{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:W74AZM7T6CIRXXMBN3XGIRXBWX","short_pith_number":"pith:W74AZM7T","schema_version":"1.0","canonical_sha256":"b7f80cb3f3f0911bdd816eee6446e1b5cd04453c028612fe35925929868dc615","source":{"kind":"arxiv","id":"1001.0191","version":2},"attestation_state":"computed","paper":{"title":"Group gradings on restricted Cartan type Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mikhail Kochetov, Yuri Bahturin","submitted_at":"2009-12-31T23:40:32Z","abstract_excerpt":"For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism group schemes, which we determine for the simple restricted Lie algebras of types S(m;1) and H(m;1). The ground field is assumed to be algebraically closed of characteristic p>3."},"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":"1001.0191","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-12-31T23:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"c13a31c0032386e19af48be75919d571b1b7b97826042f4e08db20275c5f9f87","abstract_canon_sha256":"09f6935bbd726fc666442da8185048cf52da1301804b5a096670821905ebf206"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:29.617767Z","signature_b64":"jgOtdLrlLI9ZkY0NhP93YK3md1mw8oSxWPIbTEqt9YJg3XzPhwb1NSe5uErCvypfxIJFpaXif/kKHLfBbl9HCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7f80cb3f3f0911bdd816eee6446e1b5cd04453c028612fe35925929868dc615","last_reissued_at":"2026-05-18T03:39:29.616964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:29.616964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Group gradings on restricted Cartan type Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mikhail Kochetov, Yuri Bahturin","submitted_at":"2009-12-31T23:40:32Z","abstract_excerpt":"For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple restricted Lie algebras of types W(m;1) and S(m;1) (m>=2), in terms of numerical and group-theoretical invariants. Our main tool is automorphism group schemes, which we determine for the simple restricted Lie algebras of types S(m;1) and H(m;1). The ground field is assumed to be algebraically closed of characteristic p>3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0191","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":"1001.0191","created_at":"2026-05-18T03:39:29.617091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.0191v2","created_at":"2026-05-18T03:39:29.617091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0191","created_at":"2026-05-18T03:39:29.617091+00:00"},{"alias_kind":"pith_short_12","alias_value":"W74AZM7T6CIR","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"W74AZM7T6CIRXXMB","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"W74AZM7T","created_at":"2026-05-18T12:26:02.257875+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/W74AZM7T6CIRXXMBN3XGIRXBWX","json":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX.json","graph_json":"https://pith.science/api/pith-number/W74AZM7T6CIRXXMBN3XGIRXBWX/graph.json","events_json":"https://pith.science/api/pith-number/W74AZM7T6CIRXXMBN3XGIRXBWX/events.json","paper":"https://pith.science/paper/W74AZM7T"},"agent_actions":{"view_html":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX","download_json":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX.json","view_paper":"https://pith.science/paper/W74AZM7T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.0191&json=true","fetch_graph":"https://pith.science/api/pith-number/W74AZM7T6CIRXXMBN3XGIRXBWX/graph.json","fetch_events":"https://pith.science/api/pith-number/W74AZM7T6CIRXXMBN3XGIRXBWX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX/action/storage_attestation","attest_author":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX/action/author_attestation","sign_citation":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX/action/citation_signature","submit_replication":"https://pith.science/pith/W74AZM7T6CIRXXMBN3XGIRXBWX/action/replication_record"}},"created_at":"2026-05-18T03:39:29.617091+00:00","updated_at":"2026-05-18T03:39:29.617091+00:00"}