{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ASPV5AM7MDJB3UYIWQ76HB4QLI","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":"3a5498cfc4874a6e83c6901034035e541195e6a7d66c4a3e9d5d8d081665ad5b","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-28T20:39:13Z","title_canon_sha256":"4b6966f15d3cd266e132c08ee8d50ccd9f213d4679214fdcc6712c1746d5172c"},"schema_version":"1.0","source":{"id":"1505.07854","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07854","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07854v2","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07854","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"ASPV5AM7MDJB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASPV5AM7MDJB3UYI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASPV5AM7","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d954621e08067a4e2290f593ba7b0de712a24fa81dadb25190da1eaf8774a4a0","target":"graph","created_at":"2026-05-18T01:23:12Z","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 provide a straightforward generalization of a positive map in $M_3(\\mathbb{C})$ considered recently by Miller and Olkiewicz \\cite{Miller}. It is proved that these maps are optimal and indecomposable. As a byproduct we provide a class of PPT entangled states in $d \\otimes d$.","authors_text":"Adam Rutkowski, Dariusz Chru\\'sci\\'nski, Gniewomir Sarbicki","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-28T20:39:13Z","title":"A class of bistochastic positive optimal maps in $M_d(\\mathbb{C})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07854","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":"sha256:8a3eeb7b72c4dce90830d2450d32e6ad585e91c3438382b5a7a69fa646c40fa5","target":"record","created_at":"2026-05-18T01:23:12Z","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":"3a5498cfc4874a6e83c6901034035e541195e6a7d66c4a3e9d5d8d081665ad5b","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-05-28T20:39:13Z","title_canon_sha256":"4b6966f15d3cd266e132c08ee8d50ccd9f213d4679214fdcc6712c1746d5172c"},"schema_version":"1.0","source":{"id":"1505.07854","kind":"arxiv","version":2}},"canonical_sha256":"049f5e819f60d21dd308b43fe387905a295af80ab58d4978d8539f12caa98134","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"049f5e819f60d21dd308b43fe387905a295af80ab58d4978d8539f12caa98134","first_computed_at":"2026-05-18T01:23:12.238073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:12.238073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ocESpW5+sdP5rcT+LeR89L7qfEUt8dh2v9EfthWV+DNSyUhmIAawT6SZ3mVRWlewn2PUu+h6R9vdUOcM+WxkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:12.238690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07854","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3eeb7b72c4dce90830d2450d32e6ad585e91c3438382b5a7a69fa646c40fa5","sha256:d954621e08067a4e2290f593ba7b0de712a24fa81dadb25190da1eaf8774a4a0"],"state_sha256":"bc90175cd7455569093991ea1b6f5cac906fe7e53361335751aa92f336c2a1f4"}