{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BWXYE7AHW34QN5YK2QSYG72Y5R","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":"ef0bc548d295b95924e7e343db0fa97d20042360b309056634335e980d5d57ca","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-13T04:31:43Z","title_canon_sha256":"1ed9a39ffafd7c5190a742cdc2ff0bab7fad44a48ddd9bd2ce5d57f4e378d038"},"schema_version":"1.0","source":{"id":"1012.2630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2630","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2630v2","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2630","created_at":"2026-05-18T03:37:09Z"},{"alias_kind":"pith_short_12","alias_value":"BWXYE7AHW34Q","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BWXYE7AHW34QN5YK","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BWXYE7AH","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:97cc68da6f179ded5049a01332d5a0019ca3a80ae0942003e2ff72f9ec26f85a","target":"graph","created_at":"2026-05-18T03:37:09Z","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":"We provide a classification of entangled states that uses new discrete entanglement invariants. The invariants are defined by algebraic properties of linear maps associated with the states. We prove a theorem on a correspondence between the invariants and sets of equivalent classes of entangled states. The new method works for an arbitrary finite number of finite-dimensional state subspaces. As an application of the method, we considered a large selection of cases of three subspaces of various dimensions. We also obtain an entanglement classification of four qubits, where we find 27 fundamenta","authors_text":"Roman V. Buniy, Thomas W. Kephart","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-13T04:31:43Z","title":"An algebraic classification of entangled states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2630","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":"sha256:3978ba3f36f030a570bbde5a11c508598251211434f86f15029fc50e3dd3a5b2","target":"record","created_at":"2026-05-18T03:37:09Z","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":"ef0bc548d295b95924e7e343db0fa97d20042360b309056634335e980d5d57ca","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-13T04:31:43Z","title_canon_sha256":"1ed9a39ffafd7c5190a742cdc2ff0bab7fad44a48ddd9bd2ce5d57f4e378d038"},"schema_version":"1.0","source":{"id":"1012.2630","kind":"arxiv","version":2}},"canonical_sha256":"0daf827c07b6f906f70ad425837f58ec7faf81c70f947145759953bd04d66cc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0daf827c07b6f906f70ad425837f58ec7faf81c70f947145759953bd04d66cc5","first_computed_at":"2026-05-18T03:37:09.293618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:09.293618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Ivaa8N/SwUUK2Kxcdy7FNbX0fMtvH4UFMaF/Z2wBdFUJi/vPPJUCsFxtrvSim+3Puu6XBB+9FeZUo0wgYrZCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:09.294611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3978ba3f36f030a570bbde5a11c508598251211434f86f15029fc50e3dd3a5b2","sha256:97cc68da6f179ded5049a01332d5a0019ca3a80ae0942003e2ff72f9ec26f85a"],"state_sha256":"07f4d369726fdb1eb20c83163ed572b0d777704866f8d54d729dd137561cae1f"}