{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:YOW7DXUYWDM3AURZF22NL7N2SD","short_pith_number":"pith:YOW7DXUY","canonical_record":{"source":{"id":"math-ph/0406010","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-06-04T16:13:24Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"59ae45849fde0ee56c2de9edf75a7c2ecd14a9e89f71bc8dc404b54c4bd88836","abstract_canon_sha256":"25d7d4e35b9eb5e03d6e8a4f17467ce364a5d579c964365a8025de00b7a6a7c1"},"schema_version":"1.0"},"canonical_sha256":"c3adf1de98b0d9b052392eb4d5fdba90eb7032d8c021788ab306d4b56d8fca0b","source":{"kind":"arxiv","id":"math-ph/0406010","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0406010","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0406010v2","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0406010","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"YOW7DXUYWDM3","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_16","alias_value":"YOW7DXUYWDM3AURZ","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_8","alias_value":"YOW7DXUY","created_at":"2026-07-04T14:34:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:YOW7DXUYWDM3AURZF22NL7N2SD","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0406010","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-06-04T16:13:24Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"59ae45849fde0ee56c2de9edf75a7c2ecd14a9e89f71bc8dc404b54c4bd88836","abstract_canon_sha256":"25d7d4e35b9eb5e03d6e8a4f17467ce364a5d579c964365a8025de00b7a6a7c1"},"schema_version":"1.0"},"canonical_sha256":"c3adf1de98b0d9b052392eb4d5fdba90eb7032d8c021788ab306d4b56d8fca0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:34:00.860811Z","signature_b64":"rkq3rAhA7dVVEz5XwpIMfR2mlGlvbphu0Sgaaf202e+3/51Oe8yDLDD5NGblrBIiof1ZYfr1blwqeSAd4PHeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3adf1de98b0d9b052392eb4d5fdba90eb7032d8c021788ab306d4b56d8fca0b","last_reissued_at":"2026-07-04T14:34:00.860437Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:34:00.860437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0406010","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":"2026-07-04T14:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2tbCxgqkgdnuyr963kAetk9gcxbFymu7cMcE68S7fv9+EnqwPvozvhfkp6S1HSWy6iCY63iJBByXC0RhURttAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:49:03.250914Z"},"content_sha256":"602edf5ee7668a50614e6cf4fc2e495f46b843a1825df2bff040c9975f970a71","schema_version":"1.0","event_id":"sha256:602edf5ee7668a50614e6cf4fc2e495f46b843a1825df2bff040c9975f970a71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:YOW7DXUYWDM3AURZF22NL7N2SD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple proof of the Jamiolkowski criterion for complete positivity of linear maps","license":"","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"D. Salgado, J.L. Sanchez-Gomez, M. Ferrero","submitted_at":"2004-06-04T16:13:24Z","abstract_excerpt":"We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a systematic method to give any set of Kraus matrices of its Kraus decomposition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0406010","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0406010/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":"2026-07-04T14:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVTad7oxrJL0DfZtgpAXZnQwenBh1OPutXVQsmEMXmaV01+/lqDhGeCUM3cRCu13yIP7dJz8ms7dwjmoVOz0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T22:49:03.251264Z"},"content_sha256":"9be956b1bb6208d9a8ce327f675e5eacbae7767cbf904b79447b7e03906ac1dd","schema_version":"1.0","event_id":"sha256:9be956b1bb6208d9a8ce327f675e5eacbae7767cbf904b79447b7e03906ac1dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOW7DXUYWDM3AURZF22NL7N2SD/bundle.json","state_url":"https://pith.science/pith/YOW7DXUYWDM3AURZF22NL7N2SD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOW7DXUYWDM3AURZF22NL7N2SD/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":"2026-07-04T22:49:03Z","links":{"resolver":"https://pith.science/pith/YOW7DXUYWDM3AURZF22NL7N2SD","bundle":"https://pith.science/pith/YOW7DXUYWDM3AURZF22NL7N2SD/bundle.json","state":"https://pith.science/pith/YOW7DXUYWDM3AURZF22NL7N2SD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOW7DXUYWDM3AURZF22NL7N2SD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:YOW7DXUYWDM3AURZF22NL7N2SD","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":"25d7d4e35b9eb5e03d6e8a4f17467ce364a5d579c964365a8025de00b7a6a7c1","cross_cats_sorted":["math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-06-04T16:13:24Z","title_canon_sha256":"59ae45849fde0ee56c2de9edf75a7c2ecd14a9e89f71bc8dc404b54c4bd88836"},"schema_version":"1.0","source":{"id":"math-ph/0406010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0406010","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0406010v2","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0406010","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"YOW7DXUYWDM3","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_16","alias_value":"YOW7DXUYWDM3AURZ","created_at":"2026-07-04T14:34:00Z"},{"alias_kind":"pith_short_8","alias_value":"YOW7DXUY","created_at":"2026-07-04T14:34:00Z"}],"graph_snapshots":[{"event_id":"sha256:9be956b1bb6208d9a8ce327f675e5eacbae7767cbf904b79447b7e03906ac1dd","target":"graph","created_at":"2026-07-04T14:34:00Z","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/math-ph/0406010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a systematic method to give any set of Kraus matrices of its Kraus decomposition.","authors_text":"D. Salgado, J.L. Sanchez-Gomez, M. Ferrero","cross_cats":["math.MP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-06-04T16:13:24Z","title":"A simple proof of the Jamiolkowski criterion for complete positivity of linear maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0406010","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":"sha256:602edf5ee7668a50614e6cf4fc2e495f46b843a1825df2bff040c9975f970a71","target":"record","created_at":"2026-07-04T14:34:00Z","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":"25d7d4e35b9eb5e03d6e8a4f17467ce364a5d579c964365a8025de00b7a6a7c1","cross_cats_sorted":["math.MP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-06-04T16:13:24Z","title_canon_sha256":"59ae45849fde0ee56c2de9edf75a7c2ecd14a9e89f71bc8dc404b54c4bd88836"},"schema_version":"1.0","source":{"id":"math-ph/0406010","kind":"arxiv","version":2}},"canonical_sha256":"c3adf1de98b0d9b052392eb4d5fdba90eb7032d8c021788ab306d4b56d8fca0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3adf1de98b0d9b052392eb4d5fdba90eb7032d8c021788ab306d4b56d8fca0b","first_computed_at":"2026-07-04T14:34:00.860437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:34:00.860437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rkq3rAhA7dVVEz5XwpIMfR2mlGlvbphu0Sgaaf202e+3/51Oe8yDLDD5NGblrBIiof1ZYfr1blwqeSAd4PHeCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:34:00.860811Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0406010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:602edf5ee7668a50614e6cf4fc2e495f46b843a1825df2bff040c9975f970a71","sha256:9be956b1bb6208d9a8ce327f675e5eacbae7767cbf904b79447b7e03906ac1dd"],"state_sha256":"f6fd68edab161edcf9043b1b404ae7553ae4a74d37ec20530c44f7c0c6db6d55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKiYhxzQFwRD/8LRacDa98O0KnABNZjsHH/ah1lRNzYF6KSxzTpzrJRW/t617ito5z+8X7qBAjB5fEYGQ9MJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T22:49:03.253047Z","bundle_sha256":"ef877194f7977607ff9333fbc49d2d5c3dab9a434150cf10253f414657ea80b0"}}