{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3AIJHOZ7XDAL4RUPZWJPMAHTCY","short_pith_number":"pith:3AIJHOZ7","canonical_record":{"source":{"id":"1211.0386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-11-02T08:02:48Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"10c1e408f9ae7801b4e7597567749eeb4912846d281e8669591f70640292de0c","abstract_canon_sha256":"8204a55709a86fa8b11711f4769cb702d0ea8e3b8c176c9729ffb19849168863"},"schema_version":"1.0"},"canonical_sha256":"d81093bb3fb8c0be468fcd92f600f3161ddb3bc33083c30ed1055f8c73352f55","source":{"kind":"arxiv","id":"1211.0386","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0386","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0386v2","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0386","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"3AIJHOZ7XDAL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3AIJHOZ7XDAL4RUP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3AIJHOZ7","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3AIJHOZ7XDAL4RUPZWJPMAHTCY","target":"record","payload":{"canonical_record":{"source":{"id":"1211.0386","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-11-02T08:02:48Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"10c1e408f9ae7801b4e7597567749eeb4912846d281e8669591f70640292de0c","abstract_canon_sha256":"8204a55709a86fa8b11711f4769cb702d0ea8e3b8c176c9729ffb19849168863"},"schema_version":"1.0"},"canonical_sha256":"d81093bb3fb8c0be468fcd92f600f3161ddb3bc33083c30ed1055f8c73352f55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.465637Z","signature_b64":"jYhSJ+pvS1GR4WBjw5TqEtRMksSL71ITCYD4ctgNUAEJNlhYW58cUBFZqP4CUJhBozkTaTE7AFcrqSJnGlFgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d81093bb3fb8c0be468fcd92f600f3161ddb3bc33083c30ed1055f8c73352f55","last_reissued_at":"2026-05-18T03:31:06.464909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.464909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.0386","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":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FD6ApIaDTDeo/7/Y3M0aZ+rW2LzSAJ1STFdsUFg7OkjWzrpj7vm1yLQuBmBMHzRAHXGQ4DZ1/qOjLOhPzALODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:22:16.841405Z"},"content_sha256":"6ba0eb2ae45972ab9f05167924d14d2b4519675cb25cc634007837d665d52816","schema_version":"1.0","event_id":"sha256:6ba0eb2ae45972ab9f05167924d14d2b4519675cb25cc634007837d665d52816"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3AIJHOZ7XDAL4RUPZWJPMAHTCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Criteria and new classes of k-positive maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"quant-ph","authors_text":"Chi-Kwong Li, Jinchuan Hou, Nung-sing Sze, Xiaofei Qi, Yiu-Tung Poon","submitted_at":"2012-11-02T08:02:48Z","abstract_excerpt":"We study k-positive maps on operators. Proofs are given to different positivity criteria. Special attention is on positive maps arising in the study of quantum information science. Results of other researchers are extended and improved. New classes of positive maps are constructed. Some open questions are answered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0386","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":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R5+g4JJqK5rQ5Z8YtCLf8iL3GPqEJ16BvbtnZvLSofjTRAYSKxx30zGh42S+smhu+9OjYE7e8QpgYc4NmDw0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T09:22:16.841848Z"},"content_sha256":"cea0c3defefe935b09f1c7a3782aa0af9dc57e3642f68a5c050c95b5507ee26e","schema_version":"1.0","event_id":"sha256:cea0c3defefe935b09f1c7a3782aa0af9dc57e3642f68a5c050c95b5507ee26e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/bundle.json","state_url":"https://pith.science/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/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":"2026-05-28T09:22:16Z","links":{"resolver":"https://pith.science/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY","bundle":"https://pith.science/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/bundle.json","state":"https://pith.science/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3AIJHOZ7XDAL4RUPZWJPMAHTCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3AIJHOZ7XDAL4RUPZWJPMAHTCY","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":"8204a55709a86fa8b11711f4769cb702d0ea8e3b8c176c9729ffb19849168863","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-11-02T08:02:48Z","title_canon_sha256":"10c1e408f9ae7801b4e7597567749eeb4912846d281e8669591f70640292de0c"},"schema_version":"1.0","source":{"id":"1211.0386","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0386","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0386v2","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0386","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"3AIJHOZ7XDAL","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3AIJHOZ7XDAL4RUP","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3AIJHOZ7","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:cea0c3defefe935b09f1c7a3782aa0af9dc57e3642f68a5c050c95b5507ee26e","target":"graph","created_at":"2026-05-18T03:31:06Z","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":"We study k-positive maps on operators. Proofs are given to different positivity criteria. Special attention is on positive maps arising in the study of quantum information science. Results of other researchers are extended and improved. New classes of positive maps are constructed. Some open questions are answered.","authors_text":"Chi-Kwong Li, Jinchuan Hou, Nung-sing Sze, Xiaofei Qi, Yiu-Tung Poon","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-11-02T08:02:48Z","title":"Criteria and new classes of k-positive maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0386","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":"sha256:6ba0eb2ae45972ab9f05167924d14d2b4519675cb25cc634007837d665d52816","target":"record","created_at":"2026-05-18T03:31:06Z","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":"8204a55709a86fa8b11711f4769cb702d0ea8e3b8c176c9729ffb19849168863","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-11-02T08:02:48Z","title_canon_sha256":"10c1e408f9ae7801b4e7597567749eeb4912846d281e8669591f70640292de0c"},"schema_version":"1.0","source":{"id":"1211.0386","kind":"arxiv","version":2}},"canonical_sha256":"d81093bb3fb8c0be468fcd92f600f3161ddb3bc33083c30ed1055f8c73352f55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d81093bb3fb8c0be468fcd92f600f3161ddb3bc33083c30ed1055f8c73352f55","first_computed_at":"2026-05-18T03:31:06.464909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:06.464909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jYhSJ+pvS1GR4WBjw5TqEtRMksSL71ITCYD4ctgNUAEJNlhYW58cUBFZqP4CUJhBozkTaTE7AFcrqSJnGlFgAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:06.465637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0386","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba0eb2ae45972ab9f05167924d14d2b4519675cb25cc634007837d665d52816","sha256:cea0c3defefe935b09f1c7a3782aa0af9dc57e3642f68a5c050c95b5507ee26e"],"state_sha256":"c0fd06f07403c4e39de3bdd13a54bd1fe0bcb012ae331c83517f1cb6745ab85a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dlXBPkcD0/cj2uWF3jCT9eb1D784oUFCy20Xh71cEaEZIV8BNuVulCKgwQkeuaqaKMrZh6Qer/LlUk+PNwIHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T09:22:16.843792Z","bundle_sha256":"b04ad2cd3660b0a357ae1e8f4335696e6694110382e39eeba1dbc78968a3a281"}}