{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:L4MYJKG2V7KFB7ALTDK6A3QDKQ","short_pith_number":"pith:L4MYJKG2","canonical_record":{"source":{"id":"1703.07392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-21T19:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"88fa8c19d9b07d08df70c5e952ead287d029df90576bf98b04168d1099351677","abstract_canon_sha256":"9de792f41a7b3e315efd50f45407a7fa9e8eefbdf5058b3c87fa979cc46b8228"},"schema_version":"1.0"},"canonical_sha256":"5f1984a8daafd450fc0b98d5e06e035436736b74d36c98354a50b9fb3fdfbbe4","source":{"kind":"arxiv","id":"1703.07392","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07392","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07392v1","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07392","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"L4MYJKG2V7KF","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L4MYJKG2V7KFB7AL","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L4MYJKG2","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:L4MYJKG2V7KFB7ALTDK6A3QDKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-21T19:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"88fa8c19d9b07d08df70c5e952ead287d029df90576bf98b04168d1099351677","abstract_canon_sha256":"9de792f41a7b3e315efd50f45407a7fa9e8eefbdf5058b3c87fa979cc46b8228"},"schema_version":"1.0"},"canonical_sha256":"5f1984a8daafd450fc0b98d5e06e035436736b74d36c98354a50b9fb3fdfbbe4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:08.919770Z","signature_b64":"vJukwODTHDMCeUugS+EFI4JJODK1BoPPmmaeDypTIJdu9UCkAwZ5+wvwH1QdLlI76iMhOFHAPiCe3U+jIbvSBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f1984a8daafd450fc0b98d5e06e035436736b74d36c98354a50b9fb3fdfbbe4","last_reissued_at":"2026-05-18T00:48:08.919202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:08.919202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07392","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":"2026-05-18T00:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LSam6vJ84x89/XOg5LHuE2Yo21NGIeKA2JamUCwf8mp7Ea87ViML4SfdtV1zsyhX69lsFjWCo67o4Rnv/j/BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:32:21.885964Z"},"content_sha256":"b6c5233ccbf8d0e3b5de5dd78b4f9f3a3868b25132620131a3d6643887c520e5","schema_version":"1.0","event_id":"sha256:b6c5233ccbf8d0e3b5de5dd78b4f9f3a3868b25132620131a3d6643887c520e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:L4MYJKG2V7KFB7ALTDK6A3QDKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Further generalizations, refinements, and reverses of the Young and Heinz inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fuad Kittaneh, Yousef Al-Manasrah","submitted_at":"2017-03-21T19:05:36Z","abstract_excerpt":"In this paper, we give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars. Applications to unitarily invariant norm inequalities involving positive semidefinite matrices are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07392","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":"2026-05-18T00:48:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Rsl10KFsx8hrrdhKgueb64R8W0dQ6bnwfXogp1pGV2aA8MwsL4gKmbDOMSifVx1x9BMNLkr6CoK52AEOYJ4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T11:32:21.886301Z"},"content_sha256":"1cd65f6b779dcf89ab452620156b7e3ad8b8ddc4bfd55a2275458b73b9189431","schema_version":"1.0","event_id":"sha256:1cd65f6b779dcf89ab452620156b7e3ad8b8ddc4bfd55a2275458b73b9189431"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/bundle.json","state_url":"https://pith.science/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/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":"2026-06-08T11:32:21Z","links":{"resolver":"https://pith.science/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ","bundle":"https://pith.science/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/bundle.json","state":"https://pith.science/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4MYJKG2V7KFB7ALTDK6A3QDKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L4MYJKG2V7KFB7ALTDK6A3QDKQ","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":"9de792f41a7b3e315efd50f45407a7fa9e8eefbdf5058b3c87fa979cc46b8228","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-21T19:05:36Z","title_canon_sha256":"88fa8c19d9b07d08df70c5e952ead287d029df90576bf98b04168d1099351677"},"schema_version":"1.0","source":{"id":"1703.07392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07392","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07392v1","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07392","created_at":"2026-05-18T00:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"L4MYJKG2V7KF","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L4MYJKG2V7KFB7AL","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L4MYJKG2","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:1cd65f6b779dcf89ab452620156b7e3ad8b8ddc4bfd55a2275458b73b9189431","target":"graph","created_at":"2026-05-18T00:48:08Z","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 give a new inequality for convex functions of real variables, and we apply this inequality to obtain considerable generalizations, refinements, and reverses of the Young and Heinz inequalities for positive scalars. Applications to unitarily invariant norm inequalities involving positive semidefinite matrices are also given.","authors_text":"Fuad Kittaneh, Yousef Al-Manasrah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-21T19:05:36Z","title":"Further generalizations, refinements, and reverses of the Young and Heinz inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07392","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:b6c5233ccbf8d0e3b5de5dd78b4f9f3a3868b25132620131a3d6643887c520e5","target":"record","created_at":"2026-05-18T00:48:08Z","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":"9de792f41a7b3e315efd50f45407a7fa9e8eefbdf5058b3c87fa979cc46b8228","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-21T19:05:36Z","title_canon_sha256":"88fa8c19d9b07d08df70c5e952ead287d029df90576bf98b04168d1099351677"},"schema_version":"1.0","source":{"id":"1703.07392","kind":"arxiv","version":1}},"canonical_sha256":"5f1984a8daafd450fc0b98d5e06e035436736b74d36c98354a50b9fb3fdfbbe4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f1984a8daafd450fc0b98d5e06e035436736b74d36c98354a50b9fb3fdfbbe4","first_computed_at":"2026-05-18T00:48:08.919202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:08.919202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vJukwODTHDMCeUugS+EFI4JJODK1BoPPmmaeDypTIJdu9UCkAwZ5+wvwH1QdLlI76iMhOFHAPiCe3U+jIbvSBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:08.919770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6c5233ccbf8d0e3b5de5dd78b4f9f3a3868b25132620131a3d6643887c520e5","sha256:1cd65f6b779dcf89ab452620156b7e3ad8b8ddc4bfd55a2275458b73b9189431"],"state_sha256":"cef44522f1732145c8844a70f623a82997086a291e4710939c441aec6e0c14db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KcLV2evLSlxNQMBseXX9wSpFmEgir+HQfX/MhDBsT7xXdBbVzwgCKK5eT6qv7QrlX2VyrdJENgBTeB91+V4zAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T11:32:21.888152Z","bundle_sha256":"2fca03b84cd7bcf9541e45ede68e901575787e554f68ed21e5b209407c3cd435"}}