{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:5TZUS6FHG7SLVFZUIOZ5VDXGDB","short_pith_number":"pith:5TZUS6FH","schema_version":"1.0","canonical_sha256":"ecf34978a737e4ba973443b3da8ee6187f97b93465d6decdecbfd29b70ff4951","source":{"kind":"arxiv","id":"2410.07292","version":1},"attestation_state":"computed","paper":{"title":"Birational equivalence of the Zassenhaus varieties for basic classical Lie superalgebras and their purely-even reductive Lie subalgebras in odd characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Shu, Lisun Zheng, Ye Ren","submitted_at":"2024-10-09T15:41:04Z","abstract_excerpt":"Let $\\mathfrak{g}=\\mathfrak{g}_{\\bar 0}\\oplus\\mathfrak{g}_{\\bar 1}$ be a basic classical Lie superalgebra over an algebraically closed field $\\textbf{k}$ of characteristic $p>2$. Denote by $\\mathcal{Z}$ the center of the universal enveloping algebra $U(\\mathfrak{g})$. Then $\\mathcal{Z}$ turns out to be finitely-generated purely-even commutative algebra without nonzero divisors.\n  In this paper, we demonstrate that the fraction $\\text{Frac}(\\mathcal{Z})$ is isomorphic to $\\text{Frac}(\\mathfrak{Z})$ for the center $\\mathfrak{Z}$ of $U(\\mathfrak{g}_{\\bar 0})$. Consequently, both Zassenhaus variet"},"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":"2410.07292","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2024-10-09T15:41:04Z","cross_cats_sorted":[],"title_canon_sha256":"1e7e8061af09cbfe26fa69750151e47d8a3e8a71d0eca9f11ec09ab2a265a2e9","abstract_canon_sha256":"4c6c191dbbfe44f72fa15971508959bb6045039e992d584411b13951efcd36f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:18:34.086719Z","signature_b64":"2lDc+JzOuljEsibv3ZIfC2Cy8tA5qJ72XTVe6OlhE6E8/qqU2uI+nUl/t1c4p85ymG2Dx6VfhLP3bSCnpIq6Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf34978a737e4ba973443b3da8ee6187f97b93465d6decdecbfd29b70ff4951","last_reissued_at":"2026-07-05T09:18:34.086237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:18:34.086237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birational equivalence of the Zassenhaus varieties for basic classical Lie superalgebras and their purely-even reductive Lie subalgebras in odd characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Shu, Lisun Zheng, Ye Ren","submitted_at":"2024-10-09T15:41:04Z","abstract_excerpt":"Let $\\mathfrak{g}=\\mathfrak{g}_{\\bar 0}\\oplus\\mathfrak{g}_{\\bar 1}$ be a basic classical Lie superalgebra over an algebraically closed field $\\textbf{k}$ of characteristic $p>2$. Denote by $\\mathcal{Z}$ the center of the universal enveloping algebra $U(\\mathfrak{g})$. Then $\\mathcal{Z}$ turns out to be finitely-generated purely-even commutative algebra without nonzero divisors.\n  In this paper, we demonstrate that the fraction $\\text{Frac}(\\mathcal{Z})$ is isomorphic to $\\text{Frac}(\\mathfrak{Z})$ for the center $\\mathfrak{Z}$ of $U(\\mathfrak{g}_{\\bar 0})$. Consequently, both Zassenhaus variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.07292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2410.07292","created_at":"2026-07-05T09:18:34.086294+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.07292v1","created_at":"2026-07-05T09:18:34.086294+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07292","created_at":"2026-07-05T09:18:34.086294+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TZUS6FHG7SL","created_at":"2026-07-05T09:18:34.086294+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TZUS6FHG7SLVFZU","created_at":"2026-07-05T09:18:34.086294+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TZUS6FH","created_at":"2026-07-05T09:18:34.086294+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/5TZUS6FHG7SLVFZUIOZ5VDXGDB","json":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB.json","graph_json":"https://pith.science/api/pith-number/5TZUS6FHG7SLVFZUIOZ5VDXGDB/graph.json","events_json":"https://pith.science/api/pith-number/5TZUS6FHG7SLVFZUIOZ5VDXGDB/events.json","paper":"https://pith.science/paper/5TZUS6FH"},"agent_actions":{"view_html":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB","download_json":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB.json","view_paper":"https://pith.science/paper/5TZUS6FH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.07292&json=true","fetch_graph":"https://pith.science/api/pith-number/5TZUS6FHG7SLVFZUIOZ5VDXGDB/graph.json","fetch_events":"https://pith.science/api/pith-number/5TZUS6FHG7SLVFZUIOZ5VDXGDB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB/action/storage_attestation","attest_author":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB/action/author_attestation","sign_citation":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB/action/citation_signature","submit_replication":"https://pith.science/pith/5TZUS6FHG7SLVFZUIOZ5VDXGDB/action/replication_record"}},"created_at":"2026-07-05T09:18:34.086294+00:00","updated_at":"2026-07-05T09:18:34.086294+00:00"}