{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZSK732MPRRYGCUFVWX6NE2OTB4","short_pith_number":"pith:ZSK732MP","canonical_record":{"source":{"id":"1611.01194","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-03T21:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"000b3e813023d1899919c990926ecc8ac6f356013365d2ec3e923ce1e7b4050a","abstract_canon_sha256":"f51f418ceecb823b6ed6d9d1b0424dc8387c366ad732c58c2f428494685881ab"},"schema_version":"1.0"},"canonical_sha256":"cc95fde98f8c706150b5b5fcd269d30f053c8bda134e95c3e50ef0ac77774b2f","source":{"kind":"arxiv","id":"1611.01194","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01194","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01194v2","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01194","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZSK732MPRRYG","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZSK732MPRRYGCUFV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZSK732MP","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZSK732MPRRYGCUFVWX6NE2OTB4","target":"record","payload":{"canonical_record":{"source":{"id":"1611.01194","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-03T21:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"000b3e813023d1899919c990926ecc8ac6f356013365d2ec3e923ce1e7b4050a","abstract_canon_sha256":"f51f418ceecb823b6ed6d9d1b0424dc8387c366ad732c58c2f428494685881ab"},"schema_version":"1.0"},"canonical_sha256":"cc95fde98f8c706150b5b5fcd269d30f053c8bda134e95c3e50ef0ac77774b2f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:44.622626Z","signature_b64":"1LDL+b/i1mzbK5Dw6vzYlWNnN3atVghu4rLKNG1UOFFuaPDRFlul+sNCW/I7SDaPV1hhyikk2FvKlGBzSa0FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc95fde98f8c706150b5b5fcd269d30f053c8bda134e95c3e50ef0ac77774b2f","last_reissued_at":"2026-05-17T23:52:44.621944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:44.621944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.01194","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjohPaq4xA/7ysUt4lV5pYe0qapPUpbVG5PcMRoZ2uUTFmD+epDqXtPixtqt9lAWWs5HvMbT/AXTEvW4aR9CCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:21:59.209682Z"},"content_sha256":"0fa9de55862c8d656afb357b631116ccad11c9e7304347a56a185b1d53b82334","schema_version":"1.0","event_id":"sha256:0fa9de55862c8d656afb357b631116ccad11c9e7304347a56a185b1d53b82334"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZSK732MPRRYGCUFVWX6NE2OTB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex set of quantum states with positive partial transpose analysed by hit and run algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Beno\\^it Collins, Karol \\.Zyczkowski, Konrad Szyma\\'nski, Tomasz Szarek","submitted_at":"2016-11-03T21:11:26Z","abstract_excerpt":"The convex set of quantum states of a composite $K \\times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For $K\\ge 3$ this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive. The level density of the PPT states is shown to differ from the Marchenko-Pastur distribution, supported in [0,4] and corresponding asymptotically to the ent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01194","kind":"arxiv","version":2},"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":"2026-05-17T23:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aAkka9/vcu5ZhYdCNGYoqD6xkdcO0nznnvnQwRImkaLQ/mlPmjMryNg+GfhURdqAENmvnF6eH1sfZsvwBrv2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:21:59.210033Z"},"content_sha256":"83bac84df3eb386ae1cf2054760b6ba5385e88dc4d0a3b34cd46d02e78ef7e18","schema_version":"1.0","event_id":"sha256:83bac84df3eb386ae1cf2054760b6ba5385e88dc4d0a3b34cd46d02e78ef7e18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/bundle.json","state_url":"https://pith.science/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/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":"2026-05-30T13:21:59Z","links":{"resolver":"https://pith.science/pith/ZSK732MPRRYGCUFVWX6NE2OTB4","bundle":"https://pith.science/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/bundle.json","state":"https://pith.science/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSK732MPRRYGCUFVWX6NE2OTB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZSK732MPRRYGCUFVWX6NE2OTB4","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":"f51f418ceecb823b6ed6d9d1b0424dc8387c366ad732c58c2f428494685881ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-03T21:11:26Z","title_canon_sha256":"000b3e813023d1899919c990926ecc8ac6f356013365d2ec3e923ce1e7b4050a"},"schema_version":"1.0","source":{"id":"1611.01194","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01194","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01194v2","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01194","created_at":"2026-05-17T23:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"ZSK732MPRRYG","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZSK732MPRRYGCUFV","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZSK732MP","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:83bac84df3eb386ae1cf2054760b6ba5385e88dc4d0a3b34cd46d02e78ef7e18","target":"graph","created_at":"2026-05-17T23:52:44Z","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 convex set of quantum states of a composite $K \\times K$ system with positive partial transpose is analysed. A version of the hit and run algorithm is used to generate a sequence of random points covering this set uniformly and an estimation for the convergence speed of the algorithm is derived. For $K\\ge 3$ this algorithm works faster than sampling over the entire set of states and verifying whether the partial transpose is positive. The level density of the PPT states is shown to differ from the Marchenko-Pastur distribution, supported in [0,4] and corresponding asymptotically to the ent","authors_text":"Beno\\^it Collins, Karol \\.Zyczkowski, Konrad Szyma\\'nski, Tomasz Szarek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-03T21:11:26Z","title":"Convex set of quantum states with positive partial transpose analysed by hit and run algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01194","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":"sha256:0fa9de55862c8d656afb357b631116ccad11c9e7304347a56a185b1d53b82334","target":"record","created_at":"2026-05-17T23:52:44Z","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":"f51f418ceecb823b6ed6d9d1b0424dc8387c366ad732c58c2f428494685881ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-11-03T21:11:26Z","title_canon_sha256":"000b3e813023d1899919c990926ecc8ac6f356013365d2ec3e923ce1e7b4050a"},"schema_version":"1.0","source":{"id":"1611.01194","kind":"arxiv","version":2}},"canonical_sha256":"cc95fde98f8c706150b5b5fcd269d30f053c8bda134e95c3e50ef0ac77774b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc95fde98f8c706150b5b5fcd269d30f053c8bda134e95c3e50ef0ac77774b2f","first_computed_at":"2026-05-17T23:52:44.621944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:44.621944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1LDL+b/i1mzbK5Dw6vzYlWNnN3atVghu4rLKNG1UOFFuaPDRFlul+sNCW/I7SDaPV1hhyikk2FvKlGBzSa0FCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:44.622626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01194","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fa9de55862c8d656afb357b631116ccad11c9e7304347a56a185b1d53b82334","sha256:83bac84df3eb386ae1cf2054760b6ba5385e88dc4d0a3b34cd46d02e78ef7e18"],"state_sha256":"ca5cdd07895799eda299b0f3017630112f085fb238ed2216d9b22d5f46ced613"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PY/IRgh2ocz2PouGXc3uMmmY/Wtkx9HpH1RDAjurhGideUkDIfm0N2qQbFDv7CVkb/f5jqRSx7GcuI8M35QUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:21:59.211993Z","bundle_sha256":"d6e600300bcea039ae54aa3af025bd98722539f23cd7c3992ec8f3d7f7bd7aeb"}}