{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:KAC52XGJDWVLQVGT2G3ARGOHRC","short_pith_number":"pith:KAC52XGJ","canonical_record":{"source":{"id":"0910.1365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-07T20:50:02Z","cross_cats_sorted":[],"title_canon_sha256":"ef17e100229e70c659b15b2ee567e6e798f5df9e58972c3ab263ff102802e81f","abstract_canon_sha256":"11534d3f268d3e1e6483ed8e75c29e4d254dfb5bfaab499fc4d599922afb7d49"},"schema_version":"1.0"},"canonical_sha256":"5005dd5cc91daab854d3d1b60899c788a33ec1e7e0ea3a34171848c56cef5a7b","source":{"kind":"arxiv","id":"0910.1365","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:KAC52XGJDWVLQVGT2G3ARGOHRC","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-10-07T20:50:02Z","cross_cats_sorted":[],"title_canon_sha256":"ef17e100229e70c659b15b2ee567e6e798f5df9e58972c3ab263ff102802e81f","abstract_canon_sha256":"11534d3f268d3e1e6483ed8e75c29e4d254dfb5bfaab499fc4d599922afb7d49"},"schema_version":"1.0"},"canonical_sha256":"5005dd5cc91daab854d3d1b60899c788a33ec1e7e0ea3a34171848c56cef5a7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:46.451950Z","signature_b64":"hJqceZ1e8bpXskU0s2I0SFJFMxLP0ssmPbRm3QT3QDGZet5EmjER2q2N/OAOIKf9t0P3WuKZATrH3hc8IQxFAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5005dd5cc91daab854d3d1b60899c788a33ec1e7e0ea3a34171848c56cef5a7b","last_reissued_at":"2026-05-18T04:40:46.451249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:46.451249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1365","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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBlq4vQyL90CLPU3UObBpdrs7kPWL8OMvwMcAWvkmZzD/TuTGqIInLvX/XWU7v7IjFwNHrwJA8hVfRBRnuraBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:39:14.442921Z"},"content_sha256":"d72944e0dcc571c33c300c158bdab97f6f0f735c04ef8ecdb2ac6c08a1fdfc90","schema_version":"1.0","event_id":"sha256:d72944e0dcc571c33c300c158bdab97f6f0f735c04ef8ecdb2ac6c08a1fdfc90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:KAC52XGJDWVLQVGT2G3ARGOHRC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Geometric Measures of Entanglement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"K. Uyanik, S. Turgut","submitted_at":"2009-10-07T20:50:02Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1365","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":""},"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":"2026-05-18T04:40:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A1DPHs+eA+/wnSn2Oizymg0Q4RD6hZkMqwCxcMLuu+rbnteJxPeOPmGYNoXX6llrKHc0tbK68EdThr3TlIFMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:39:14.443264Z"},"content_sha256":"4dfd4eeecace6a49acee2b9239782bcd11cd92a91477904e867e7cf5f93de635","schema_version":"1.0","event_id":"sha256:4dfd4eeecace6a49acee2b9239782bcd11cd92a91477904e867e7cf5f93de635"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/bundle.json","state_url":"https://pith.science/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/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":"2026-06-28T08:39:14Z","links":{"resolver":"https://pith.science/pith/KAC52XGJDWVLQVGT2G3ARGOHRC","bundle":"https://pith.science/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/bundle.json","state":"https://pith.science/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KAC52XGJDWVLQVGT2G3ARGOHRC/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FjCT4c8CMyb61pIiR7boEEO3pR6qGnu+R+OAJFV85IiUZok0l0rOEvWFUlql8PZDsYgdhK2VTZ3ggnPZQzEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:39:14.445166Z","bundle_sha256":"29ed6e9b75a6e3601442084f964e659962eef5bc007844574517b7734b3fe7f9"}}