{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QIZCJ3RLI7MCVAG37JQ4PAAQ2Q","short_pith_number":"pith:QIZCJ3RL","canonical_record":{"source":{"id":"1603.01004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-03T08:00:20Z","cross_cats_sorted":[],"title_canon_sha256":"156c7cb421e6295dc470b40ee26ff71279a1b939912370812f9317d155f03e48","abstract_canon_sha256":"e49fb096697c47d9a22b45b3f4123734cfab949ce7c36ef6742410bb3f4ee3a4"},"schema_version":"1.0"},"canonical_sha256":"823224ee2b47d82a80dbfa61c78010d4222ef5277b3f473fd0cd87e0d9d74a26","source":{"kind":"arxiv","id":"1603.01004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01004","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01004v2","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01004","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"QIZCJ3RLI7MC","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QIZCJ3RLI7MCVAG3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QIZCJ3RL","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QIZCJ3RLI7MCVAG37JQ4PAAQ2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-03T08:00:20Z","cross_cats_sorted":[],"title_canon_sha256":"156c7cb421e6295dc470b40ee26ff71279a1b939912370812f9317d155f03e48","abstract_canon_sha256":"e49fb096697c47d9a22b45b3f4123734cfab949ce7c36ef6742410bb3f4ee3a4"},"schema_version":"1.0"},"canonical_sha256":"823224ee2b47d82a80dbfa61c78010d4222ef5277b3f473fd0cd87e0d9d74a26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:13.724252Z","signature_b64":"CdbJh6ezNKNpcN03ciWEzsclTNWAQvL1lEAov7tRCWqMt6frKrIOpdFQII9gcaajfZ2AJY6htu91iWR3TWWoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"823224ee2b47d82a80dbfa61c78010d4222ef5277b3f473fd0cd87e0d9d74a26","last_reissued_at":"2026-05-18T01:18:13.723550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:13.723550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01004","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOG6ql4Acp4xz+ZzinjLazUf4pjuJ4zyQG1nytN4zeoPjzO8uDilfwoxyhVl/vGOxaptoKHGrt55naLDTWc9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:53:34.306363Z"},"content_sha256":"3ffa61ee4e347fda550983e92e75a6040c6d370b211df45aad174dcb47c50007","schema_version":"1.0","event_id":"sha256:3ffa61ee4e347fda550983e92e75a6040c6d370b211df45aad174dcb47c50007"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QIZCJ3RLI7MCVAG37JQ4PAAQ2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Uncertainty Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Naihuan Jing, Shao-Ming Fei, Xianqing Li-Jost, Yunlong Xiao","submitted_at":"2016-03-03T08:00:20Z","abstract_excerpt":"Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01004","kind":"arxiv","version":2},"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":"2026-05-18T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oLEngaAnBpvWZ2pUcTL+lDdkuzENX10ePCY16iu//wzkZjdxxkdQGpt1Ay+uVwrbgjiLlp6mBURMbYovPRTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:53:34.306712Z"},"content_sha256":"3be819effee889130ad072d36001df8fc4f598ae9848da764c3c741f4aa0c28c","schema_version":"1.0","event_id":"sha256:3be819effee889130ad072d36001df8fc4f598ae9848da764c3c741f4aa0c28c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/bundle.json","state_url":"https://pith.science/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/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":"2026-06-10T21:53:34Z","links":{"resolver":"https://pith.science/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q","bundle":"https://pith.science/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/bundle.json","state":"https://pith.science/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QIZCJ3RLI7MCVAG37JQ4PAAQ2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QIZCJ3RLI7MCVAG37JQ4PAAQ2Q","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":"e49fb096697c47d9a22b45b3f4123734cfab949ce7c36ef6742410bb3f4ee3a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-03T08:00:20Z","title_canon_sha256":"156c7cb421e6295dc470b40ee26ff71279a1b939912370812f9317d155f03e48"},"schema_version":"1.0","source":{"id":"1603.01004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01004","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01004v2","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01004","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"QIZCJ3RLI7MC","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QIZCJ3RLI7MCVAG3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QIZCJ3RL","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:3be819effee889130ad072d36001df8fc4f598ae9848da764c3c741f4aa0c28c","target":"graph","created_at":"2026-05-18T01:18:13Z","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":"Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted uncertainty relations to provide an optimal lower bound for all situations and remove the restriction on the quantum state. Generalization to multi-observable cases is also given and an optimal lower bound for the weighted sum of the variances is obtained in general quantum situation.","authors_text":"Naihuan Jing, Shao-Ming Fei, Xianqing Li-Jost, Yunlong Xiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-03T08:00:20Z","title":"Weighted Uncertainty Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01004","kind":"arxiv","version":2},"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":"sha256:3ffa61ee4e347fda550983e92e75a6040c6d370b211df45aad174dcb47c50007","target":"record","created_at":"2026-05-18T01:18:13Z","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":"e49fb096697c47d9a22b45b3f4123734cfab949ce7c36ef6742410bb3f4ee3a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-03-03T08:00:20Z","title_canon_sha256":"156c7cb421e6295dc470b40ee26ff71279a1b939912370812f9317d155f03e48"},"schema_version":"1.0","source":{"id":"1603.01004","kind":"arxiv","version":2}},"canonical_sha256":"823224ee2b47d82a80dbfa61c78010d4222ef5277b3f473fd0cd87e0d9d74a26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823224ee2b47d82a80dbfa61c78010d4222ef5277b3f473fd0cd87e0d9d74a26","first_computed_at":"2026-05-18T01:18:13.723550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:13.723550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CdbJh6ezNKNpcN03ciWEzsclTNWAQvL1lEAov7tRCWqMt6frKrIOpdFQII9gcaajfZ2AJY6htu91iWR3TWWoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:13.724252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ffa61ee4e347fda550983e92e75a6040c6d370b211df45aad174dcb47c50007","sha256:3be819effee889130ad072d36001df8fc4f598ae9848da764c3c741f4aa0c28c"],"state_sha256":"36715d29866f71e83bc5b66874f8768392d0d5a1f7637fccc77fe56dd19653d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VDYbRkpCZlVx3utvyPGewMe8nN9Nv75JkkOyoP1PSHWL0murQwBO6EtlqDmA3lWkxYExP5LoC5/Gs8eP2sIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:53:34.308746Z","bundle_sha256":"42ccbbb135d4bd40a1a77d998cbf8e9bb565e3514b81af1eb995c687402a3dda"}}