cf21139399876685813c3320ea79b9edb8e7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:53.285625Z","signature_b64":"U/8mJzQv9zuH9WYnwo49djThaftvAcuRR/IRYJl7s+H2pGI0MlnEZgRFDosCVZarH7gvr47ZCBHO8xgutthDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c0ae22edf02eff3e6211aae124cf21139399876685813c3320ea79b9edb8e7b","last_reissued_at":"2026-05-18T02:38:53.285210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:53.285210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.2337","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9upHErk2HH9pGz1jaL81PGqQmbiaYkMVQ2nIa2EniHjvmrLzKogIXsnkeNVDflGC5NPU6bgtFYabxrF2N7kAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:50:20.450087Z"},"content_sha256":"de1557db478d7377ff2b99cb53740453abc765ba9d2e7978bc7c632340f52a42","schema_version":"1.0","event_id":"sha256:de1557db478d7377ff2b99cb53740453abc765ba9d2e7978bc7c632340f52a42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BQFOELW7ALX7HZRBDKXBETHSCE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator inequalities related to weak 2-positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Jun Ichi Fujii, Mohammad Sal Moslehian","submitted_at":"2012-11-10T17:47:23Z","abstract_excerpt":"In this paper we introduce the notion of weak 2-positivity and present some examples. We establish some operator Cauchy--Schwarz inequalities involving the geometric mean and give some applications. In particular, we present some operator versions of Hua's inequality by using the Choi--Davis--Jensen inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2337","kind":"arxiv","version":1},"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":"2026-05-18T02:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obMQ9LK7YU/pJ7raEy3CYIIF/+vVQd1hBjkp+YggUaQ3ODRTjcKSSGjGoWyHsjDS69j2WEUNZFqIIzeb9uVUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:50:20.450486Z"},"content_sha256":"df47b9513de5449d162f7616dfa8963c8980a9d3817d99999962d8133be1b1ee","schema_version":"1.0","event_id":"sha256:df47b9513de5449d162f7616dfa8963c8980a9d3817d99999962d8133be1b1ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQFOELW7ALX7HZRBDKXBETHSCE/bundle.json","state_url":"https://pith.science/pith/BQFOELW7ALX7HZRBDKXBETHSCE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQFOELW7ALX7HZRBDKXBETHSCE/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":"2026-06-08T01:50:20Z","links":{"resolver":"https://pith.science/pith/BQFOELW7ALX7HZRBDKXBETHSCE","bundle":"https://pith.science/pith/BQFOELW7ALX7HZRBDKXBETHSCE/bundle.json","state":"https://pith.science/pith/BQFOELW7ALX7HZRBDKXBETHSCE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQFOELW7ALX7HZRBDKXBETHSCE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BQFOELW7ALX7HZRBDKXBETHSCE","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":"777da2f40c652e02d421cbcc5b0dfbe25390f87dc475a9a4660aed7c508be174","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-10T17:47:23Z","title_canon_sha256":"8e1823863cbb7ada60ba1487a294ac1de1f7d502f96593f026a318f892a41988"},"schema_version":"1.0","source":{"id":"1211.2337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.2337","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.2337v1","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.2337","created_at":"2026-05-18T02:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"BQFOELW7ALX7","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BQFOELW7ALX7HZRB","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BQFOELW7","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:df47b9513de5449d162f7616dfa8963c8980a9d3817d99999962d8133be1b1ee","target":"graph","created_at":"2026-05-18T02:38:53Z","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":"In this paper we introduce the notion of weak 2-positivity and present some examples. We establish some operator Cauchy--Schwarz inequalities involving the geometric mean and give some applications. In particular, we present some operator versions of Hua's inequality by using the Choi--Davis--Jensen inequality.","authors_text":"Jun Ichi Fujii, Mohammad Sal Moslehian","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-10T17:47:23Z","title":"Operator inequalities related to weak 2-positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.2337","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:de1557db478d7377ff2b99cb53740453abc765ba9d2e7978bc7c632340f52a42","target":"record","created_at":"2026-05-18T02:38:53Z","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":"777da2f40c652e02d421cbcc5b0dfbe25390f87dc475a9a4660aed7c508be174","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-10T17:47:23Z","title_canon_sha256":"8e1823863cbb7ada60ba1487a294ac1de1f7d502f96593f026a318f892a41988"},"schema_version":"1.0","source":{"id":"1211.2337","kind":"arxiv","version":1}},"canonical_sha256":"0c0ae22edf02eff3e6211aae124cf21139399876685813c3320ea79b9edb8e7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c0ae22edf02eff3e6211aae124cf21139399876685813c3320ea79b9edb8e7b","first_computed_at":"2026-05-18T02:38:53.285210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:53.285210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U/8mJzQv9zuH9WYnwo49djThaftvAcuRR/IRYJl7s+H2pGI0MlnEZgRFDosCVZarH7gvr47ZCBHO8xgutthDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:53.285625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.2337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de1557db478d7377ff2b99cb53740453abc765ba9d2e7978bc7c632340f52a42","sha256:df47b9513de5449d162f7616dfa8963c8980a9d3817d99999962d8133be1b1ee"],"state_sha256":"6196aee89a34737379f2201fda4dfe9a3d8719052033d6d68aa77c53638bd4b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RnmVOfmZryfg+9QP/uIKPakZHWimpOr09B19f5JhuUeK+agUokJY0uPNacSOfEICHjpJUZ4GiHh3rVuLF15wDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:50:20.453034Z","bundle_sha256":"ddc41f58acf7c9678fd3921c2762b8b4a8e615416212201ffe94ccca006c088b"}}