{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:IPAZUIJQP6SLDKHBSP3TNPZG2Q","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":"e8f2d8ed763aaeb6d3444f8194acae25c2494b578bb8f04e9c7745632b6d7064","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2002-06-18T14:50:03Z","title_canon_sha256":"edc4b2c3d25c14c485cc5c528a399401708028ebab5f0c03c8ec151ff80950c0"},"schema_version":"1.0","source":{"id":"quant-ph/0206111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0206111","created_at":"2026-07-04T16:36:05Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0206111v2","created_at":"2026-07-04T16:36:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0206111","created_at":"2026-07-04T16:36:05Z"},{"alias_kind":"pith_short_12","alias_value":"IPAZUIJQP6SL","created_at":"2026-07-04T16:36:05Z"},{"alias_kind":"pith_short_16","alias_value":"IPAZUIJQP6SLDKHB","created_at":"2026-07-04T16:36:05Z"},{"alias_kind":"pith_short_8","alias_value":"IPAZUIJQ","created_at":"2026-07-04T16:36:05Z"}],"graph_snapshots":[{"event_id":"sha256:78c6eb8a853eda0f21980407eec5875a54e9db1fbb1e3f31360c97910edd0c37","target":"graph","created_at":"2026-07-04T16:36:05Z","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/0206111/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We find that multidimensional determinants \"hyperdeterminants\", related to entanglement measures (the so-called concurrence or 3-tangle for the 2 or 3 qubits, respectively), are derived from a duality between entangled states and separable states. By means of the hyperdeterminant and its singularities, the single copy of multipartite pure entangled states is classified into an onion structure of every closed subset, similar to that by the local rank in the bipartite case. This reveals how inequivalent multipartite entangled classes are partially ordered under local actions. In particular, the ","authors_text":"Akimasa Miyake","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2002-06-18T14:50:03Z","title":"Classification of multipartite entangled states by multidimensional determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0206111","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":"sha256:7f058ef2da465e54f5e4c8d3079da67ecbb916bd784594005916567d41380903","target":"record","created_at":"2026-07-04T16:36:05Z","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":"e8f2d8ed763aaeb6d3444f8194acae25c2494b578bb8f04e9c7745632b6d7064","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"quant-ph","submitted_at":"2002-06-18T14:50:03Z","title_canon_sha256":"edc4b2c3d25c14c485cc5c528a399401708028ebab5f0c03c8ec151ff80950c0"},"schema_version":"1.0","source":{"id":"quant-ph/0206111","kind":"arxiv","version":2}},"canonical_sha256":"43c19a21307fa4b1a8e193f736bf26d411323b87819fed5d73b9702f5d98db94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c19a21307fa4b1a8e193f736bf26d411323b87819fed5d73b9702f5d98db94","first_computed_at":"2026-07-04T16:36:05.996891Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:36:05.996891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KuGNeWdjH/lm3nwVyOXj5TqXzRF+XbXtWcGruWq/w589T4ufQbPqVc0zeQM9rkio87h4um/KRU/YM6UNc/azBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T16:36:05.997243Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0206111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f058ef2da465e54f5e4c8d3079da67ecbb916bd784594005916567d41380903","sha256:78c6eb8a853eda0f21980407eec5875a54e9db1fbb1e3f31360c97910edd0c37"],"state_sha256":"6dd476f66eb053a213d085c5d9f50fa0b9761289addd83e585cda42b397090de"}