{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:KAC52XGJDWVLQVGT2G3ARGOHRC","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":"11534d3f268d3e1e6483ed8e75c29e4d254dfb5bfaab499fc4d599922afb7d49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-07T20:50:02Z","title_canon_sha256":"ef17e100229e70c659b15b2ee567e6e798f5df9e58972c3ab263ff102802e81f"},"schema_version":"1.0","source":{"id":"0910.1365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1365","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1365v2","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1365","created_at":"2026-05-18T04:40:46Z"},{"alias_kind":"pith_short_12","alias_value":"KAC52XGJDWVL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"KAC52XGJDWVLQVGT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"KAC52XGJ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:4dfd4eeecace6a49acee2b9239782bcd11cd92a91477904e867e7cf5f93de635","target":"graph","created_at":"2026-05-18T04:40:46Z","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 geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.","authors_text":"K. Uyanik, S. Turgut","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-07T20:50:02Z","title":"On the Geometric Measures of Entanglement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1365","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:d72944e0dcc571c33c300c158bdab97f6f0f735c04ef8ecdb2ac6c08a1fdfc90","target":"record","created_at":"2026-05-18T04:40:46Z","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":"11534d3f268d3e1e6483ed8e75c29e4d254dfb5bfaab499fc4d599922afb7d49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-07T20:50:02Z","title_canon_sha256":"ef17e100229e70c659b15b2ee567e6e798f5df9e58972c3ab263ff102802e81f"},"schema_version":"1.0","source":{"id":"0910.1365","kind":"arxiv","version":2}},"canonical_sha256":"5005dd5cc91daab854d3d1b60899c788a33ec1e7e0ea3a34171848c56cef5a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5005dd5cc91daab854d3d1b60899c788a33ec1e7e0ea3a34171848c56cef5a7b","first_computed_at":"2026-05-18T04:40:46.451249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:46.451249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hJqceZ1e8bpXskU0s2I0SFJFMxLP0ssmPbRm3QT3QDGZet5EmjER2q2N/OAOIKf9t0P3WuKZATrH3hc8IQxFAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:46.451950Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d72944e0dcc571c33c300c158bdab97f6f0f735c04ef8ecdb2ac6c08a1fdfc90","sha256:4dfd4eeecace6a49acee2b9239782bcd11cd92a91477904e867e7cf5f93de635"],"state_sha256":"37d831e4fb829a61d25c8e0ec8fbacd90455840bf359639d2700bda62d52c0ad"}