{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YP3UT6BO2G4EJB3XH37TGXQWJV","short_pith_number":"pith:YP3UT6BO","canonical_record":{"source":{"id":"1302.4654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T15:59:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f11a53685ebdc7f2327f35750dab1fad87c969dab8b4ce881b89ffbaad473e8c","abstract_canon_sha256":"344808005a4d2d85bf0f50aae20c35b8a02319345640903630cb2c00052d7064"},"schema_version":"1.0"},"canonical_sha256":"c3f749f82ed1b84487773eff335e164d742434e57f620274fb971fc552345aae","source":{"kind":"arxiv","id":"1302.4654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4654","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4654v1","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4654","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"YP3UT6BO2G4E","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YP3UT6BO2G4EJB3X","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YP3UT6BO","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YP3UT6BO2G4EJB3XH37TGXQWJV","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T15:59:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f11a53685ebdc7f2327f35750dab1fad87c969dab8b4ce881b89ffbaad473e8c","abstract_canon_sha256":"344808005a4d2d85bf0f50aae20c35b8a02319345640903630cb2c00052d7064"},"schema_version":"1.0"},"canonical_sha256":"c3f749f82ed1b84487773eff335e164d742434e57f620274fb971fc552345aae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:12.550532Z","signature_b64":"QY9RaGct2Y2RW5M3WYDujCa4pgOBfOeP3telN78xJHAj8ya6lrHZVNQFXpO0Ys6GfYC88VMkLD2kChSQLXBlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3f749f82ed1b84487773eff335e164d742434e57f620274fb971fc552345aae","last_reissued_at":"2026-05-18T03:33:12.549762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:12.549762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4654","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":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTxtW9N9M45m8923rJop0ob3NCMVlA2si6NdK4IFhZqpzJLYMjN/G3RXsfD4wZJiTcE4E9q+eI7Vt/89IPtXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:16:51.310477Z"},"content_sha256":"9e3c849e5084f647994bc9105dc0f388983d4af9d6d6cb308e70b20a99c9c8cb","schema_version":"1.0","event_id":"sha256:9e3c849e5084f647994bc9105dc0f388983d4af9d6d6cb308e70b20a99c9c8cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YP3UT6BO2G4EJB3XH37TGXQWJV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum entanglement in finite-dimensional Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Szil\\'ard Szalay","submitted_at":"2013-02-19T15:59:02Z","abstract_excerpt":"In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and if it is, then how much entanglement is carried by that? These questions introduce the topics of separability criteria and entanglement measures, both of which are based on the issue of classification of multipartite entanglement. In this dissertation, after reviewing these three fundamental topics for finite dimensional Hilbert spaces, I present my contrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4654","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":""},"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":"2026-05-18T03:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BT1Mzd+S84+UJNy2FaTefKaEyQa9AaLAFrsEtal2kPYoxkIlWmhkL2gvAnjpbheAwtPbnODfYQBLkr6V09RSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:16:51.310825Z"},"content_sha256":"cbda0a914699027dce3a5220f0d8ef8f4573c411f5322167d5f200ab8e79f9eb","schema_version":"1.0","event_id":"sha256:cbda0a914699027dce3a5220f0d8ef8f4573c411f5322167d5f200ab8e79f9eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/bundle.json","state_url":"https://pith.science/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/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":"2026-05-28T01:16:51Z","links":{"resolver":"https://pith.science/pith/YP3UT6BO2G4EJB3XH37TGXQWJV","bundle":"https://pith.science/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/bundle.json","state":"https://pith.science/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YP3UT6BO2G4EJB3XH37TGXQWJV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YP3UT6BO2G4EJB3XH37TGXQWJV","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":"344808005a4d2d85bf0f50aae20c35b8a02319345640903630cb2c00052d7064","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T15:59:02Z","title_canon_sha256":"f11a53685ebdc7f2327f35750dab1fad87c969dab8b4ce881b89ffbaad473e8c"},"schema_version":"1.0","source":{"id":"1302.4654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4654","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4654v1","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4654","created_at":"2026-05-18T03:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"YP3UT6BO2G4E","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YP3UT6BO2G4EJB3X","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YP3UT6BO","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:cbda0a914699027dce3a5220f0d8ef8f4573c411f5322167d5f200ab8e79f9eb","target":"graph","created_at":"2026-05-18T03:33:12Z","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 the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and if it is, then how much entanglement is carried by that? These questions introduce the topics of separability criteria and entanglement measures, both of which are based on the issue of classification of multipartite entanglement. In this dissertation, after reviewing these three fundamental topics for finite dimensional Hilbert spaces, I present my contrib","authors_text":"Szil\\'ard Szalay","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T15:59:02Z","title":"Quantum entanglement in finite-dimensional Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4654","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":"sha256:9e3c849e5084f647994bc9105dc0f388983d4af9d6d6cb308e70b20a99c9c8cb","target":"record","created_at":"2026-05-18T03:33:12Z","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":"344808005a4d2d85bf0f50aae20c35b8a02319345640903630cb2c00052d7064","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-19T15:59:02Z","title_canon_sha256":"f11a53685ebdc7f2327f35750dab1fad87c969dab8b4ce881b89ffbaad473e8c"},"schema_version":"1.0","source":{"id":"1302.4654","kind":"arxiv","version":1}},"canonical_sha256":"c3f749f82ed1b84487773eff335e164d742434e57f620274fb971fc552345aae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3f749f82ed1b84487773eff335e164d742434e57f620274fb971fc552345aae","first_computed_at":"2026-05-18T03:33:12.549762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:12.549762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QY9RaGct2Y2RW5M3WYDujCa4pgOBfOeP3telN78xJHAj8ya6lrHZVNQFXpO0Ys6GfYC88VMkLD2kChSQLXBlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:12.550532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e3c849e5084f647994bc9105dc0f388983d4af9d6d6cb308e70b20a99c9c8cb","sha256:cbda0a914699027dce3a5220f0d8ef8f4573c411f5322167d5f200ab8e79f9eb"],"state_sha256":"6cda8c10f8e073405aba49af4b72fc68245d5d2903b4b901714c4082ace2c32c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bq/3ZdmGH3zDD1zh6lgiqTiVem+6tpKDV4dYibC+gBMtlhN0pa7VWoHIzhLOZr2QY0eIG5tOVEaPbYAyQCcAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:16:51.312769Z","bundle_sha256":"87eeb863bc857c20623e0708eab517f63af686e73fce9bde1be7485461435179"}}