{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZGNK6FWEASUALWUEDEUUIY5LQI","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":"9f09f12f2b55ad969939787b4bc378cb5e7b8ada612857812f89c14b92a82a40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-26T21:19:54Z","title_canon_sha256":"08f3f3ecde8cf6899aad8b3f2c7a68e3663b2c27bbff208d9b3fc9ed1b54b687"},"schema_version":"1.0","source":{"id":"1003.5234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.5234","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1003.5234v2","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5234","created_at":"2026-05-18T02:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZGNK6FWEASUA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZGNK6FWEASUALWUE","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZGNK6FWE","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:30ccc1e52a7debcbb255eeb20d04aabac142e36841b22ac9e253ff22471d32ee","target":"graph","created_at":"2026-05-18T02:24:26Z","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 consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ has an open dense $P$-orbit. In the complement to this dense orbit, there are infinitely many orbits as soon as the number $t$ of factors in the Levi part is $\\ge 6$. In this paper, we describe the irreducible components of the complement. In particular, we show that there are at most $t-1$ irreducible components.","authors_text":"Karin Baur, Lutz Hille","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-26T21:19:54Z","title":"On the complement of the Richardson orbit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5234","kind":"arxiv","version":2},"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:ef2bc20b197f597892fc20bb657439f3443380aa2d33931374ebe5a4a7992696","target":"record","created_at":"2026-05-18T02:24:26Z","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":"9f09f12f2b55ad969939787b4bc378cb5e7b8ada612857812f89c14b92a82a40","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-03-26T21:19:54Z","title_canon_sha256":"08f3f3ecde8cf6899aad8b3f2c7a68e3663b2c27bbff208d9b3fc9ed1b54b687"},"schema_version":"1.0","source":{"id":"1003.5234","kind":"arxiv","version":2}},"canonical_sha256":"c99aaf16c404a805da8419294463ab821b59febeeba5d99f258d0bb8ccad8eb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c99aaf16c404a805da8419294463ab821b59febeeba5d99f258d0bb8ccad8eb8","first_computed_at":"2026-05-18T02:24:26.515512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:26.515512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Aib9GZrZfSm8WQ/Rrz5nooGZy7CNW3QhYjrvXyfICmOVGbBCqgbWNF5etOMFgvEx0jJpGNneOy+OIsGhUvOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:26.516095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.5234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef2bc20b197f597892fc20bb657439f3443380aa2d33931374ebe5a4a7992696","sha256:30ccc1e52a7debcbb255eeb20d04aabac142e36841b22ac9e253ff22471d32ee"],"state_sha256":"68f867de697471faa7af4b603b1f9fb678ff102f794073aee05a40b7a0918cd6"}