{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:MILNIRSIG4ZID2EIGDGLEKV2X7","short_pith_number":"pith:MILNIRSI","canonical_record":{"source":{"id":"quant-ph/0407111","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-15T10:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"54d83911fafcc8bd1694abb1c6ebdfe6aa0e16e58b8528915ec9b4765fc13172","abstract_canon_sha256":"46a7075f3216767520bda7cf2dd849ba1d45cd727dc58335a0f3ae0f31e7aa16"},"schema_version":"1.0"},"canonical_sha256":"6216d44648373281e88830ccb22ababfcdd143fdd2a7a6a7e1f72e1b732f5014","source":{"kind":"arxiv","id":"quant-ph/0407111","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407111","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407111v1","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407111","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"MILNIRSIG4ZI","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"MILNIRSIG4ZID2EI","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"MILNIRSI","created_at":"2026-07-04T16:50:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:MILNIRSIG4ZID2EIGDGLEKV2X7","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0407111","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-15T10:38:44Z","cross_cats_sorted":[],"title_canon_sha256":"54d83911fafcc8bd1694abb1c6ebdfe6aa0e16e58b8528915ec9b4765fc13172","abstract_canon_sha256":"46a7075f3216767520bda7cf2dd849ba1d45cd727dc58335a0f3ae0f31e7aa16"},"schema_version":"1.0"},"canonical_sha256":"6216d44648373281e88830ccb22ababfcdd143fdd2a7a6a7e1f72e1b732f5014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:50:21.025449Z","signature_b64":"swfOjIzmT0odp52RG2pebm8Mx+oY92pTjRcng1AQGhnPQuyWik0WkhJC/rPvdmwf/TSZ8Pxnc8coCmW3MhSdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6216d44648373281e88830ccb22ababfcdd143fdd2a7a6a7e1f72e1b732f5014","last_reissued_at":"2026-07-04T16:50:21.025078Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:50:21.025078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0407111","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":"2026-07-04T16:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9mEWbdK3s7/dUIxFuNEpDO/jMrzG/6E4EFvd5YNtfQv+bJSMi1W9O+R/q9qp3h3L9mPUfEJPfd/pOu/jAV0Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:26:12.969788Z"},"content_sha256":"caa5a8a13d18fbcb5414471f2925690fc633d318b752e770d118eecc275facdb","schema_version":"1.0","event_id":"sha256:caa5a8a13d18fbcb5414471f2925690fc633d318b752e770d118eecc275facdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:MILNIRSIG4ZID2EIGDGLEKV2X7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator-sum representation of time-dependent density operators and its applications","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"C. H. Oh, D. M. Tong, Jing-Ling Chen, L. C. Kwek, L. Ma","submitted_at":"2004-07-15T10:38:44Z","abstract_excerpt":"We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407111","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0407111/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:50:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrl33/lcXJ7nNOu1flB37t3F1t5PmpTyQe0AoH6fMjIuFkRSZKR/9ZOa4f1v5sQju0MRvlZDbzgHK38roJsuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T15:26:12.970163Z"},"content_sha256":"ba01f64f3b19394824faa1beb2ed975e230eda0b2a1b4f9c9d32001c9790f2f0","schema_version":"1.0","event_id":"sha256:ba01f64f3b19394824faa1beb2ed975e230eda0b2a1b4f9c9d32001c9790f2f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/bundle.json","state_url":"https://pith.science/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/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":"2026-07-07T15:26:12Z","links":{"resolver":"https://pith.science/pith/MILNIRSIG4ZID2EIGDGLEKV2X7","bundle":"https://pith.science/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/bundle.json","state":"https://pith.science/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MILNIRSIG4ZID2EIGDGLEKV2X7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:MILNIRSIG4ZID2EIGDGLEKV2X7","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":"46a7075f3216767520bda7cf2dd849ba1d45cd727dc58335a0f3ae0f31e7aa16","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-15T10:38:44Z","title_canon_sha256":"54d83911fafcc8bd1694abb1c6ebdfe6aa0e16e58b8528915ec9b4765fc13172"},"schema_version":"1.0","source":{"id":"quant-ph/0407111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0407111","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0407111v1","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0407111","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_12","alias_value":"MILNIRSIG4ZI","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_16","alias_value":"MILNIRSIG4ZID2EI","created_at":"2026-07-04T16:50:21Z"},{"alias_kind":"pith_short_8","alias_value":"MILNIRSI","created_at":"2026-07-04T16:50:21Z"}],"graph_snapshots":[{"event_id":"sha256:ba01f64f3b19394824faa1beb2ed975e230eda0b2a1b4f9c9d32001c9790f2f0","target":"graph","created_at":"2026-07-04T16:50:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0407111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.","authors_text":"C. H. Oh, D. M. Tong, Jing-Ling Chen, L. C. Kwek, L. Ma","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-07-15T10:38:44Z","title":"Operator-sum representation of time-dependent density operators and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0407111","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:caa5a8a13d18fbcb5414471f2925690fc633d318b752e770d118eecc275facdb","target":"record","created_at":"2026-07-04T16:50:21Z","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":"46a7075f3216767520bda7cf2dd849ba1d45cd727dc58335a0f3ae0f31e7aa16","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-07-15T10:38:44Z","title_canon_sha256":"54d83911fafcc8bd1694abb1c6ebdfe6aa0e16e58b8528915ec9b4765fc13172"},"schema_version":"1.0","source":{"id":"quant-ph/0407111","kind":"arxiv","version":1}},"canonical_sha256":"6216d44648373281e88830ccb22ababfcdd143fdd2a7a6a7e1f72e1b732f5014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6216d44648373281e88830ccb22ababfcdd143fdd2a7a6a7e1f72e1b732f5014","first_computed_at":"2026-07-04T16:50:21.025078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:50:21.025078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"swfOjIzmT0odp52RG2pebm8Mx+oY92pTjRcng1AQGhnPQuyWik0WkhJC/rPvdmwf/TSZ8Pxnc8coCmW3MhSdDA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:50:21.025449Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0407111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa5a8a13d18fbcb5414471f2925690fc633d318b752e770d118eecc275facdb","sha256:ba01f64f3b19394824faa1beb2ed975e230eda0b2a1b4f9c9d32001c9790f2f0"],"state_sha256":"dbb655f79deafaad12d13dc2cc83fab17d9bdf7a929a0e09235910d6db607384"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rr6FewvXQReOSLOm2QLS271guvSSXeONsIfGNj3y8Es16ppxWq9ujYyTEzFASD8r+YKD7v7lPR0Qk4m8X5MvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T15:26:12.972578Z","bundle_sha256":"11089301fdf10f4f65367c6fca317dd0c8361b912458ee1a6e34370527cd6f72"}}