{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:CO746IDMGO3I2FEJMQECOJXLBB","short_pith_number":"pith:CO746IDM","canonical_record":{"source":{"id":"quant-ph/9804024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-09T21:17:21Z","cross_cats_sorted":[],"title_canon_sha256":"c2fad7aaa9ed6d8b3db83768ac3465d34ada22d7f001954cbc39e702099597c4","abstract_canon_sha256":"03b75c338008047486a648b25c68bd3323044c9ac4ca64f4504ffcb7c91a7cf9"},"schema_version":"1.0"},"canonical_sha256":"13bfcf206c33b68d148964082726eb087651013c35d5dd5aabd51a8a6398fb52","source":{"kind":"arxiv","id":"quant-ph/9804024","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9804024","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9804024v1","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9804024","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"CO746IDMGO3I","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_16","alias_value":"CO746IDMGO3I2FEJ","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_8","alias_value":"CO746IDM","created_at":"2026-07-04T16:10:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:CO746IDMGO3I2FEJMQECOJXLBB","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9804024","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-09T21:17:21Z","cross_cats_sorted":[],"title_canon_sha256":"c2fad7aaa9ed6d8b3db83768ac3465d34ada22d7f001954cbc39e702099597c4","abstract_canon_sha256":"03b75c338008047486a648b25c68bd3323044c9ac4ca64f4504ffcb7c91a7cf9"},"schema_version":"1.0"},"canonical_sha256":"13bfcf206c33b68d148964082726eb087651013c35d5dd5aabd51a8a6398fb52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:10:57.718825Z","signature_b64":"COLCSUvVHxR0aFTP0qeNj3lmgywn7lD0KyS1iSNKHYIKQB+sbOOUWWmHUSaGFfUmNzyLXSLiH+dmiTIYCZjUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13bfcf206c33b68d148964082726eb087651013c35d5dd5aabd51a8a6398fb52","last_reissued_at":"2026-07-04T16:10:57.718373Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:10:57.718373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9804024","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MB4z0inLgWHWilCT5Fsz4h6yLGWlHKHuzTglNOowIjj6l5i8+0qp4+zpjbUAO37H30UnFtYzsQiKkB4zL4LrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:54:18.162149Z"},"content_sha256":"d0e807cbc25756d6145983e5897eab03546a31e2e241d98df127f1fa77430c3b","schema_version":"1.0","event_id":"sha256:d0e807cbc25756d6145983e5897eab03546a31e2e241d98df127f1fa77430c3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:CO746IDMGO3I2FEJMQECOJXLBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the volume of the set of mixed entangled states","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anna Sanpera, Karol Zyczkowski (Krakow), Maciej Lewenstein (Saclay), Pawel Horodecki (Gdansk)","submitted_at":"1998-04-09T21:17:21Z","abstract_excerpt":"A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9804024","kind":"arxiv","version":1},"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/9804024/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":"2026-07-04T16:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hjf6agwpVaL4TE3h9QKMpgjFQKezlwJZZzbyuwgZR5QOGaf54ANDjHbrcY4kU3wYj8HOnM8kDRvRqWdvl/qqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:54:18.163072Z"},"content_sha256":"680cd37333053fa8d7178e55f48cb94221c6a6e88784ba27c677353b1387b03e","schema_version":"1.0","event_id":"sha256:680cd37333053fa8d7178e55f48cb94221c6a6e88784ba27c677353b1387b03e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CO746IDMGO3I2FEJMQECOJXLBB/bundle.json","state_url":"https://pith.science/pith/CO746IDMGO3I2FEJMQECOJXLBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CO746IDMGO3I2FEJMQECOJXLBB/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":"2026-07-31T14:54:18Z","links":{"resolver":"https://pith.science/pith/CO746IDMGO3I2FEJMQECOJXLBB","bundle":"https://pith.science/pith/CO746IDMGO3I2FEJMQECOJXLBB/bundle.json","state":"https://pith.science/pith/CO746IDMGO3I2FEJMQECOJXLBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CO746IDMGO3I2FEJMQECOJXLBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:CO746IDMGO3I2FEJMQECOJXLBB","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":"03b75c338008047486a648b25c68bd3323044c9ac4ca64f4504ffcb7c91a7cf9","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-09T21:17:21Z","title_canon_sha256":"c2fad7aaa9ed6d8b3db83768ac3465d34ada22d7f001954cbc39e702099597c4"},"schema_version":"1.0","source":{"id":"quant-ph/9804024","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9804024","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9804024v1","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9804024","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"CO746IDMGO3I","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_16","alias_value":"CO746IDMGO3I2FEJ","created_at":"2026-07-04T16:10:57Z"},{"alias_kind":"pith_short_8","alias_value":"CO746IDM","created_at":"2026-07-04T16:10:57Z"}],"graph_snapshots":[{"event_id":"sha256:680cd37333053fa8d7178e55f48cb94221c6a6e88784ba27c677353b1387b03e","target":"graph","created_at":"2026-07-04T16:10:57Z","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/9804024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A natural measure in the space of density matrices describing N-dimensional quantum systems is proposed. We study the probability P that a quantum state chosen randomly with respect to the natural measure is not entangled (is separable). We find analytical lower and upper bounds for this quantity. Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate that P decreases exponentially with N. Analysis of a conditional measure of separability under the condition of fixed purity shows a clear dualism between purity and separability: entanglement is typical for pure states, ","authors_text":"Anna Sanpera, Karol Zyczkowski (Krakow), Maciej Lewenstein (Saclay), Pawel Horodecki (Gdansk)","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1998-04-09T21:17:21Z","title":"On the volume of the set of mixed entangled states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9804024","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:d0e807cbc25756d6145983e5897eab03546a31e2e241d98df127f1fa77430c3b","target":"record","created_at":"2026-07-04T16:10:57Z","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":"03b75c338008047486a648b25c68bd3323044c9ac4ca64f4504ffcb7c91a7cf9","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-04-09T21:17:21Z","title_canon_sha256":"c2fad7aaa9ed6d8b3db83768ac3465d34ada22d7f001954cbc39e702099597c4"},"schema_version":"1.0","source":{"id":"quant-ph/9804024","kind":"arxiv","version":1}},"canonical_sha256":"13bfcf206c33b68d148964082726eb087651013c35d5dd5aabd51a8a6398fb52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13bfcf206c33b68d148964082726eb087651013c35d5dd5aabd51a8a6398fb52","first_computed_at":"2026-07-04T16:10:57.718373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:10:57.718373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COLCSUvVHxR0aFTP0qeNj3lmgywn7lD0KyS1iSNKHYIKQB+sbOOUWWmHUSaGFfUmNzyLXSLiH+dmiTIYCZjUCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:10:57.718825Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9804024","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0e807cbc25756d6145983e5897eab03546a31e2e241d98df127f1fa77430c3b","sha256:680cd37333053fa8d7178e55f48cb94221c6a6e88784ba27c677353b1387b03e"],"state_sha256":"da4e478afb2a27410240438dba8a63c4fa4cbd7eda40ca45da51d70952077267"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dBOo8pOn6dlzIFs+MQTHDK6eC8XWyKa3vou4llpwsorB9c0Lk4e+B2Ypuezdy/NNaEfNSQh8udu1Bit5kg42Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T14:54:18.167734Z","bundle_sha256":"da7d21ad80e38e67736ec4eee9b750dd2657b2e2b834488a05492124d8639dca"}}