{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LHM2JE563VGIU7V7BWKX2CLZTR","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":"43345b83dd5eb1c4cd0bee1a95e642567ba383a7512734dbd8a1fc6abcd31117","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-07T01:34:09Z","title_canon_sha256":"5a65ffed8e6ec2e84311d6db406a185c8fffad965731bb9ca777ba5d495a6f7a"},"schema_version":"1.0","source":{"id":"1304.1950","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1950","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1950v3","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1950","created_at":"2026-05-18T02:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"LHM2JE563VGI","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LHM2JE563VGIU7V7","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LHM2JE56","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:59f9e9736e2052e4efe84eae10e4162ce739bd38c45a708e1874481899b2d439","target":"graph","created_at":"2026-05-18T02:16:21Z","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 Schmidt number is of crucial importance in characterizing the bipartite pure states. We explore and propose here a generalization of Schmidt number for states in multipartite systems. It is shown to be entanglement monotonic and valid for both pure and mixed states. In addition, the corresponding generalization of multipartite Schmidt coefficients is introduced. Our approach is applicable for systems with arbitrary number of parties and for arbitrary dimensions.","authors_text":"Heng Fan, Yu Guo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-07T01:34:09Z","title":"A generalization of Schmidt number for multipartite states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1950","kind":"arxiv","version":3},"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":"sha256:776700e5325c42d47db543579a1501155038a5c465ad3141ed9967215c1f4e2d","target":"record","created_at":"2026-05-18T02:16:21Z","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":"43345b83dd5eb1c4cd0bee1a95e642567ba383a7512734dbd8a1fc6abcd31117","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"quant-ph","submitted_at":"2013-04-07T01:34:09Z","title_canon_sha256":"5a65ffed8e6ec2e84311d6db406a185c8fffad965731bb9ca777ba5d495a6f7a"},"schema_version":"1.0","source":{"id":"1304.1950","kind":"arxiv","version":3}},"canonical_sha256":"59d9a493bedd4c8a7ebf0d957d09799c40f83b531efb968c5c3d2bf85b902bc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59d9a493bedd4c8a7ebf0d957d09799c40f83b531efb968c5c3d2bf85b902bc5","first_computed_at":"2026-05-18T02:16:21.507124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:21.507124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rIpK6TrROy0iFdLAXDqfRfYLL/IC6kDUO0RaWootYFYuOJI85A/2cLdLy/dgmLRIu0oYm/yMTT6E+0l1gS5fCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:21.507817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1950","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776700e5325c42d47db543579a1501155038a5c465ad3141ed9967215c1f4e2d","sha256:59f9e9736e2052e4efe84eae10e4162ce739bd38c45a708e1874481899b2d439"],"state_sha256":"0ae8679c6040745dc4d86fc7ec27baf88c17a6c25600d3092838e89df6aff73b"}