{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O6SW3AS5ZB3V45G4UMECIHKRQY","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":"4f53d015c1145ef7639bc8e30f40136c4afe72911921eb6492a006bf18537e68","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-18T13:09:57Z","title_canon_sha256":"3b28d9dca729bca7b5b9d2764d92f97a6b6f42a1b28b5f2ea9e098b9f4fc1e0e"},"schema_version":"1.0","source":{"id":"1303.4239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4239","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4239v1","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4239","created_at":"2026-05-18T03:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"O6SW3AS5ZB3V","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6SW3AS5ZB3V45G4","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6SW3AS5","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:2ca216f08a634c685c14478f842269a10eda2a9d4626b1d3ac2cba3ca71fe66f","target":"graph","created_at":"2026-05-18T03:30:39Z","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":"We compute the number of orbit types for simply connected simple algebraic groups over algebraically closed fields as well as for compact simply connected simple Lie groups. We also compute the number of orbit types for the adjoint action of these groups on their Lie algebras. We also prove that the genus number of a connected reductive algebraic group coincides with the genus number of its semisimple part.","authors_text":"Anirban Bose","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-18T13:09:57Z","title":"On the Genus number of Algebraic groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4239","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":"sha256:1e0d3228c021c5e4920ca05ecdad25d24dd9f1cf1b8ef164d5bda39a96365a4a","target":"record","created_at":"2026-05-18T03:30:39Z","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":"4f53d015c1145ef7639bc8e30f40136c4afe72911921eb6492a006bf18537e68","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-03-18T13:09:57Z","title_canon_sha256":"3b28d9dca729bca7b5b9d2764d92f97a6b6f42a1b28b5f2ea9e098b9f4fc1e0e"},"schema_version":"1.0","source":{"id":"1303.4239","kind":"arxiv","version":1}},"canonical_sha256":"77a56d825dc8775e74dca308241d51862e016e6916538df2b15657d8c6036bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a56d825dc8775e74dca308241d51862e016e6916538df2b15657d8c6036bef","first_computed_at":"2026-05-18T03:30:39.155501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:39.155501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"przBPfYqoRNppi26eAyi+fehLB/7O9jlLhu6oXVg+a6OUnqCn6ys4iNk2CcGki2jGEkewauM5zWMaTQeNpNwBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:39.156535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e0d3228c021c5e4920ca05ecdad25d24dd9f1cf1b8ef164d5bda39a96365a4a","sha256:2ca216f08a634c685c14478f842269a10eda2a9d4626b1d3ac2cba3ca71fe66f"],"state_sha256":"7c036ac6f55e5e002d1e5046c250f344d980738fc12821e5d10607b7ec7f5845"}