{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VVBQLOOCERY6KRDICDET5SSAVO","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":"40e3bc42bb53c6c601b80b4494b6d7b5b11078cc72e2c98ad86789397a3a9bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-20T08:53:29Z","title_canon_sha256":"ea66e788aeb0fedf296d959c84d7c1c70513e1b92b7fb7acaf45c462311993e9"},"schema_version":"1.0","source":{"id":"1202.4255","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4255","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4255v2","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4255","created_at":"2026-05-18T01:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"VVBQLOOCERY6","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VVBQLOOCERY6KRDI","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VVBQLOOC","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:3d19be6307ea2797802ab12fea4754a64caf53854d8e3c049fab187284a6eac1","target":"graph","created_at":"2026-05-18T01:58:23Z","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":"In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.","authors_text":"Seung-Hyeok Kye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-20T08:53:29Z","title":"Facial structures for various notions of positivity and applications to the theory of entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4255","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:bbda2ccf92799482c708453d506d947fccace77dfab0d1145df41c6bd0d4e627","target":"record","created_at":"2026-05-18T01:58:23Z","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":"40e3bc42bb53c6c601b80b4494b6d7b5b11078cc72e2c98ad86789397a3a9bf3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-02-20T08:53:29Z","title_canon_sha256":"ea66e788aeb0fedf296d959c84d7c1c70513e1b92b7fb7acaf45c462311993e9"},"schema_version":"1.0","source":{"id":"1202.4255","kind":"arxiv","version":2}},"canonical_sha256":"ad4305b9c22471e5446810c93eca40ab9574c19bd3a109182cbf4e4699640b8a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad4305b9c22471e5446810c93eca40ab9574c19bd3a109182cbf4e4699640b8a","first_computed_at":"2026-05-18T01:58:23.675531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:58:23.675531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bkddJ6pcGoOuW+cLin1yTxoDCqRMUK4PSCX8JErdY7+IzZ5ZsB4cn1KXfTPNQiMo6A/+ibWKw1pVcZgGLuMDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:58:23.676025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4255","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbda2ccf92799482c708453d506d947fccace77dfab0d1145df41c6bd0d4e627","sha256:3d19be6307ea2797802ab12fea4754a64caf53854d8e3c049fab187284a6eac1"],"state_sha256":"7309cf409ff51d6a0ec72fc635cf6782e078afbdc68e8749a9a81ee6874c83c3"}