{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BYVTULKG7GRH2ZOVUCPLST2FGE","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":"99ac8907967e9fafacdd74b9e6c1d88996fd4404044ab443766f01d3b5568e40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-04-29T13:55:01Z","title_canon_sha256":"298c0356351366ae27a6f4ade8fdf981214d30af98d04f41a1814e5c83d52628"},"schema_version":"1.0","source":{"id":"0904.4493","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4493","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4493v4","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4493","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"BYVTULKG7GRH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BYVTULKG7GRH2ZOV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BYVTULKG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:652acd356b96a28efb119f1e734a53a27c2a57e00c35d6910f2a968d6ab9225f","target":"graph","created_at":"2026-05-18T03:59:49Z","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 give a pattern avoidance criterion to classify the orbits of Sp(p,C) x Sp(q,C) (resp. GL(n,C)) on the flag variety of type C_{p+q} (resp. D_n) with rationally smooth closure. We show that all such orbit closures fiber (with smooth fiber) over a smaller flag variety, and hence are in fact smooth. In addition we prove that the classification is insensitive to isogeny.","authors_text":"Peter E. Trapa, William M. McGovern","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-04-29T13:55:01Z","title":"Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4493","kind":"arxiv","version":4},"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":"sha256:59b88bdb72d232502d8eb6618d1af979516440c84bcc2446ae51f831a0eaa16a","target":"record","created_at":"2026-05-18T03:59:49Z","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":"99ac8907967e9fafacdd74b9e6c1d88996fd4404044ab443766f01d3b5568e40","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-04-29T13:55:01Z","title_canon_sha256":"298c0356351366ae27a6f4ade8fdf981214d30af98d04f41a1814e5c83d52628"},"schema_version":"1.0","source":{"id":"0904.4493","kind":"arxiv","version":4}},"canonical_sha256":"0e2b3a2d46f9a27d65d5a09eb94f45310ab9134bda7659ffa8d9917078459c6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e2b3a2d46f9a27d65d5a09eb94f45310ab9134bda7659ffa8d9917078459c6c","first_computed_at":"2026-05-18T03:59:49.779135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.779135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LqMbvfbrQNg3+iGRL0nSjuoPvHxfaAJOmN1OpaXrjsRzZ2oN6DPG0gDbGlR2KCQdjevBCW1GFNLBw8vYJfqvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.779609Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4493","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59b88bdb72d232502d8eb6618d1af979516440c84bcc2446ae51f831a0eaa16a","sha256:652acd356b96a28efb119f1e734a53a27c2a57e00c35d6910f2a968d6ab9225f"],"state_sha256":"296ed11e5808764388c06e723246b0f2bbef7e222d5b1cf180f00bd510470953"}