{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:WARDM3M5IYWHHWGJ7AQQU472X4","short_pith_number":"pith:WARDM3M5","canonical_record":{"source":{"id":"0907.1049","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-06T17:05:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"00d267130f6b6c89abbbd3d56e38ead678289dab8bf32504cc2e99c4c2946b66","abstract_canon_sha256":"8606d8f0ff055f5a8d279eb27efb51873435e34e2946b6cf082175ff6654c089"},"schema_version":"1.0"},"canonical_sha256":"b022366d9d462c73d8c9f8210a73fabf1668b124ff902fe80e71846134007c01","source":{"kind":"arxiv","id":"0907.1049","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1049","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1049v4","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1049","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"WARDM3M5IYWH","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WARDM3M5IYWHHWGJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WARDM3M5","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:WARDM3M5IYWHHWGJ7AQQU472X4","target":"record","payload":{"canonical_record":{"source":{"id":"0907.1049","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-06T17:05:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"00d267130f6b6c89abbbd3d56e38ead678289dab8bf32504cc2e99c4c2946b66","abstract_canon_sha256":"8606d8f0ff055f5a8d279eb27efb51873435e34e2946b6cf082175ff6654c089"},"schema_version":"1.0"},"canonical_sha256":"b022366d9d462c73d8c9f8210a73fabf1668b124ff902fe80e71846134007c01","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:21.630440Z","signature_b64":"VvSo//x9M75A4bJAvgVISnm9wkjEx/7SfrLbDRaV599LpDvYk5TvQ7AjFBF+iQUuK/aflpC2IJvPYIGelrLlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b022366d9d462c73d8c9f8210a73fabf1668b124ff902fe80e71846134007c01","last_reissued_at":"2026-05-18T03:27:21.629860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:21.629860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.1049","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cT2TsMpkMaU5EyVVie6ACBhQoPNTWGNNA+2mQCXHEhQaMxfuk/RjPhI4pRscmzb8HhqAnFQ77MOfDVqQAAICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:54:55.623153Z"},"content_sha256":"c7120244485ea54bce105ac0d4d96c35049b778ce04e9cf88fe9b64dabada40d","schema_version":"1.0","event_id":"sha256:c7120244485ea54bce105ac0d4d96c35049b778ce04e9cf88fe9b64dabada40d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:WARDM3M5IYWHHWGJ7AQQU472X4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closures of K-orbits in the flag variety for SU*(2n)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"William M. McGovern","submitted_at":"2009-07-06T17:05:54Z","abstract_excerpt":"We characterize the Sp_{2n} orbits in the flag variety for SL_{2n} with rationally smooth closure via a pattern avoidance criterion, also showing that the singular and rationally singular loci of such orbit closures coincide."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1049","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:27:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caIE6fjKuWPq6qlN4UPSRbFwx/8+10m6rQ8AhI5CLdGlyw2vykSQdNBN16Txnhyvts0L4x93fu/fJ0Oico1oAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:54:55.623514Z"},"content_sha256":"218bea46b90b399f765e46b4d112155d6da39db1100f87dee40ae3b0a467b794","schema_version":"1.0","event_id":"sha256:218bea46b90b399f765e46b4d112155d6da39db1100f87dee40ae3b0a467b794"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WARDM3M5IYWHHWGJ7AQQU472X4/bundle.json","state_url":"https://pith.science/pith/WARDM3M5IYWHHWGJ7AQQU472X4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WARDM3M5IYWHHWGJ7AQQU472X4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-02T10:54:55Z","links":{"resolver":"https://pith.science/pith/WARDM3M5IYWHHWGJ7AQQU472X4","bundle":"https://pith.science/pith/WARDM3M5IYWHHWGJ7AQQU472X4/bundle.json","state":"https://pith.science/pith/WARDM3M5IYWHHWGJ7AQQU472X4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WARDM3M5IYWHHWGJ7AQQU472X4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:WARDM3M5IYWHHWGJ7AQQU472X4","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":"8606d8f0ff055f5a8d279eb27efb51873435e34e2946b6cf082175ff6654c089","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-06T17:05:54Z","title_canon_sha256":"00d267130f6b6c89abbbd3d56e38ead678289dab8bf32504cc2e99c4c2946b66"},"schema_version":"1.0","source":{"id":"0907.1049","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1049","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1049v4","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1049","created_at":"2026-05-18T03:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"WARDM3M5IYWH","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"WARDM3M5IYWHHWGJ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"WARDM3M5","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:218bea46b90b399f765e46b4d112155d6da39db1100f87dee40ae3b0a467b794","target":"graph","created_at":"2026-05-18T03:27:21Z","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 characterize the Sp_{2n} orbits in the flag variety for SL_{2n} with rationally smooth closure via a pattern avoidance criterion, also showing that the singular and rationally singular loci of such orbit closures coincide.","authors_text":"William M. McGovern","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-06T17:05:54Z","title":"Closures of K-orbits in the flag variety for SU*(2n)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1049","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:c7120244485ea54bce105ac0d4d96c35049b778ce04e9cf88fe9b64dabada40d","target":"record","created_at":"2026-05-18T03:27:21Z","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":"8606d8f0ff055f5a8d279eb27efb51873435e34e2946b6cf082175ff6654c089","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2009-07-06T17:05:54Z","title_canon_sha256":"00d267130f6b6c89abbbd3d56e38ead678289dab8bf32504cc2e99c4c2946b66"},"schema_version":"1.0","source":{"id":"0907.1049","kind":"arxiv","version":4}},"canonical_sha256":"b022366d9d462c73d8c9f8210a73fabf1668b124ff902fe80e71846134007c01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b022366d9d462c73d8c9f8210a73fabf1668b124ff902fe80e71846134007c01","first_computed_at":"2026-05-18T03:27:21.629860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:21.629860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VvSo//x9M75A4bJAvgVISnm9wkjEx/7SfrLbDRaV599LpDvYk5TvQ7AjFBF+iQUuK/aflpC2IJvPYIGelrLlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:21.630440Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.1049","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7120244485ea54bce105ac0d4d96c35049b778ce04e9cf88fe9b64dabada40d","sha256:218bea46b90b399f765e46b4d112155d6da39db1100f87dee40ae3b0a467b794"],"state_sha256":"f2bf0a0899a89fea5a8143f923e78434ed545bde7cb675673cb28ee92181480d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7h4E5/6B7WIeZkHyxnZWR7I2Qg9Zqy0IRuwlJx1dmMuKibGdZSS0eAXJKaLsvc5chjtdNOmlo5nyYTVqIR7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:54:55.625601Z","bundle_sha256":"d4f8cb5d6564bbb6c67927783e4092691c06f47f3b0d9bedc81047407ee1fad9"}}