{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2002:AKVB4YFTXJU57ZUDCDOOQFSQRZ","short_pith_number":"pith:AKVB4YFT","schema_version":"1.0","canonical_sha256":"02aa1e60b3ba69dfe68310dce816508e4cb047e33a62165d2b5b790eba011c6d","source":{"kind":"arxiv","id":"quant-ph/0212069","version":6},"attestation_state":"computed","paper":{"title":"The polynomial invariants of four qubits","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J.-G. Luque, J.-Y. Thibon","submitted_at":"2002-12-11T15:17:11Z","abstract_excerpt":"We describe explicitly the algebra of polynomial functions on the Hilbert space of four qubit states which are invariant under the SLOCC group $SL(2,{\\mathbb C})^{4}$. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants."},"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":"quant-ph/0212069","kind":"arxiv","version":6},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2002-12-11T15:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"5fabd9ef81d467239f88de92265a43bf4c6f9c438f8f8a9416d1f6557c66a3c3","abstract_canon_sha256":"af7f00d7e44c94431abc1405acff3a3aab58b88e092a9bde0140e3c9b90a7ed9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.400287Z","signature_b64":"XvSeS9lFo016pqLVjKJ7VdcoWesd3y6E9VLaQiedqd3tgFgBm2hn0UXCx1E7AstvzR/5SMFDZjrObpNBpNrTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02aa1e60b3ba69dfe68310dce816508e4cb047e33a62165d2b5b790eba011c6d","last_reissued_at":"2026-05-18T03:34:00.399369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.399369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The polynomial invariants of four qubits","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"J.-G. Luque, J.-Y. Thibon","submitted_at":"2002-12-11T15:17:11Z","abstract_excerpt":"We describe explicitly the algebra of polynomial functions on the Hilbert space of four qubit states which are invariant under the SLOCC group $SL(2,{\\mathbb C})^{4}$. From this description, we obtain a closed formula for the hyperdeterminant in terms of low degree invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0212069","kind":"arxiv","version":6},"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":"quant-ph/0212069","created_at":"2026-05-18T03:34:00.399523+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0212069v6","created_at":"2026-05-18T03:34:00.399523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0212069","created_at":"2026-05-18T03:34:00.399523+00:00"},{"alias_kind":"pith_short_12","alias_value":"AKVB4YFTXJU5","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_16","alias_value":"AKVB4YFTXJU57ZUD","created_at":"2026-05-18T12:25:50.845339+00:00"},{"alias_kind":"pith_short_8","alias_value":"AKVB4YFT","created_at":"2026-05-18T12:25:50.845339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.02097","citing_title":"Separability from Multipartite Measures","ref_index":31,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02097","citing_title":"Separability from Multipartite Measures","ref_index":31,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ","json":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ.json","graph_json":"https://pith.science/api/pith-number/AKVB4YFTXJU57ZUDCDOOQFSQRZ/graph.json","events_json":"https://pith.science/api/pith-number/AKVB4YFTXJU57ZUDCDOOQFSQRZ/events.json","paper":"https://pith.science/paper/AKVB4YFT"},"agent_actions":{"view_html":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ","download_json":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ.json","view_paper":"https://pith.science/paper/AKVB4YFT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0212069&json=true","fetch_graph":"https://pith.science/api/pith-number/AKVB4YFTXJU57ZUDCDOOQFSQRZ/graph.json","fetch_events":"https://pith.science/api/pith-number/AKVB4YFTXJU57ZUDCDOOQFSQRZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ/action/storage_attestation","attest_author":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ/action/author_attestation","sign_citation":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ/action/citation_signature","submit_replication":"https://pith.science/pith/AKVB4YFTXJU57ZUDCDOOQFSQRZ/action/replication_record"}},"created_at":"2026-05-18T03:34:00.399523+00:00","updated_at":"2026-05-18T03:34:00.399523+00:00"}