{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DJNQFYI2ZHSEMMB4WYX6HJYDSW","short_pith_number":"pith:DJNQFYI2","canonical_record":{"source":{"id":"1512.04585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-11T16:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"be4c32bab1a92e4b6522b38eca4231e00306737fb69332b57ceea74077d8edbf","abstract_canon_sha256":"c5a0af410a7dc24e2a2c4be51c6e3ed727463a653ef461e2a0ee7b0b3135551b"},"schema_version":"1.0"},"canonical_sha256":"1a5b02e11ac9e446303cb62fe3a703959e60858c3dcdc77c0a979a488b6385dd","source":{"kind":"arxiv","id":"1512.04585","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04585","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04585v1","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04585","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"DJNQFYI2ZHSE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DJNQFYI2ZHSEMMB4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DJNQFYI2","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DJNQFYI2ZHSEMMB4WYX6HJYDSW","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04585","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-11T16:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"be4c32bab1a92e4b6522b38eca4231e00306737fb69332b57ceea74077d8edbf","abstract_canon_sha256":"c5a0af410a7dc24e2a2c4be51c6e3ed727463a653ef461e2a0ee7b0b3135551b"},"schema_version":"1.0"},"canonical_sha256":"1a5b02e11ac9e446303cb62fe3a703959e60858c3dcdc77c0a979a488b6385dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:19.833125Z","signature_b64":"2EHfTMnAPIsxQYxS4os12i4FYR3x8kB0+GKPM+1UMGGc5wwSSqNBWfnJH6m5bswyD4HRh08iOH8iVgMZIFCBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a5b02e11ac9e446303cb62fe3a703959e60858c3dcdc77c0a979a488b6385dd","last_reissued_at":"2026-05-18T01:24:19.832765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:19.832765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04585","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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8d7XI2mutp3Dgx/yBRQHi12P64HEsqXi3GU/eGwtFr0/mQVmAf3TPQX6xNci1NDPJ64l+DpbcouzqA4S9eV1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:14:11.512056Z"},"content_sha256":"1d230e6ebb82949a392f877b01e961f03da28c538ccf4eb3b0093eb30a67c708","schema_version":"1.0","event_id":"sha256:1d230e6ebb82949a392f877b01e961f03da28c538ccf4eb3b0093eb30a67c708"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DJNQFYI2ZHSEMMB4WYX6HJYDSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inequality for t-geometric means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dinh Trung Hoa","submitted_at":"2015-12-11T16:49:00Z","abstract_excerpt":"In this note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04585","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":"2026-05-18T01:24:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzkHoRW2Zd2QiugVXu3itvRM+pjpujt35BH4/Mkq/LnOJRZxGyQJp3o7OpcdiRuuKCCyk4JFRi0wNehyLOBRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:14:11.512410Z"},"content_sha256":"54f45828632dd6cea4cf6b8d608a9dfad21ab96d477518d2b03802c8e5067685","schema_version":"1.0","event_id":"sha256:54f45828632dd6cea4cf6b8d608a9dfad21ab96d477518d2b03802c8e5067685"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/bundle.json","state_url":"https://pith.science/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/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":"2026-06-24T18:14:11Z","links":{"resolver":"https://pith.science/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW","bundle":"https://pith.science/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/bundle.json","state":"https://pith.science/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJNQFYI2ZHSEMMB4WYX6HJYDSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DJNQFYI2ZHSEMMB4WYX6HJYDSW","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":"c5a0af410a7dc24e2a2c4be51c6e3ed727463a653ef461e2a0ee7b0b3135551b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-11T16:49:00Z","title_canon_sha256":"be4c32bab1a92e4b6522b38eca4231e00306737fb69332b57ceea74077d8edbf"},"schema_version":"1.0","source":{"id":"1512.04585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04585","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04585v1","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04585","created_at":"2026-05-18T01:24:19Z"},{"alias_kind":"pith_short_12","alias_value":"DJNQFYI2ZHSE","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DJNQFYI2ZHSEMMB4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DJNQFYI2","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:54f45828632dd6cea4cf6b8d608a9dfad21ab96d477518d2b03802c8e5067685","target":"graph","created_at":"2026-05-18T01:24:19Z","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 note we prove an inequality for t-geometric means that immediately implies the recent results of Audenaert [2] and Hayajneh-Kittaneh [6].","authors_text":"Dinh Trung Hoa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-11T16:49:00Z","title":"An inequality for t-geometric means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04585","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":"sha256:1d230e6ebb82949a392f877b01e961f03da28c538ccf4eb3b0093eb30a67c708","target":"record","created_at":"2026-05-18T01:24:19Z","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":"c5a0af410a7dc24e2a2c4be51c6e3ed727463a653ef461e2a0ee7b0b3135551b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-11T16:49:00Z","title_canon_sha256":"be4c32bab1a92e4b6522b38eca4231e00306737fb69332b57ceea74077d8edbf"},"schema_version":"1.0","source":{"id":"1512.04585","kind":"arxiv","version":1}},"canonical_sha256":"1a5b02e11ac9e446303cb62fe3a703959e60858c3dcdc77c0a979a488b6385dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a5b02e11ac9e446303cb62fe3a703959e60858c3dcdc77c0a979a488b6385dd","first_computed_at":"2026-05-18T01:24:19.832765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:19.832765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2EHfTMnAPIsxQYxS4os12i4FYR3x8kB0+GKPM+1UMGGc5wwSSqNBWfnJH6m5bswyD4HRh08iOH8iVgMZIFCBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:19.833125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d230e6ebb82949a392f877b01e961f03da28c538ccf4eb3b0093eb30a67c708","sha256:54f45828632dd6cea4cf6b8d608a9dfad21ab96d477518d2b03802c8e5067685"],"state_sha256":"2f87b7f54b94e6d19ec1d48fb6a4726ee7b8500c96b4bf9248018a3f51d3475f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYTur/wAw7DekYdekDJakEIAVZWPRhJ/f6lIaclQl2Av6zyBuhDsrZjRA/yPJ9hJgoq81y/D1FqMPdz8ZxajCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:14:11.514461Z","bundle_sha256":"ecff090288653ca543eee92e0e5efe8f7c07f961b1435cc107c0c3f2abffd9e1"}}