{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IGG7AAIFRHOQO5AKWPMTPS6Q6T","short_pith_number":"pith:IGG7AAIF","canonical_record":{"source":{"id":"1012.0632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-03T03:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"0e8da17e0488cdaf97c1d2ee54b8cc0e03369910f3365d974b83c1ab173bebf5","abstract_canon_sha256":"45cbde497309e047d19bcdbacaa131d35176fcf486b7afbe38c2e276789c4145"},"schema_version":"1.0"},"canonical_sha256":"418df0010589dd07740ab3d937cbd0f4d233b00128526f2ed9bccf0568d88ec3","source":{"kind":"arxiv","id":"1012.0632","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0632","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0632v2","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0632","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"IGG7AAIFRHOQ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IGG7AAIFRHOQO5AK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IGG7AAIF","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IGG7AAIFRHOQO5AKWPMTPS6Q6T","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0632","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-03T03:58:21Z","cross_cats_sorted":[],"title_canon_sha256":"0e8da17e0488cdaf97c1d2ee54b8cc0e03369910f3365d974b83c1ab173bebf5","abstract_canon_sha256":"45cbde497309e047d19bcdbacaa131d35176fcf486b7afbe38c2e276789c4145"},"schema_version":"1.0"},"canonical_sha256":"418df0010589dd07740ab3d937cbd0f4d233b00128526f2ed9bccf0568d88ec3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:35.605874Z","signature_b64":"V2lAhveYE0eVRAHHwgI1Ikl7CvK+/NbMDgf5L6S7Gw0Qgb/S0rHSEQDV+xYVOyknoK9DbqkA8Yd/DxPEgzgVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"418df0010589dd07740ab3d937cbd0f4d233b00128526f2ed9bccf0568d88ec3","last_reissued_at":"2026-05-18T02:04:35.605241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:35.605241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0632","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":"2026-05-18T02:04:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O1kezZFRhLGxoRsVuuale1S7JNWG4tA8ylVrxG+9j/+odBIPU0ii7bs+LjtlhMQKnIqyzX8qERXPU1tklWo5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:51:55.379056Z"},"content_sha256":"be72ed6bc3aef760cef2074dd080326321a13bd699e77d3c663f28e83d0a3c59","schema_version":"1.0","event_id":"sha256:be72ed6bc3aef760cef2074dd080326321a13bd699e77d3c663f28e83d0a3c59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IGG7AAIFRHOQO5AKWPMTPS6Q6T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalizations of Quantum Discord","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jianwei Xu","submitted_at":"2010-12-03T03:58:21Z","abstract_excerpt":"The original definition of quantum discord of bipartite states was defined over projective measurements, in this paper we discuss some generalizations of it. These generalizations are defined over general measurements, rank-one general measurements or Neumark extension measurements. We investigate the nonnegativity, zero-discord sets of all these quantum discords and some properties about them."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0632","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":"2026-05-18T02:04:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVUTfMjEc96QdTXoNNSC6Mw/DKWBSM+R09VwSx6WAiTlOasIMD5/Wgi9I0Fpa1rNy8nq/UU3ckoV5GdyPxSXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:51:55.379832Z"},"content_sha256":"d109b47f3bf0236f9ffa50d358940921e479b66e2855e6421d0b92ad4a3edb5b","schema_version":"1.0","event_id":"sha256:d109b47f3bf0236f9ffa50d358940921e479b66e2855e6421d0b92ad4a3edb5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/bundle.json","state_url":"https://pith.science/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/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":"2026-05-31T14:51:55Z","links":{"resolver":"https://pith.science/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T","bundle":"https://pith.science/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/bundle.json","state":"https://pith.science/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGG7AAIFRHOQO5AKWPMTPS6Q6T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IGG7AAIFRHOQO5AKWPMTPS6Q6T","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":"45cbde497309e047d19bcdbacaa131d35176fcf486b7afbe38c2e276789c4145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-03T03:58:21Z","title_canon_sha256":"0e8da17e0488cdaf97c1d2ee54b8cc0e03369910f3365d974b83c1ab173bebf5"},"schema_version":"1.0","source":{"id":"1012.0632","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0632","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0632v2","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0632","created_at":"2026-05-18T02:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"IGG7AAIFRHOQ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IGG7AAIFRHOQO5AK","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IGG7AAIF","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:d109b47f3bf0236f9ffa50d358940921e479b66e2855e6421d0b92ad4a3edb5b","target":"graph","created_at":"2026-05-18T02:04:35Z","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":"The original definition of quantum discord of bipartite states was defined over projective measurements, in this paper we discuss some generalizations of it. These generalizations are defined over general measurements, rank-one general measurements or Neumark extension measurements. We investigate the nonnegativity, zero-discord sets of all these quantum discords and some properties about them.","authors_text":"Jianwei Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-03T03:58:21Z","title":"Generalizations of Quantum Discord"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0632","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:be72ed6bc3aef760cef2074dd080326321a13bd699e77d3c663f28e83d0a3c59","target":"record","created_at":"2026-05-18T02:04:35Z","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":"45cbde497309e047d19bcdbacaa131d35176fcf486b7afbe38c2e276789c4145","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-03T03:58:21Z","title_canon_sha256":"0e8da17e0488cdaf97c1d2ee54b8cc0e03369910f3365d974b83c1ab173bebf5"},"schema_version":"1.0","source":{"id":"1012.0632","kind":"arxiv","version":2}},"canonical_sha256":"418df0010589dd07740ab3d937cbd0f4d233b00128526f2ed9bccf0568d88ec3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"418df0010589dd07740ab3d937cbd0f4d233b00128526f2ed9bccf0568d88ec3","first_computed_at":"2026-05-18T02:04:35.605241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:35.605241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V2lAhveYE0eVRAHHwgI1Ikl7CvK+/NbMDgf5L6S7Gw0Qgb/S0rHSEQDV+xYVOyknoK9DbqkA8Yd/DxPEgzgVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:35.605874Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0632","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be72ed6bc3aef760cef2074dd080326321a13bd699e77d3c663f28e83d0a3c59","sha256:d109b47f3bf0236f9ffa50d358940921e479b66e2855e6421d0b92ad4a3edb5b"],"state_sha256":"5f4f9caf6fd3311041d01ecb3f4eb7dc1f6f86648d1f47f5d6415065df3f9686"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UBCDTPXyisZnlXI5UaTByK8hNm92wU4ZjKB6MFAMkYElbBVgveiNfl6bw+e1JSpuN0oy+c48AguuPzKNzbNrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:51:55.383790Z","bundle_sha256":"b34cc422829250d032e218ae2744bd499e863227e519b0abd196d89aafc437ae"}}