{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:HDKGSJB6YXUVJS3LUSHHJVMEJO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"82907ea1cda8d62437453368ddb2e03be03ee44a0ffdba04a4048a4ddf20f7fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-08-06T17:18:48Z","title_canon_sha256":"347b2e84147e8ced1a61f323c5671869b00371bb3105cd2c744460cc37744949"},"schema_version":"1.0","source":{"id":"0908.0906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0906","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0906v1","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0906","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"HDKGSJB6YXUV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"HDKGSJB6YXUVJS3L","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"HDKGSJB6","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:49eb75bd64fd8e554b96ed9048b11382cf0e9ea8dcb9d1a369ff5c0fa593c142","target":"graph","created_at":"2026-05-18T03:39:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a given abelian group G, we classify the isomorphism classes of G-gradings on the simple Lie algebras of types A_n (n >= 1), B_n (n >= 2), C_n (n >= 3) and D_n (n > 4), in terms of numerical and group-theoretical invariants. The ground field is assumed to be algebraically closed of characteristic different from 2.","authors_text":"Mikhail Kotchetov, Yuri Bahturin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-08-06T17:18:48Z","title":"Classification of group gradings on simple Lie algebras of types A, B, C and D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0906","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:867058a18957ac681d5938e9aaf6914baedd57cfefb8b4a545e53946949c5309","target":"record","created_at":"2026-05-18T03:39:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"82907ea1cda8d62437453368ddb2e03be03ee44a0ffdba04a4048a4ddf20f7fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-08-06T17:18:48Z","title_canon_sha256":"347b2e84147e8ced1a61f323c5671869b00371bb3105cd2c744460cc37744949"},"schema_version":"1.0","source":{"id":"0908.0906","kind":"arxiv","version":1}},"canonical_sha256":"38d469243ec5e954cb6ba48e74d5844b8db8906c8f480e0bee225845d52a17bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38d469243ec5e954cb6ba48e74d5844b8db8906c8f480e0bee225845d52a17bf","first_computed_at":"2026-05-18T03:39:29.666501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:29.666501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nqeLOEBEjwxpHJ+ZPYw4u47atsnkExql0H+gPwWkWi8XY/uzqGJdTzfOIzsGGbA0B6uaWQmqVmLZQTmJZwtWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:29.667275Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:867058a18957ac681d5938e9aaf6914baedd57cfefb8b4a545e53946949c5309","sha256:49eb75bd64fd8e554b96ed9048b11382cf0e9ea8dcb9d1a369ff5c0fa593c142"],"state_sha256":"fb9cd5aabe73d6459b4667d09327312e6c27df3ae81a47e2b26c0b8fbff5cfd8"}