{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HJGMXBQJVDOVHZRDL6A5VXXI3K","short_pith_number":"pith:HJGMXBQJ","canonical_record":{"source":{"id":"1406.1277","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-06-05T06:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"2347a59354eb710ca216d7887df123ba56f5222d2a81997dab64c1415848365f","abstract_canon_sha256":"16938e9536a9cd9105d35a744d0b4f6eb349db23bebe697e9bc046987ba64904"},"schema_version":"1.0"},"canonical_sha256":"3a4ccb8609a8dd53e6235f81dadee8daa7dbe91c847d3d15284e930968647fc3","source":{"kind":"arxiv","id":"1406.1277","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1277","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1277v3","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1277","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"pith_short_12","alias_value":"HJGMXBQJVDOV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJGMXBQJVDOVHZRD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJGMXBQJ","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HJGMXBQJVDOVHZRDL6A5VXXI3K","target":"record","payload":{"canonical_record":{"source":{"id":"1406.1277","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-06-05T06:57:03Z","cross_cats_sorted":[],"title_canon_sha256":"2347a59354eb710ca216d7887df123ba56f5222d2a81997dab64c1415848365f","abstract_canon_sha256":"16938e9536a9cd9105d35a744d0b4f6eb349db23bebe697e9bc046987ba64904"},"schema_version":"1.0"},"canonical_sha256":"3a4ccb8609a8dd53e6235f81dadee8daa7dbe91c847d3d15284e930968647fc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:58.627149Z","signature_b64":"RwgGFrVb4mIPjQh8iEXe2Tw8UtxtQbzH53nnWv86fB5CD5jWs+2zH/DAk09cnh0slnFGmD1CGuAGJ42v7tgtDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a4ccb8609a8dd53e6235f81dadee8daa7dbe91c847d3d15284e930968647fc3","last_reissued_at":"2026-05-18T02:23:58.626502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:58.626502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.1277","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8G8eDEyeAgpsnnvw/dfX916g5+J/mnzwc4OieHFuzpeNFP9qzYCIhFLH4zBT9fo4R8jWEYuMwY5Doxib5RDDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:59:10.857805Z"},"content_sha256":"3b15ed533521e604e274d8f34c211fe782d0650f743774ac83d70728e163f639","schema_version":"1.0","event_id":"sha256:3b15ed533521e604e274d8f34c211fe782d0650f743774ac83d70728e163f639"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HJGMXBQJVDOVHZRDL6A5VXXI3K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive reduction from spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Reeb, Ion Nechita, Maria Anastasia Jivulescu, Nicolae Lupa","submitted_at":"2014-06-05T06:57:03Z","abstract_excerpt":"We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear inequalities, which the spectrum has to verify. Our conditions become explicit when one of the two subsystems is a qubit, as well as for further sets of states. Finally, we introduce a family of simple entanglement criteria for spectra, closely related to the reduction and positive partial transpose criteria, which also provide new insight into the set of spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1277","kind":"arxiv","version":3},"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":"2026-05-18T02:23:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHnl0993d0Up++p2KXjD9SBhwqodj1LqD1yhvLR3X3yTQdtxqn87FBfEK5oRZsI1OZud2cVQ71HtdrtBjcUjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:59:10.858143Z"},"content_sha256":"7b523f1f1133410c87facee1847b558558911500126228c9ac45385e98fdae06","schema_version":"1.0","event_id":"sha256:7b523f1f1133410c87facee1847b558558911500126228c9ac45385e98fdae06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/bundle.json","state_url":"https://pith.science/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/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":"2026-06-27T03:59:10Z","links":{"resolver":"https://pith.science/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K","bundle":"https://pith.science/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/bundle.json","state":"https://pith.science/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJGMXBQJVDOVHZRDL6A5VXXI3K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HJGMXBQJVDOVHZRDL6A5VXXI3K","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":"16938e9536a9cd9105d35a744d0b4f6eb349db23bebe697e9bc046987ba64904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-06-05T06:57:03Z","title_canon_sha256":"2347a59354eb710ca216d7887df123ba56f5222d2a81997dab64c1415848365f"},"schema_version":"1.0","source":{"id":"1406.1277","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.1277","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"arxiv_version","alias_value":"1406.1277v3","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1277","created_at":"2026-05-18T02:23:58Z"},{"alias_kind":"pith_short_12","alias_value":"HJGMXBQJVDOV","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HJGMXBQJVDOVHZRD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HJGMXBQJ","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:7b523f1f1133410c87facee1847b558558911500126228c9ac45385e98fdae06","target":"graph","created_at":"2026-05-18T02:23:58Z","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 the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear inequalities, which the spectrum has to verify. Our conditions become explicit when one of the two subsystems is a qubit, as well as for further sets of states. Finally, we introduce a family of simple entanglement criteria for spectra, closely related to the reduction and positive partial transpose criteria, which also provide new insight into the set of spec","authors_text":"David Reeb, Ion Nechita, Maria Anastasia Jivulescu, Nicolae Lupa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-06-05T06:57:03Z","title":"Positive reduction from spectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1277","kind":"arxiv","version":3},"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":"sha256:3b15ed533521e604e274d8f34c211fe782d0650f743774ac83d70728e163f639","target":"record","created_at":"2026-05-18T02:23:58Z","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":"16938e9536a9cd9105d35a744d0b4f6eb349db23bebe697e9bc046987ba64904","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-06-05T06:57:03Z","title_canon_sha256":"2347a59354eb710ca216d7887df123ba56f5222d2a81997dab64c1415848365f"},"schema_version":"1.0","source":{"id":"1406.1277","kind":"arxiv","version":3}},"canonical_sha256":"3a4ccb8609a8dd53e6235f81dadee8daa7dbe91c847d3d15284e930968647fc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a4ccb8609a8dd53e6235f81dadee8daa7dbe91c847d3d15284e930968647fc3","first_computed_at":"2026-05-18T02:23:58.626502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:58.626502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RwgGFrVb4mIPjQh8iEXe2Tw8UtxtQbzH53nnWv86fB5CD5jWs+2zH/DAk09cnh0slnFGmD1CGuAGJ42v7tgtDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:58.627149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.1277","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b15ed533521e604e274d8f34c211fe782d0650f743774ac83d70728e163f639","sha256:7b523f1f1133410c87facee1847b558558911500126228c9ac45385e98fdae06"],"state_sha256":"304212fe36374488cd5a1ccf734d9e8da65bcc8972b931bda405923c4e4fe4e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m9wUVrfKmwRcwUN4cUigMWIJ9qx1XcK4xW994KrLsq3b1UKQdbI0Kr9Be5+46RVIQM1rg74PM0yh1FAUwJAkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:59:10.859985Z","bundle_sha256":"234ad0067a7d891eb6947622c4e05b90093a682ebff9c8d68b22302a3e0b27a1"}}