{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BWXYE7AHW34QN5YK2QSYG72Y5R","short_pith_number":"pith:BWXYE7AH","schema_version":"1.0","canonical_sha256":"0daf827c07b6f906f70ad425837f58ec7faf81c70f947145759953bd04d66cc5","source":{"kind":"arxiv","id":"1012.2630","version":2},"attestation_state":"computed","paper":{"title":"An algebraic classification of entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Roman V. Buniy, Thomas W. Kephart","submitted_at":"2010-12-13T04:31:43Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2630","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-12-13T04:31:43Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"1ed9a39ffafd7c5190a742cdc2ff0bab7fad44a48ddd9bd2ce5d57f4e378d038","abstract_canon_sha256":"ef0bc548d295b95924e7e343db0fa97d20042360b309056634335e980d5d57ca"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:09.294611Z","signature_b64":"9Ivaa8N/SwUUK2Kxcdy7FNbX0fMtvH4UFMaF/Z2wBdFUJi/vPPJUCsFxtrvSim+3Puu6XBB+9FeZUo0wgYrZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0daf827c07b6f906f70ad425837f58ec7faf81c70f947145759953bd04d66cc5","last_reissued_at":"2026-05-18T03:37:09.293618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:09.293618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algebraic classification of entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Roman V. Buniy, Thomas W. Kephart","submitted_at":"2010-12-13T04:31:43Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2630","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.2630","created_at":"2026-05-18T03:37:09.293782+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2630v2","created_at":"2026-05-18T03:37:09.293782+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2630","created_at":"2026-05-18T03:37:09.293782+00:00"},{"alias_kind":"pith_short_12","alias_value":"BWXYE7AHW34Q","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"BWXYE7AHW34QN5YK","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"BWXYE7AH","created_at":"2026-05-18T12:26:05.355336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2412.10728","citing_title":"Tripartite entanglement of qudits","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R","json":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R.json","graph_json":"https://pith.science/api/pith-number/BWXYE7AHW34QN5YK2QSYG72Y5R/graph.json","events_json":"https://pith.science/api/pith-number/BWXYE7AHW34QN5YK2QSYG72Y5R/events.json","paper":"https://pith.science/paper/BWXYE7AH"},"agent_actions":{"view_html":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R","download_json":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R.json","view_paper":"https://pith.science/paper/BWXYE7AH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2630&json=true","fetch_graph":"https://pith.science/api/pith-number/BWXYE7AHW34QN5YK2QSYG72Y5R/graph.json","fetch_events":"https://pith.science/api/pith-number/BWXYE7AHW34QN5YK2QSYG72Y5R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R/action/storage_attestation","attest_author":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R/action/author_attestation","sign_citation":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R/action/citation_signature","submit_replication":"https://pith.science/pith/BWXYE7AHW34QN5YK2QSYG72Y5R/action/replication_record"}},"created_at":"2026-05-18T03:37:09.293782+00:00","updated_at":"2026-05-18T03:37:09.293782+00:00"}