{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:6QP7JYAVODMUIGFHFVPNDOS4TV","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":"9d11e3c2aa7e1bbf4c977500eae936ab9117b7ffc56e01de2c68d8a8f60a0571","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-05-17T16:30:19Z","title_canon_sha256":"ab8f241f790d4b1bb252e3a03994c64d0088f82c2a0dac6672607a81e6b47773"},"schema_version":"1.0","source":{"id":"0705.2561","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.2561","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"0705.2561v2","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.2561","created_at":"2026-05-18T04:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"6QP7JYAVODMU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"6QP7JYAVODMUIGFH","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"6QP7JYAV","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:45d91ec727ff6362184c8acf17abd629532a0bf3e6711276f33003b34679aadd","target":"graph","created_at":"2026-05-18T04:24:04Z","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 density matrix of a graph is the combinatorial laplacian matrix of a graph normalized to have unit trace. In this paper we generalize the entanglement properties of mixed density matrices from combinatorial laplacian matrices of graphs discussed in Braunstein {\\it et al.} Annals of Combinatorics, {\\bf 10}(2006)291 to tripartite states. Then we proved that the degree condition defined in Braunstein {\\it et al.} Phys. Rev. A {\\bf 73}, (2006)012320 is sufficient and necessary for the tripartite separability of the density matrix of a nearest point graph.","authors_text":"Zhen Wang, Zhixi Wang","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2007-05-17T16:30:19Z","title":"The tripartite separability of density matrices of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.2561","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":"sha256:3c53a37c43ccefba9d9968dcca51d0ec275239a3645f36f368e7fe4c77477cd6","target":"record","created_at":"2026-05-18T04:24:04Z","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":"9d11e3c2aa7e1bbf4c977500eae936ab9117b7ffc56e01de2c68d8a8f60a0571","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2007-05-17T16:30:19Z","title_canon_sha256":"ab8f241f790d4b1bb252e3a03994c64d0088f82c2a0dac6672607a81e6b47773"},"schema_version":"1.0","source":{"id":"0705.2561","kind":"arxiv","version":2}},"canonical_sha256":"f41ff4e01570d94418a72d5ed1ba5c9d64a848fbf8de8638801f054f177614b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f41ff4e01570d94418a72d5ed1ba5c9d64a848fbf8de8638801f054f177614b6","first_computed_at":"2026-05-18T04:24:04.466551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:04.466551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iK8Pzelq6r3M93fZGmamAbG5EgrlTTqylsqZwXqRL+sE8NoCXOQx5BluWpqgjyAJuA2HE1aL8XYdI+wm7EznAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:04.467161Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.2561","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c53a37c43ccefba9d9968dcca51d0ec275239a3645f36f368e7fe4c77477cd6","sha256:45d91ec727ff6362184c8acf17abd629532a0bf3e6711276f33003b34679aadd"],"state_sha256":"66a090d300744d9860998d0a58e7c643a4e6e0eaf1fce56723fd19b6f27a2239"}