{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:N6J2YTMPLWYF5ZQMMMLQUY5UQJ","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":"7dd41b33f615d6783deec195494f9f6dac5dd7dcd16fb32011fdbcbd388e86ba","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-05T09:09:39Z","title_canon_sha256":"b6db2f1be3b12104394392961bfd97eb0db3f64f20b7faef446caed7421d2fab"},"schema_version":"1.0","source":{"id":"math/0103022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0103022","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"math/0103022v1","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0103022","created_at":"2026-05-18T01:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"N6J2YTMPLWYF","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"N6J2YTMPLWYF5ZQM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"N6J2YTMP","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:6ceb7ce1b83f0b0ac1017acd57d8a9bad803711ca6da2f45a1326d1ce269bffa","target":"graph","created_at":"2026-05-18T01:05:37Z","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":"Following Contou-Carrere [CC], we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the Tits building associated to the situation. We prove that the rational smoothness of a Schubert variety can be expressed in terms of a subspace of the Zariski tangent space called, the combinatorial tangent space. For this, we use a characterization of rational smoothness of a Schubert variety introduced by Carrell and Peterson [CP].","authors_text":"St\\'ephane Gaussent","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-03-05T09:09:39Z","title":"Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0103022","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":"sha256:24fbf04618a6d3e229eb26b96690969d683a19dd8bd20809b73cf30792b71f72","target":"record","created_at":"2026-05-18T01:05:37Z","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":"7dd41b33f615d6783deec195494f9f6dac5dd7dcd16fb32011fdbcbd388e86ba","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2001-03-05T09:09:39Z","title_canon_sha256":"b6db2f1be3b12104394392961bfd97eb0db3f64f20b7faef446caed7421d2fab"},"schema_version":"1.0","source":{"id":"math/0103022","kind":"arxiv","version":1}},"canonical_sha256":"6f93ac4d8f5db05ee60c63170a63b482761975c67b1a6b6b025c65905c4f8cc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f93ac4d8f5db05ee60c63170a63b482761975c67b1a6b6b025c65905c4f8cc0","first_computed_at":"2026-05-18T01:05:37.875523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:37.875523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y9W8E+av5xG8y3/Zqr7YMpW6sSP+Hc8x4pHZ7URpbYBf10LKeBN5fPFKLjvU8+2opYIJQLb41rK6eLoEnjgeDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:37.875919Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0103022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24fbf04618a6d3e229eb26b96690969d683a19dd8bd20809b73cf30792b71f72","sha256:6ceb7ce1b83f0b0ac1017acd57d8a9bad803711ca6da2f45a1326d1ce269bffa"],"state_sha256":"a661e40f36e0958235530a6bebe725f93e452f2e86f9ee40f22ce6acd28bd1c2"}