{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6N7YCU5WMLDCUPGSUGPF72LKM5","short_pith_number":"pith:6N7YCU5W","canonical_record":{"source":{"id":"1611.02741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-03T00:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"17f2feccff9b589985f53d8b72f63556f9007f19f94e53df4556ec85ddbc481e","abstract_canon_sha256":"ea2b33432c9b3129afb7f9dbb62233df6e64ae31bf538a8ba88571ef0e70e17e"},"schema_version":"1.0"},"canonical_sha256":"f37f8153b662c62a3cd2a19e5fe96a67531917e3db2b5cb2ee46285cc43ba40b","source":{"kind":"arxiv","id":"1611.02741","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02741","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02741v1","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02741","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"6N7YCU5WMLDC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6N7YCU5WMLDCUPGS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6N7YCU5W","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6N7YCU5WMLDCUPGSUGPF72LKM5","target":"record","payload":{"canonical_record":{"source":{"id":"1611.02741","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-03T00:29:42Z","cross_cats_sorted":[],"title_canon_sha256":"17f2feccff9b589985f53d8b72f63556f9007f19f94e53df4556ec85ddbc481e","abstract_canon_sha256":"ea2b33432c9b3129afb7f9dbb62233df6e64ae31bf538a8ba88571ef0e70e17e"},"schema_version":"1.0"},"canonical_sha256":"f37f8153b662c62a3cd2a19e5fe96a67531917e3db2b5cb2ee46285cc43ba40b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:43.834813Z","signature_b64":"x+W/HEucDMv9KleUTRlb68tuWWigBR/IB5M92lykTIbjZCq/Z/GN31SY4pExI7ROXckhzMWLX/Jfvil4hBQ+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f37f8153b662c62a3cd2a19e5fe96a67531917e3db2b5cb2ee46285cc43ba40b","last_reissued_at":"2026-05-18T00:59:43.834021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:43.834021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.02741","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":"2026-05-18T00:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkR2qsWwQrp//CN0WLjvQ2PAjbl2HBnvmLATo0uipTeY+NcDqrS+B/kjAkXjAZBoBfh+H3JkTNo67V/vMW6nAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:47:59.256543Z"},"content_sha256":"f93e184d64c928b62707a9296f00a8f43212ff95ef1bd2475b1de1c773f9119e","schema_version":"1.0","event_id":"sha256:f93e184d64c928b62707a9296f00a8f43212ff95ef1bd2475b1de1c773f9119e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6N7YCU5WMLDCUPGSUGPF72LKM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic Weighted Geometric Mean in Hermitian Unital Banach Star-Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Silvestru Sever Dragomir","submitted_at":"2016-11-03T00:29:42Z","abstract_excerpt":"In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02741","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":"2026-05-18T00:59:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NgKx7mIfXWKGYCJWLvcu61hRBXPRVFexBMK7vSj3MwF8ZKbu/V9HbZUskAc13on+dupuo4GBXLdQaR85u4yJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T23:47:59.256876Z"},"content_sha256":"633662fc54257cab92fa5c54e12b3e2a8ac020a6a7718754dc79b951f92344a2","schema_version":"1.0","event_id":"sha256:633662fc54257cab92fa5c54e12b3e2a8ac020a6a7718754dc79b951f92344a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/bundle.json","state_url":"https://pith.science/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/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":"2026-06-08T23:47:59Z","links":{"resolver":"https://pith.science/pith/6N7YCU5WMLDCUPGSUGPF72LKM5","bundle":"https://pith.science/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/bundle.json","state":"https://pith.science/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6N7YCU5WMLDCUPGSUGPF72LKM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6N7YCU5WMLDCUPGSUGPF72LKM5","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":"ea2b33432c9b3129afb7f9dbb62233df6e64ae31bf538a8ba88571ef0e70e17e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-03T00:29:42Z","title_canon_sha256":"17f2feccff9b589985f53d8b72f63556f9007f19f94e53df4556ec85ddbc481e"},"schema_version":"1.0","source":{"id":"1611.02741","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02741","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02741v1","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02741","created_at":"2026-05-18T00:59:43Z"},{"alias_kind":"pith_short_12","alias_value":"6N7YCU5WMLDC","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6N7YCU5WMLDCUPGS","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6N7YCU5W","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:633662fc54257cab92fa5c54e12b3e2a8ac020a6a7718754dc79b951f92344a2","target":"graph","created_at":"2026-05-18T00:59:43Z","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 quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.","authors_text":"Silvestru Sever Dragomir","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-03T00:29:42Z","title":"Quadratic Weighted Geometric Mean in Hermitian Unital Banach Star-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02741","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:f93e184d64c928b62707a9296f00a8f43212ff95ef1bd2475b1de1c773f9119e","target":"record","created_at":"2026-05-18T00:59:43Z","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":"ea2b33432c9b3129afb7f9dbb62233df6e64ae31bf538a8ba88571ef0e70e17e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-11-03T00:29:42Z","title_canon_sha256":"17f2feccff9b589985f53d8b72f63556f9007f19f94e53df4556ec85ddbc481e"},"schema_version":"1.0","source":{"id":"1611.02741","kind":"arxiv","version":1}},"canonical_sha256":"f37f8153b662c62a3cd2a19e5fe96a67531917e3db2b5cb2ee46285cc43ba40b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f37f8153b662c62a3cd2a19e5fe96a67531917e3db2b5cb2ee46285cc43ba40b","first_computed_at":"2026-05-18T00:59:43.834021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:43.834021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x+W/HEucDMv9KleUTRlb68tuWWigBR/IB5M92lykTIbjZCq/Z/GN31SY4pExI7ROXckhzMWLX/Jfvil4hBQ+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:43.834813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02741","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f93e184d64c928b62707a9296f00a8f43212ff95ef1bd2475b1de1c773f9119e","sha256:633662fc54257cab92fa5c54e12b3e2a8ac020a6a7718754dc79b951f92344a2"],"state_sha256":"2bd0039002e0c7a7f9b73d766be6a8689ebb19945f2e17e31ff8fc4ad1ad6ab3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4u7yD8y6E3quurZ1sTbw3Nda+ghseG2vlT7WgJmvsyDI6OiuUfxkQ+A8n1/REB7Z2jGbuOKJiN+iFg00pdTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T23:47:59.258657Z","bundle_sha256":"59cc82a51271c9137e2035cff2791907abc18d94200c847cb45715c510be3a34"}}