{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:BYVTULKG7GRH2ZOVUCPLST2FGE","short_pith_number":"pith:BYVTULKG","schema_version":"1.0","canonical_sha256":"0e2b3a2d46f9a27d65d5a09eb94f45310ab9134bda7659ffa8d9917078459c6c","source":{"kind":"arxiv","id":"0904.4493","version":4},"attestation_state":"computed","paper":{"title":"Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Peter E. Trapa, William M. McGovern","submitted_at":"2009-04-29T13:55:01Z","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."},"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":"0904.4493","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-04-29T13:55:01Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"298c0356351366ae27a6f4ade8fdf981214d30af98d04f41a1814e5c83d52628","abstract_canon_sha256":"99ac8907967e9fafacdd74b9e6c1d88996fd4404044ab443766f01d3b5568e40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.779609Z","signature_b64":"LqMbvfbrQNg3+iGRL0nSjuoPvHxfaAJOmN1OpaXrjsRzZ2oN6DPG0gDbGlR2KCQdjevBCW1GFNLBw8vYJfqvCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e2b3a2d46f9a27d65d5a09eb94f45310ab9134bda7659ffa8d9917078459c6c","last_reissued_at":"2026-05-18T03:59:49.779135Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.779135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Peter E. Trapa, William M. McGovern","submitted_at":"2009-04-29T13:55:01Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4493","kind":"arxiv","version":4},"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":"0904.4493","created_at":"2026-05-18T03:59:49.779204+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.4493v4","created_at":"2026-05-18T03:59:49.779204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4493","created_at":"2026-05-18T03:59:49.779204+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYVTULKG7GRH","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYVTULKG7GRH2ZOV","created_at":"2026-05-18T12:25:58.837520+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYVTULKG","created_at":"2026-05-18T12:25:58.837520+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/BYVTULKG7GRH2ZOVUCPLST2FGE","json":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE.json","graph_json":"https://pith.science/api/pith-number/BYVTULKG7GRH2ZOVUCPLST2FGE/graph.json","events_json":"https://pith.science/api/pith-number/BYVTULKG7GRH2ZOVUCPLST2FGE/events.json","paper":"https://pith.science/paper/BYVTULKG"},"agent_actions":{"view_html":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE","download_json":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE.json","view_paper":"https://pith.science/paper/BYVTULKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.4493&json=true","fetch_graph":"https://pith.science/api/pith-number/BYVTULKG7GRH2ZOVUCPLST2FGE/graph.json","fetch_events":"https://pith.science/api/pith-number/BYVTULKG7GRH2ZOVUCPLST2FGE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE/action/storage_attestation","attest_author":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE/action/author_attestation","sign_citation":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE/action/citation_signature","submit_replication":"https://pith.science/pith/BYVTULKG7GRH2ZOVUCPLST2FGE/action/replication_record"}},"created_at":"2026-05-18T03:59:49.779204+00:00","updated_at":"2026-05-18T03:59:49.779204+00:00"}