{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:GGVQTTJ4JIEH6NDZA3LUMHCJDL","short_pith_number":"pith:GGVQTTJ4","canonical_record":{"source":{"id":"quant-ph/0605251","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-05-31T16:26:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d567ba35f103ba5c2ebcde6a5e8eb85462821bff8f0fb8d7c169332c011babbf","abstract_canon_sha256":"9d4351d5c2aba728c3b9945e32e8a834ad4879e92d7ff6f7099d12ce8ae7ac84"},"schema_version":"1.0"},"canonical_sha256":"31ab09cd3c4a087f347906d7461c491ae977dca3fab5ee8e297658fb523c1d46","source":{"kind":"arxiv","id":"quant-ph/0605251","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0605251","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0605251v2","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0605251","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"GGVQTTJ4JIEH","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"GGVQTTJ4JIEH6NDZ","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"GGVQTTJ4","created_at":"2026-07-04T14:58:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:GGVQTTJ4JIEH6NDZA3LUMHCJDL","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0605251","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2006-05-31T16:26:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d567ba35f103ba5c2ebcde6a5e8eb85462821bff8f0fb8d7c169332c011babbf","abstract_canon_sha256":"9d4351d5c2aba728c3b9945e32e8a834ad4879e92d7ff6f7099d12ce8ae7ac84"},"schema_version":"1.0"},"canonical_sha256":"31ab09cd3c4a087f347906d7461c491ae977dca3fab5ee8e297658fb523c1d46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:58:17.165381Z","signature_b64":"2YCT1l4g5pVN6BDs9uyGAoTmWBtVkAJzau4zNgRWc4dQ9FVNN5z1+ruYR/SShC9VJbpJjOAnQeBc4AeQ7w8eAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ab09cd3c4a087f347906d7461c491ae977dca3fab5ee8e297658fb523c1d46","last_reissued_at":"2026-07-04T14:58:17.164965Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:58:17.164965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0605251","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":"2026-07-04T14:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6qVnsVd6r964p5HBIvJNvVdF9BkY3bzGcw5OIMuDLP7yYe7ms3XeuWOTFwLPhzfIsXqIVHh63om/fpsvv0YBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:05:42.085636Z"},"content_sha256":"6e4595a41e4cad1cfa2a8720774827980cb94fc935f89cfa6cee8b57d9ec9166","schema_version":"1.0","event_id":"sha256:6e4595a41e4cad1cfa2a8720774827980cb94fc935f89cfa6cee8b57d9ec9166"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:GGVQTTJ4JIEH6NDZA3LUMHCJDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution of G-concurrence of random pure states","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"(2) Fachbereich Physik, 3) ((1) Centrum Fizyki Teoretycznej, (3) Instytut Fizyki im. Smoluchowskiego, Campus Duisburg, Duisburg, Germany, Hans-Juergen Sommers (2), Karol Zyczkowski (1, Krakow, Poland, Poland), Polska Akademia Nauk, Universitat Duisburg-Essen, Uniwersytet Jagiellonski, Valerio Cappellini (1), Warszawa","submitted_at":"2006-05-31T16:26:33Z","abstract_excerpt":"Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant we characterize the probability distribution P(D). Similar results are obtained for the rescaled N-th root of the determinant, called G-concurrence. We show that in the limit $N\\to\\infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0605251","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0605251/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:58:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yfmHrltECcLfyr3q6pPBGaDu+x1foTn7R/7SKin+4e9ZJ7cZ7JwIFLP8Ts9TBFQ2EIpv8J8CuxPyE7IdgfQdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:05:42.086126Z"},"content_sha256":"7922cf9aa53e75b3c1a995aa5c9a1eba65456e9b3effd90eef6ef9c0be587d85","schema_version":"1.0","event_id":"sha256:7922cf9aa53e75b3c1a995aa5c9a1eba65456e9b3effd90eef6ef9c0be587d85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/bundle.json","state_url":"https://pith.science/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/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":"2026-08-06T20:05:42Z","links":{"resolver":"https://pith.science/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL","bundle":"https://pith.science/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/bundle.json","state":"https://pith.science/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGVQTTJ4JIEH6NDZA3LUMHCJDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:GGVQTTJ4JIEH6NDZA3LUMHCJDL","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":"9d4351d5c2aba728c3b9945e32e8a834ad4879e92d7ff6f7099d12ce8ae7ac84","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-05-31T16:26:33Z","title_canon_sha256":"d567ba35f103ba5c2ebcde6a5e8eb85462821bff8f0fb8d7c169332c011babbf"},"schema_version":"1.0","source":{"id":"quant-ph/0605251","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0605251","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0605251v2","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0605251","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_12","alias_value":"GGVQTTJ4JIEH","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_16","alias_value":"GGVQTTJ4JIEH6NDZ","created_at":"2026-07-04T14:58:17Z"},{"alias_kind":"pith_short_8","alias_value":"GGVQTTJ4","created_at":"2026-07-04T14:58:17Z"}],"graph_snapshots":[{"event_id":"sha256:7922cf9aa53e75b3c1a995aa5c9a1eba65456e9b3effd90eef6ef9c0be587d85","target":"graph","created_at":"2026-07-04T14:58:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/0605251/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Average entanglement of random pure states of an N x N composite system is analyzed. We compute the average value of the determinant D of the reduced state, which forms an entanglement monotone. Calculating higher moments of the determinant we characterize the probability distribution P(D). Similar results are obtained for the rescaled N-th root of the determinant, called G-concurrence. We show that in the limit $N\\to\\infty$ this quantity becomes concentrated at a single point G=1/e. The position of the concentration point changes if one consider an arbitrary N x K bipartite system, in the joi","authors_text":"(2) Fachbereich Physik, 3) ((1) Centrum Fizyki Teoretycznej, (3) Instytut Fizyki im. Smoluchowskiego, Campus Duisburg, Duisburg, Germany, Hans-Juergen Sommers (2), Karol Zyczkowski (1, Krakow, Poland, Poland), Polska Akademia Nauk, Universitat Duisburg-Essen, Uniwersytet Jagiellonski, Valerio Cappellini (1), Warszawa","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-05-31T16:26:33Z","title":"Distribution of G-concurrence of random pure states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0605251","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":"sha256:6e4595a41e4cad1cfa2a8720774827980cb94fc935f89cfa6cee8b57d9ec9166","target":"record","created_at":"2026-07-04T14:58:17Z","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":"9d4351d5c2aba728c3b9945e32e8a834ad4879e92d7ff6f7099d12ce8ae7ac84","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2006-05-31T16:26:33Z","title_canon_sha256":"d567ba35f103ba5c2ebcde6a5e8eb85462821bff8f0fb8d7c169332c011babbf"},"schema_version":"1.0","source":{"id":"quant-ph/0605251","kind":"arxiv","version":2}},"canonical_sha256":"31ab09cd3c4a087f347906d7461c491ae977dca3fab5ee8e297658fb523c1d46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ab09cd3c4a087f347906d7461c491ae977dca3fab5ee8e297658fb523c1d46","first_computed_at":"2026-07-04T14:58:17.164965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:58:17.164965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2YCT1l4g5pVN6BDs9uyGAoTmWBtVkAJzau4zNgRWc4dQ9FVNN5z1+ruYR/SShC9VJbpJjOAnQeBc4AeQ7w8eAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:58:17.165381Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0605251","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e4595a41e4cad1cfa2a8720774827980cb94fc935f89cfa6cee8b57d9ec9166","sha256:7922cf9aa53e75b3c1a995aa5c9a1eba65456e9b3effd90eef6ef9c0be587d85"],"state_sha256":"29aa724f55edd5b7a4c6430dbbc7e1996f3e18a41f45642f19b6045c86c80ab5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SHNaTrA32PFb9ajzO+ytf0YJunoGXI5yR6deXJ8BVgaJCRP2fDQT03qurBiMaGiCH4c8SZ23KdOr6eVFaTCoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T20:05:42.089377Z","bundle_sha256":"7681a9535f7cb3efb9d8751b009fc8cf834425a2e05c81fa9b2654309c6e5988"}}