{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NXECFBFTF74BXRMAU77BTW2RDP","short_pith_number":"pith:NXECFBFT","canonical_record":{"source":{"id":"1804.03840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-11T07:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"788a9e00d02e49637fe6e80aa38b4ec926b83c1de2fbad2388c8f53b9ecf82f6","abstract_canon_sha256":"92ff03f619e216fd8c890856f3c7b9d58ee6c76da1347e010b205c48710dd5de"},"schema_version":"1.0"},"canonical_sha256":"6dc82284b32ff81bc580a7fe19db511bf0fbd2ba99063c1fbbed16c516e67747","source":{"kind":"arxiv","id":"1804.03840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03840","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03840v1","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03840","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"NXECFBFTF74B","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NXECFBFTF74BXRMA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NXECFBFT","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NXECFBFTF74BXRMAU77BTW2RDP","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-11T07:18:29Z","cross_cats_sorted":[],"title_canon_sha256":"788a9e00d02e49637fe6e80aa38b4ec926b83c1de2fbad2388c8f53b9ecf82f6","abstract_canon_sha256":"92ff03f619e216fd8c890856f3c7b9d58ee6c76da1347e010b205c48710dd5de"},"schema_version":"1.0"},"canonical_sha256":"6dc82284b32ff81bc580a7fe19db511bf0fbd2ba99063c1fbbed16c516e67747","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:42.906400Z","signature_b64":"wX+6f9goU8O+7hLPOmCWnJZCqwx6TRKP8YxBXt6ffwFUFqYSIaBgKVj5pGm6OhGqlkxHPisAQO+Y2TQryuvjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dc82284b32ff81bc580a7fe19db511bf0fbd2ba99063c1fbbed16c516e67747","last_reissued_at":"2026-05-18T00:18:42.905908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:42.905908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03840","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":"2026-05-18T00:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMcZWfQ9aN0c0q6R+UcJchbUh5qRTipLj866j7msephpABdamImN6JIr6mXoVXR/m7B8e6u3jSPsCd8D4SOwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:49.096161Z"},"content_sha256":"c9bfc1f02a65184baf1a34a757b073cb9e78e1a1edc48804b3ff66d996e9bc05","schema_version":"1.0","event_id":"sha256:c9bfc1f02a65184baf1a34a757b073cb9e78e1a1edc48804b3ff66d996e9bc05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NXECFBFTF74BXRMAU77BTW2RDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangle inequalities in coherence measures and entanglement concurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Chengjie Zhang, Wenlong You, Yue Dai, Yuli Dong","submitted_at":"2018-04-11T07:18:29Z","abstract_excerpt":"We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-$2$ state $\\varrho$ can be expressed as a convex combination of two pure states, i.e., $\\varrho=p_{1}|\\psi_{1}\\rangle\\langle\\psi_{1}|+p_{2}|\\psi_{2}\\rangle\\langle\\psi_{2}|$, a triangle inequality can be established as $\\big{|}E(|\\Psi_{1}\\rangle)-E(|\\Psi_{2}\\rangle)\\big{|}\\leq E(\\varrho)\\leq E(|\\Psi_{1}\\rangle)+E(|\\Psi_{2}\\rangle)$, where $|\\Psi_{1}\\rangle=\\sqrt{p_{1}}|\\psi_{1}\\rangle$ and $|\\Psi_{2}\\rangle=\\sqrt{p_{2}}|\\psi_{2}\\rangle$, $E$ can be considered either coherence measur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03840","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":"2026-05-18T00:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZBTMaRicAA/fNLbwhOnVy5NT/eLc/9Hp3rAOK1rmBDvq1aC6AHvI5JknM7lu3Q3r2TQyeYGX2/jLKtcdwAzBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:43:49.096542Z"},"content_sha256":"5c1612d484b90b134ebcdeadfad0c2f819f827cef9b0f2d31769b489ba3869c6","schema_version":"1.0","event_id":"sha256:5c1612d484b90b134ebcdeadfad0c2f819f827cef9b0f2d31769b489ba3869c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXECFBFTF74BXRMAU77BTW2RDP/bundle.json","state_url":"https://pith.science/pith/NXECFBFTF74BXRMAU77BTW2RDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXECFBFTF74BXRMAU77BTW2RDP/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":"2026-06-04T03:43:49Z","links":{"resolver":"https://pith.science/pith/NXECFBFTF74BXRMAU77BTW2RDP","bundle":"https://pith.science/pith/NXECFBFTF74BXRMAU77BTW2RDP/bundle.json","state":"https://pith.science/pith/NXECFBFTF74BXRMAU77BTW2RDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXECFBFTF74BXRMAU77BTW2RDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NXECFBFTF74BXRMAU77BTW2RDP","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":"92ff03f619e216fd8c890856f3c7b9d58ee6c76da1347e010b205c48710dd5de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-11T07:18:29Z","title_canon_sha256":"788a9e00d02e49637fe6e80aa38b4ec926b83c1de2fbad2388c8f53b9ecf82f6"},"schema_version":"1.0","source":{"id":"1804.03840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03840","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03840v1","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03840","created_at":"2026-05-18T00:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"NXECFBFTF74B","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NXECFBFTF74BXRMA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NXECFBFT","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:5c1612d484b90b134ebcdeadfad0c2f819f827cef9b0f2d31769b489ba3869c6","target":"graph","created_at":"2026-05-18T00:18:42Z","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 provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-$2$ state $\\varrho$ can be expressed as a convex combination of two pure states, i.e., $\\varrho=p_{1}|\\psi_{1}\\rangle\\langle\\psi_{1}|+p_{2}|\\psi_{2}\\rangle\\langle\\psi_{2}|$, a triangle inequality can be established as $\\big{|}E(|\\Psi_{1}\\rangle)-E(|\\Psi_{2}\\rangle)\\big{|}\\leq E(\\varrho)\\leq E(|\\Psi_{1}\\rangle)+E(|\\Psi_{2}\\rangle)$, where $|\\Psi_{1}\\rangle=\\sqrt{p_{1}}|\\psi_{1}\\rangle$ and $|\\Psi_{2}\\rangle=\\sqrt{p_{2}}|\\psi_{2}\\rangle$, $E$ can be considered either coherence measur","authors_text":"Chengjie Zhang, Wenlong You, Yue Dai, Yuli Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-11T07:18:29Z","title":"Triangle inequalities in coherence measures and entanglement concurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03840","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:c9bfc1f02a65184baf1a34a757b073cb9e78e1a1edc48804b3ff66d996e9bc05","target":"record","created_at":"2026-05-18T00:18:42Z","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":"92ff03f619e216fd8c890856f3c7b9d58ee6c76da1347e010b205c48710dd5de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-04-11T07:18:29Z","title_canon_sha256":"788a9e00d02e49637fe6e80aa38b4ec926b83c1de2fbad2388c8f53b9ecf82f6"},"schema_version":"1.0","source":{"id":"1804.03840","kind":"arxiv","version":1}},"canonical_sha256":"6dc82284b32ff81bc580a7fe19db511bf0fbd2ba99063c1fbbed16c516e67747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dc82284b32ff81bc580a7fe19db511bf0fbd2ba99063c1fbbed16c516e67747","first_computed_at":"2026-05-18T00:18:42.905908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:42.905908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wX+6f9goU8O+7hLPOmCWnJZCqwx6TRKP8YxBXt6ffwFUFqYSIaBgKVj5pGm6OhGqlkxHPisAQO+Y2TQryuvjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:42.906400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9bfc1f02a65184baf1a34a757b073cb9e78e1a1edc48804b3ff66d996e9bc05","sha256:5c1612d484b90b134ebcdeadfad0c2f819f827cef9b0f2d31769b489ba3869c6"],"state_sha256":"89c53c4f7554fe1ecf6a27535aa54d24276273ccd7843dccadd307dc07bcc558"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aq7RrMZNHLLdRYURAPM/476yVxobSrCtCrzKneieh8Si+Zxn1KtBIk8SNdjHxt2hkfbAz26EMHit8hiuUhOcBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:43:49.100432Z","bundle_sha256":"3457e19cacd09c1d0a499806bddb85e5aeaecc2096f4c1f63fdbf8b0808a7151"}}