{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KFNWT5753QM6J3NLEAR3F6TI33","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":"6e573a3b8192e61c96a746ee910421738d7d6bad6157dfdddca58d6e6443db28","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-02-27T17:41:36Z","title_canon_sha256":"007e9ead55b132430d70503e77e9f75d9f33ebd5d1320becd7703c524b9cc81e"},"schema_version":"1.0","source":{"id":"0902.4877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.4877","created_at":"2026-05-18T02:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"0902.4877v1","created_at":"2026-05-18T02:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.4877","created_at":"2026-05-18T02:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"KFNWT5753QM6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KFNWT5753QM6J3NL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KFNWT575","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:90abbe0082fe1c18fa6f06121a04725ae0c77ab0095f723fdc1104b754193388","target":"graph","created_at":"2026-05-18T02:14:38Z","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":"The structure of cones of positive and k-positive maps acting on a finite-dimensional Hilbert space is investigated. Special emphasis is given to their duality relations to the sets of superpositive and k-superpositive maps. We characterize k-positive and k-superpositive maps with regard to their properties under taking compositions. A number of results obtained for maps are also rephrased for the corresponding cones of block positive, k-block positive, separable and k-separable operators, due to the Jamiolkowski-Choi isomorphism. Generalizations to a situation where no such simple isomorphism","authors_text":"Erling Stormer, Karol Zyczkowski, Lukasz Skowronek","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-02-27T17:41:36Z","title":"Cones of positive maps and their duality relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.4877","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":"sha256:2a8e8d414fa73698a602d8a9cc5b78a402164800b85350573dfba9dd5a7d9f46","target":"record","created_at":"2026-05-18T02:14:38Z","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":"6e573a3b8192e61c96a746ee910421738d7d6bad6157dfdddca58d6e6443db28","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-02-27T17:41:36Z","title_canon_sha256":"007e9ead55b132430d70503e77e9f75d9f33ebd5d1320becd7703c524b9cc81e"},"schema_version":"1.0","source":{"id":"0902.4877","kind":"arxiv","version":1}},"canonical_sha256":"515b69f7fddc19e4edab2023b2fa68decf2ad3102577a291588d339e1f2ff66f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515b69f7fddc19e4edab2023b2fa68decf2ad3102577a291588d339e1f2ff66f","first_computed_at":"2026-05-18T02:14:38.222092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:38.222092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eor5aSM2+5OCqkwNH9IYShzD+yrFPnPiXDqdFCJbx2e4H82eIF8b39C4YyFNBdoi43XeJof3rmr3+z8Ns17FCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:38.222870Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.4877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8e8d414fa73698a602d8a9cc5b78a402164800b85350573dfba9dd5a7d9f46","sha256:90abbe0082fe1c18fa6f06121a04725ae0c77ab0095f723fdc1104b754193388"],"state_sha256":"7e3a02fed558ed0352b82125de51d0da159c22c79e5bad96c3c86087861da11f"}