{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NPKIF5USH2GUFFPD7CCD6UHDPV","short_pith_number":"pith:NPKIF5US","canonical_record":{"source":{"id":"1304.5918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T11:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"bade529b552bb83d3314c50d1d6d446c27a63005d646f536c642eee2fbdfc686","abstract_canon_sha256":"87c5c8dba43be6bc397a37e5eb65dfed18d4b004fc6c5a287eaf96934ce1b36a"},"schema_version":"1.0"},"canonical_sha256":"6bd482f6923e8d4295e3f8843f50e37d546cda3211119b41d5fa34f08c0841cc","source":{"kind":"arxiv","id":"1304.5918","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5918","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5918v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5918","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"NPKIF5USH2GU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPKIF5USH2GUFFPD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPKIF5US","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NPKIF5USH2GUFFPD7CCD6UHDPV","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T11:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"bade529b552bb83d3314c50d1d6d446c27a63005d646f536c642eee2fbdfc686","abstract_canon_sha256":"87c5c8dba43be6bc397a37e5eb65dfed18d4b004fc6c5a287eaf96934ce1b36a"},"schema_version":"1.0"},"canonical_sha256":"6bd482f6923e8d4295e3f8843f50e37d546cda3211119b41d5fa34f08c0841cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:23.774241Z","signature_b64":"CbCPZZ5hRJ1sr7Cc5NG8S5CtuLhmEUvvrWlMxd76BbrvFGCrc+vBlGf9trQJscEXi/Sg4LztMlMGVmX+Jq7bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bd482f6923e8d4295e3f8843f50e37d546cda3211119b41d5fa34f08c0841cc","last_reissued_at":"2026-05-18T03:27:23.773549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:23.773549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5918","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":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shtC5oFuPH9K2OGC7g40A1fdNFsbxO7a/sFx2EuiThDT+yVeQMzkD0z44NVjqW6Y1d/HGS2wPbSrZ38XJAn8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:17:18.281398Z"},"content_sha256":"d454a6b6b1b8e6e1ef7529d06442b8cecd20d3ff8bf2de8a6964b879610056de","schema_version":"1.0","event_id":"sha256:d454a6b6b1b8e6e1ef7529d06442b8cecd20d3ff8bf2de8a6964b879610056de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NPKIF5USH2GUFFPD7CCD6UHDPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kraus representation for maps and master equation in spin star model with layered environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Hadi Mehrabpour, Mahmoud Mahdian","submitted_at":"2013-04-22T11:38:36Z","abstract_excerpt":"Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of an exactly solvable dynamic of one-qubit open system in layered environment . On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quant"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5918","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":"2026-05-18T03:27:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yxzPESNUH4FNdH+MgN3EAUXq5mPKtKVivQNGF1p1eFhxz2yIxVT8YtEtvSvNRKJRDA629y29D0dx91C6zyUVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:17:18.281745Z"},"content_sha256":"6a477f00bf58b3e018fb1d1c2c9f2cd3f5a4ace5ac8a7427f9a80a1c67f97905","schema_version":"1.0","event_id":"sha256:6a477f00bf58b3e018fb1d1c2c9f2cd3f5a4ace5ac8a7427f9a80a1c67f97905"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/bundle.json","state_url":"https://pith.science/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/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":"2026-07-08T23:17:18Z","links":{"resolver":"https://pith.science/pith/NPKIF5USH2GUFFPD7CCD6UHDPV","bundle":"https://pith.science/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/bundle.json","state":"https://pith.science/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NPKIF5USH2GUFFPD7CCD6UHDPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NPKIF5USH2GUFFPD7CCD6UHDPV","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":"87c5c8dba43be6bc397a37e5eb65dfed18d4b004fc6c5a287eaf96934ce1b36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T11:38:36Z","title_canon_sha256":"bade529b552bb83d3314c50d1d6d446c27a63005d646f536c642eee2fbdfc686"},"schema_version":"1.0","source":{"id":"1304.5918","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5918","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5918v1","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5918","created_at":"2026-05-18T03:27:23Z"},{"alias_kind":"pith_short_12","alias_value":"NPKIF5USH2GU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NPKIF5USH2GUFFPD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NPKIF5US","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:6a477f00bf58b3e018fb1d1c2c9f2cd3f5a4ace5ac8a7427f9a80a1c67f97905","target":"graph","created_at":"2026-05-18T03:27:23Z","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":"Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and master equation of an exactly solvable dynamic of one-qubit open system in layered environment . On the other hand, we obtain exact Nakajima-Zwanzig (NZ) and time-convolutionless (TCL) master equation from the maps. Finally, we study a simple example to consider the relation between CP maps and initial quantum correlation and show that vanishing initial quant","authors_text":"Hadi Mehrabpour, Mahmoud Mahdian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T11:38:36Z","title":"Kraus representation for maps and master equation in spin star model with layered environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5918","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:d454a6b6b1b8e6e1ef7529d06442b8cecd20d3ff8bf2de8a6964b879610056de","target":"record","created_at":"2026-05-18T03:27:23Z","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":"87c5c8dba43be6bc397a37e5eb65dfed18d4b004fc6c5a287eaf96934ce1b36a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-22T11:38:36Z","title_canon_sha256":"bade529b552bb83d3314c50d1d6d446c27a63005d646f536c642eee2fbdfc686"},"schema_version":"1.0","source":{"id":"1304.5918","kind":"arxiv","version":1}},"canonical_sha256":"6bd482f6923e8d4295e3f8843f50e37d546cda3211119b41d5fa34f08c0841cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bd482f6923e8d4295e3f8843f50e37d546cda3211119b41d5fa34f08c0841cc","first_computed_at":"2026-05-18T03:27:23.773549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:23.773549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CbCPZZ5hRJ1sr7Cc5NG8S5CtuLhmEUvvrWlMxd76BbrvFGCrc+vBlGf9trQJscEXi/Sg4LztMlMGVmX+Jq7bCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:23.774241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5918","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d454a6b6b1b8e6e1ef7529d06442b8cecd20d3ff8bf2de8a6964b879610056de","sha256:6a477f00bf58b3e018fb1d1c2c9f2cd3f5a4ace5ac8a7427f9a80a1c67f97905"],"state_sha256":"bf68bbfaa52eeba5b414fa41a89757ea8fb9e4e62db6ea4be6a43ba9016043e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hbXf0btjHvTZ51xjY3pmliqN5DB/kmJZ+FSaWE6BZr7UY/rNT0wmMXVXmFAIRmd+bG9u8FSOYTaXNmx14fiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T23:17:18.283783Z","bundle_sha256":"02bc76cdb2eb403fe955e7acc39cf57c5381fe6418c0f119e792d6347dea8a0b"}}