{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UQQ23W5JIKJRMBLM3VT6LBOMDJ","short_pith_number":"pith:UQQ23W5J","canonical_record":{"source":{"id":"1207.1479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T22:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"d1746182212fd7971d391f27d13eba73302dc63c30db6d2c53e97c3063790b98","abstract_canon_sha256":"d3011f4bb8c3c67a775c5b22980115393f38be2a27537971f708fc1801819980"},"schema_version":"1.0"},"canonical_sha256":"a421addba9429316056cdd67e585cc1a671fc24f28fb195764027fd7b15f24ed","source":{"kind":"arxiv","id":"1207.1479","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1479","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1479v1","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1479","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"UQQ23W5JIKJR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UQQ23W5JIKJRMBLM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UQQ23W5J","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UQQ23W5JIKJRMBLM3VT6LBOMDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1479","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T22:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"d1746182212fd7971d391f27d13eba73302dc63c30db6d2c53e97c3063790b98","abstract_canon_sha256":"d3011f4bb8c3c67a775c5b22980115393f38be2a27537971f708fc1801819980"},"schema_version":"1.0"},"canonical_sha256":"a421addba9429316056cdd67e585cc1a671fc24f28fb195764027fd7b15f24ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:37.039816Z","signature_b64":"hhHhOAFdWmtylqEdHbabF8SIRnZFEvbHDIUic4EGCG2FKTpTMz5Hq3+t8BGw0amCfsJMhM15NB3ToNN01uF6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a421addba9429316056cdd67e585cc1a671fc24f28fb195764027fd7b15f24ed","last_reissued_at":"2026-05-18T03:51:37.039356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:37.039356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1479","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":"2026-05-18T03:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/fKEPwPJhLdpCh684b7DrtNRHHQHa16x/A2lwOCV36ZnM6S2Hkr98gCLJ079hX98UjB/Lg2VywHDqNjpS7pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:01:56.309652Z"},"content_sha256":"c4f621b509e2becceaefe4e3dc85f5cea71165d85821a96745b2de6f02e54bc9","schema_version":"1.0","event_id":"sha256:c4f621b509e2becceaefe4e3dc85f5cea71165d85821a96745b2de6f02e54bc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UQQ23W5JIKJRMBLM3VT6LBOMDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norms and Cones in the Theory of Quantum Entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Nathaniel Johnston","submitted_at":"2012-07-05T22:44:20Z","abstract_excerpt":"There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as \"more\" or \"less\" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity prop"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1479","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":"2026-05-18T03:51:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/ZdWRryWFuzBePPI5evav1dzHk/EdosjQwNt8Mdh7jAgAGow/cWyEyXC39/XeVgaZWrIsnYH0USRKsg+jMqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:01:56.309994Z"},"content_sha256":"9f2feafdb0ee41f0e84652ccd848c128f6e3957652d80588661cd1e63bd7f1f9","schema_version":"1.0","event_id":"sha256:9f2feafdb0ee41f0e84652ccd848c128f6e3957652d80588661cd1e63bd7f1f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/bundle.json","state_url":"https://pith.science/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/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":"2026-06-04T17:01:56Z","links":{"resolver":"https://pith.science/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ","bundle":"https://pith.science/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/bundle.json","state":"https://pith.science/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQQ23W5JIKJRMBLM3VT6LBOMDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UQQ23W5JIKJRMBLM3VT6LBOMDJ","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":"d3011f4bb8c3c67a775c5b22980115393f38be2a27537971f708fc1801819980","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T22:44:20Z","title_canon_sha256":"d1746182212fd7971d391f27d13eba73302dc63c30db6d2c53e97c3063790b98"},"schema_version":"1.0","source":{"id":"1207.1479","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1479","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1479v1","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1479","created_at":"2026-05-18T03:51:37Z"},{"alias_kind":"pith_short_12","alias_value":"UQQ23W5JIKJR","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UQQ23W5JIKJRMBLM","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UQQ23W5J","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:9f2feafdb0ee41f0e84652ccd848c128f6e3957652d80588661cd1e63bd7f1f9","target":"graph","created_at":"2026-05-18T03:51:37Z","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":"There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as \"more\" or \"less\" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity prop","authors_text":"Nathaniel Johnston","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T22:44:20Z","title":"Norms and Cones in the Theory of Quantum Entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1479","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:c4f621b509e2becceaefe4e3dc85f5cea71165d85821a96745b2de6f02e54bc9","target":"record","created_at":"2026-05-18T03:51:37Z","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":"d3011f4bb8c3c67a775c5b22980115393f38be2a27537971f708fc1801819980","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-07-05T22:44:20Z","title_canon_sha256":"d1746182212fd7971d391f27d13eba73302dc63c30db6d2c53e97c3063790b98"},"schema_version":"1.0","source":{"id":"1207.1479","kind":"arxiv","version":1}},"canonical_sha256":"a421addba9429316056cdd67e585cc1a671fc24f28fb195764027fd7b15f24ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a421addba9429316056cdd67e585cc1a671fc24f28fb195764027fd7b15f24ed","first_computed_at":"2026-05-18T03:51:37.039356Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:37.039356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhHhOAFdWmtylqEdHbabF8SIRnZFEvbHDIUic4EGCG2FKTpTMz5Hq3+t8BGw0amCfsJMhM15NB3ToNN01uF6Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:37.039816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1479","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4f621b509e2becceaefe4e3dc85f5cea71165d85821a96745b2de6f02e54bc9","sha256:9f2feafdb0ee41f0e84652ccd848c128f6e3957652d80588661cd1e63bd7f1f9"],"state_sha256":"9796010ed36581c283610cae8436dcc06ab4d99c17cac30df3a868504c81c6fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"80U8GPK8PVaFL4z7slzOjLigW2sww7XWqEPr01Dj5BDP94J16vjjSQyDdfP6JhYBZxUWSctQ83Rj1Anr/0/4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:01:56.312014Z","bundle_sha256":"ace85ea9b2e3a6f9450c58521e9d892f26d8678b9219fec233e9b2f428f50a9f"}}