{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:RT7Z6LDFOXA3XDMKEW5TKAMLX3","short_pith_number":"pith:RT7Z6LDF","canonical_record":{"source":{"id":"quant-ph/9703004","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1997-03-04T17:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"27c7e6a460a07b00481da5c0c5cff12d6541d1236478396836d6c6477e3cc220","abstract_canon_sha256":"f4796b7c4826cff2b61a7b0ae20b50dfe1da841582e1d9743fdcaaee4c046251"},"schema_version":"1.0"},"canonical_sha256":"8cff9f2c6575c1bb8d8a25bb35018bbef45153c9b36cf3fe0a090ebfd08d418f","source":{"kind":"arxiv","id":"quant-ph/9703004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9703004","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9703004v2","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9703004","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"RT7Z6LDFOXA3","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"RT7Z6LDFOXA3XDMK","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"RT7Z6LDF","created_at":"2026-07-04T16:06:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:RT7Z6LDFOXA3XDMKEW5TKAMLX3","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9703004","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1997-03-04T17:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"27c7e6a460a07b00481da5c0c5cff12d6541d1236478396836d6c6477e3cc220","abstract_canon_sha256":"f4796b7c4826cff2b61a7b0ae20b50dfe1da841582e1d9743fdcaaee4c046251"},"schema_version":"1.0"},"canonical_sha256":"8cff9f2c6575c1bb8d8a25bb35018bbef45153c9b36cf3fe0a090ebfd08d418f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:28.462788Z","signature_b64":"yL6O6sEfbEvsaemka4HpcxM3y1uD0Mx+Q4D82OskzDEeD/FjBUC23MyIJrMHXsGCyMZRvT6T+MxrtCRy4mENAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8cff9f2c6575c1bb8d8a25bb35018bbef45153c9b36cf3fe0a090ebfd08d418f","last_reissued_at":"2026-07-04T16:06:28.462439Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:28.462439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9703004","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":"2026-07-04T16:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvurXOqqmnsVtcCksjBSEdGXDmqjt6JQ27PSw+t3i/AzUk3xX7jXSR/NcS5y2gR3D06KY2hgZoNhbWUnN8l7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T18:34:09.308583Z"},"content_sha256":"b5fa036151a894d15ed3027fae2d5f4ef43ec1d38fe59b653708282d43e77572","schema_version":"1.0","event_id":"sha256:b5fa036151a894d15ed3027fae2d5f4ef43ec1d38fe59b653708282d43e77572"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:RT7Z6LDFOXA3XDMKEW5TKAMLX3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separability criterion and inseparable mixed states with positive partial transposition","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Pawel Horodecki","submitted_at":"1997-03-04T17:25:38Z","abstract_excerpt":"It is shown that any separable state on Hilbert space ${\\cal H}={\\cal H}_1\\otimes{\\cal H}_2$, can be written as a convex combination of N pure product states with $N\\leq (dim{\\cal H})^2$. Then a new separability criterion for mixed states in terms of range of density matrix is obtained. It is used in construction of inseparable mixed states with positive partial transposition in the case of $3\\times 3$ and $2\\times 4$ systems. The states represent an entanglement which is hidden in a more subtle way than it has been known so far."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9703004","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/quant-ph/9703004/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":"2026-07-04T16:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RpBM+p+LKz2Su7J/+ps2wsJFYNLpdYagX8V/hORzEnIsR0e+DUdtdliaCnoc7j+wwmun88h6lzdgQbHyDyDhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T18:34:09.308960Z"},"content_sha256":"3cc962b33a3c528c77812dcfbce5abb8d43ef421c93f4e7fa5e0c0e7fa5c6241","schema_version":"1.0","event_id":"sha256:3cc962b33a3c528c77812dcfbce5abb8d43ef421c93f4e7fa5e0c0e7fa5c6241"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/bundle.json","state_url":"https://pith.science/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/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":"2026-07-13T18:34:09Z","links":{"resolver":"https://pith.science/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3","bundle":"https://pith.science/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/bundle.json","state":"https://pith.science/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RT7Z6LDFOXA3XDMKEW5TKAMLX3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:RT7Z6LDFOXA3XDMKEW5TKAMLX3","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":"f4796b7c4826cff2b61a7b0ae20b50dfe1da841582e1d9743fdcaaee4c046251","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1997-03-04T17:25:38Z","title_canon_sha256":"27c7e6a460a07b00481da5c0c5cff12d6541d1236478396836d6c6477e3cc220"},"schema_version":"1.0","source":{"id":"quant-ph/9703004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9703004","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9703004v2","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9703004","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"RT7Z6LDFOXA3","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_16","alias_value":"RT7Z6LDFOXA3XDMK","created_at":"2026-07-04T16:06:28Z"},{"alias_kind":"pith_short_8","alias_value":"RT7Z6LDF","created_at":"2026-07-04T16:06:28Z"}],"graph_snapshots":[{"event_id":"sha256:3cc962b33a3c528c77812dcfbce5abb8d43ef421c93f4e7fa5e0c0e7fa5c6241","target":"graph","created_at":"2026-07-04T16:06:28Z","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/9703004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that any separable state on Hilbert space ${\\cal H}={\\cal H}_1\\otimes{\\cal H}_2$, can be written as a convex combination of N pure product states with $N\\leq (dim{\\cal H})^2$. Then a new separability criterion for mixed states in terms of range of density matrix is obtained. It is used in construction of inseparable mixed states with positive partial transposition in the case of $3\\times 3$ and $2\\times 4$ systems. The states represent an entanglement which is hidden in a more subtle way than it has been known so far.","authors_text":"Pawel Horodecki","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1997-03-04T17:25:38Z","title":"Separability criterion and inseparable mixed states with positive partial transposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9703004","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:b5fa036151a894d15ed3027fae2d5f4ef43ec1d38fe59b653708282d43e77572","target":"record","created_at":"2026-07-04T16:06:28Z","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":"f4796b7c4826cff2b61a7b0ae20b50dfe1da841582e1d9743fdcaaee4c046251","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1997-03-04T17:25:38Z","title_canon_sha256":"27c7e6a460a07b00481da5c0c5cff12d6541d1236478396836d6c6477e3cc220"},"schema_version":"1.0","source":{"id":"quant-ph/9703004","kind":"arxiv","version":2}},"canonical_sha256":"8cff9f2c6575c1bb8d8a25bb35018bbef45153c9b36cf3fe0a090ebfd08d418f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8cff9f2c6575c1bb8d8a25bb35018bbef45153c9b36cf3fe0a090ebfd08d418f","first_computed_at":"2026-07-04T16:06:28.462439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:06:28.462439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yL6O6sEfbEvsaemka4HpcxM3y1uD0Mx+Q4D82OskzDEeD/FjBUC23MyIJrMHXsGCyMZRvT6T+MxrtCRy4mENAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:06:28.462788Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9703004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5fa036151a894d15ed3027fae2d5f4ef43ec1d38fe59b653708282d43e77572","sha256:3cc962b33a3c528c77812dcfbce5abb8d43ef421c93f4e7fa5e0c0e7fa5c6241"],"state_sha256":"3feb6195c99fce228e29feaf2e35a07ef9e972a0ab70d127b714dac8340cbc92"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYu7xXrwDtQpQfyJlDLMjhMNt7Gc28ESYidXhLfwVmHa/o7ixPstwrnuE9uwkedLTQ7mYrr+LAoYCuo63cZ5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T18:34:09.311236Z","bundle_sha256":"485c446795beaac6f812c5478c7e048e9b2437047e2fc83be394d091ef1b570b"}}