{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:F626LGAR7YZESNKKK7YZZ2R5NK","short_pith_number":"pith:F626LGAR","schema_version":"1.0","canonical_sha256":"2fb5e59811fe3249354a57f19cea3d6a8ae5452406cbf8acece01df0041d645d","source":{"kind":"arxiv","id":"0912.0172","version":1},"attestation_state":"computed","paper":{"title":"Balanced Tripartite Entanglement, the Alternating Group A4 and the Lie Algebra $sl(3,C) \\oplus u(1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP","math.RT","quant-ph"],"primary_cat":"math-ph","authors_text":"Metod Saniga (ASTRINSTSAV), Michel Planat (FEMTO-ST), Peter Levay (BUTE)","submitted_at":"2009-12-01T14:57:29Z","abstract_excerpt":"We discuss three important classes of three-qubit entangled states and their encoding into quantum gates, finite groups and Lie algebras. States of the GHZ and W-type correspond to pure tripartite and bipartite entanglement, respectively. We introduce another generic class B of three-qubit states, that have balanced entanglement over two and three parties. We show how to realize the largest cristallographic group $W(E_8)$ in terms of three-qubit gates (with real entries) encoding states of type GHZ or W [M. Planat, {\\it Clifford group dipoles and the enactment of Weyl/Coxeter group $W(E_8)$ by"},"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":"0912.0172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-12-01T14:57:29Z","cross_cats_sorted":["math.GR","math.MP","math.RT","quant-ph"],"title_canon_sha256":"6798a3aaccd231d053beabc18537122c7d7e90add587e801935040b124a61d12","abstract_canon_sha256":"fa2b0c2cbc979022b0cf33b9524f568ae3cbe6a747915d815d5751a3fa32d0b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:35.147870Z","signature_b64":"z7D17ZP3ZyeI8fCnF9mXIQOmtP50e25HC01o5+48S2sVo2EQfXrPCvEtRyNWRY6om4YZMKIUGxDcOKNd+kcyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fb5e59811fe3249354a57f19cea3d6a8ae5452406cbf8acece01df0041d645d","last_reissued_at":"2026-05-18T02:10:35.147122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:35.147122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Balanced Tripartite Entanglement, the Alternating Group A4 and the Lie Algebra $sl(3,C) \\oplus u(1)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.MP","math.RT","quant-ph"],"primary_cat":"math-ph","authors_text":"Metod Saniga (ASTRINSTSAV), Michel Planat (FEMTO-ST), Peter Levay (BUTE)","submitted_at":"2009-12-01T14:57:29Z","abstract_excerpt":"We discuss three important classes of three-qubit entangled states and their encoding into quantum gates, finite groups and Lie algebras. States of the GHZ and W-type correspond to pure tripartite and bipartite entanglement, respectively. We introduce another generic class B of three-qubit states, that have balanced entanglement over two and three parties. We show how to realize the largest cristallographic group $W(E_8)$ in terms of three-qubit gates (with real entries) encoding states of type GHZ or W [M. Planat, {\\it Clifford group dipoles and the enactment of Weyl/Coxeter group $W(E_8)$ by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0172","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0912.0172","created_at":"2026-05-18T02:10:35.147242+00:00"},{"alias_kind":"arxiv_version","alias_value":"0912.0172v1","created_at":"2026-05-18T02:10:35.147242+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0172","created_at":"2026-05-18T02:10:35.147242+00:00"},{"alias_kind":"pith_short_12","alias_value":"F626LGAR7YZE","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"F626LGAR7YZESNKK","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"F626LGAR","created_at":"2026-05-18T12:25:59.703012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK","json":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK.json","graph_json":"https://pith.science/api/pith-number/F626LGAR7YZESNKKK7YZZ2R5NK/graph.json","events_json":"https://pith.science/api/pith-number/F626LGAR7YZESNKKK7YZZ2R5NK/events.json","paper":"https://pith.science/paper/F626LGAR"},"agent_actions":{"view_html":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK","download_json":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK.json","view_paper":"https://pith.science/paper/F626LGAR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0912.0172&json=true","fetch_graph":"https://pith.science/api/pith-number/F626LGAR7YZESNKKK7YZZ2R5NK/graph.json","fetch_events":"https://pith.science/api/pith-number/F626LGAR7YZESNKKK7YZZ2R5NK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK/action/storage_attestation","attest_author":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK/action/author_attestation","sign_citation":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK/action/citation_signature","submit_replication":"https://pith.science/pith/F626LGAR7YZESNKKK7YZZ2R5NK/action/replication_record"}},"created_at":"2026-05-18T02:10:35.147242+00:00","updated_at":"2026-05-18T02:10:35.147242+00:00"}