{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:WY5F6HYKIGJY27WLUUXDFIV5LL","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":"c8a8d8d18e53ded3d24cbe1db08d22a9f673fe850ea33ea1def5defbc519dcf5","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-07T13:20:20Z","title_canon_sha256":"0208accdaa198f0af91852b1f24b5896e2ef2d336f35926ca1bec6a5079a455e"},"schema_version":"1.0","source":{"id":"quant-ph/0412051","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0412051","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0412051v2","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0412051","created_at":"2026-05-18T01:08:45Z"},{"alias_kind":"pith_short_12","alias_value":"WY5F6HYKIGJY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"WY5F6HYKIGJY27WL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"WY5F6HYK","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:dbca27db9f48ec4645967e6feb66a80de51d115442f6ecdcee72318e770c4e3c","target":"graph","created_at":"2026-05-18T01:08:45Z","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 paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, bi- and three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite state by relating to a quadric space defined by two-by-two subdeterminants.","authors_text":"Gunnar Bj\\\"ork, Hoshang Heydari","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2004-12-07T13:20:20Z","title":"Complex multi-projective variety and entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0412051","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:aa627e73325e1ca8f00ec18d3dfa414f8e03abd890b51523a4549d07765ed252","target":"record","created_at":"2026-05-18T01:08:45Z","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":"c8a8d8d18e53ded3d24cbe1db08d22a9f673fe850ea33ea1def5defbc519dcf5","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2004-12-07T13:20:20Z","title_canon_sha256":"0208accdaa198f0af91852b1f24b5896e2ef2d336f35926ca1bec6a5079a455e"},"schema_version":"1.0","source":{"id":"quant-ph/0412051","kind":"arxiv","version":2}},"canonical_sha256":"b63a5f1f0a41938d7ecba52e32a2bd5adbb7903b6798d48dce7299c64344636b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b63a5f1f0a41938d7ecba52e32a2bd5adbb7903b6798d48dce7299c64344636b","first_computed_at":"2026-05-18T01:08:45.737273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:45.737273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k0YIv6hg2jtFvbOlGsv2MaT7ee2Jf06WD81Gci1wR6v7QMz0LXkpAg4DGtsIFL99qIIz5Y/7Fj6vq2O+/5RJAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:45.737638Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0412051","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa627e73325e1ca8f00ec18d3dfa414f8e03abd890b51523a4549d07765ed252","sha256:dbca27db9f48ec4645967e6feb66a80de51d115442f6ecdcee72318e770c4e3c"],"state_sha256":"187960000484e6a48e4b8eb2d7db7ff07f04273611e181bfad14e922cfa00706"}