{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:D2NX627FWAWD2KJJZLLNQN7W7Z","short_pith_number":"pith:D2NX627F","schema_version":"1.0","canonical_sha256":"1e9b7f6be5b02c3d2929cad6d837f6fe73ee1a62e5d86267544b3127d91e8d60","source":{"kind":"arxiv","id":"1905.09573","version":1},"attestation_state":"computed","paper":{"title":"Smoothness of Schubert varieties indexed by involutions in finite simply laced types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Hultman, Vincent Umutabazi","submitted_at":"2019-05-23T10:28:11Z","abstract_excerpt":"We prove that in finite, simply laced types, every Schubert variety indexed by an involution which is not the longest element of some parabolic subgroup is singular."},"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":"1905.09573","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-23T10:28:11Z","cross_cats_sorted":[],"title_canon_sha256":"4552e8b07bd258588d12ad9648dbbcd307d4a561bd243bf37f7d79a0aeaa2e59","abstract_canon_sha256":"f1a21a752aeea2f62fabb719ae04eb1bedb332bffa9e4039c91a9bf40b9bfb59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:16.679984Z","signature_b64":"3n1EahpWK0nTA4MdX9AD5ti1z313Qb4n4PIW853cWnGNPqNMl28ODy+xnn0xmmKzw0UH30/eDqNqJN/HmuQuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e9b7f6be5b02c3d2929cad6d837f6fe73ee1a62e5d86267544b3127d91e8d60","last_reissued_at":"2026-05-17T23:45:16.679407Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:16.679407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smoothness of Schubert varieties indexed by involutions in finite simply laced types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Axel Hultman, Vincent Umutabazi","submitted_at":"2019-05-23T10:28:11Z","abstract_excerpt":"We prove that in finite, simply laced types, every Schubert variety indexed by an involution which is not the longest element of some parabolic subgroup is singular."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.09573","kind":"arxiv","version":1},"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":"1905.09573","created_at":"2026-05-17T23:45:16.679526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.09573v1","created_at":"2026-05-17T23:45:16.679526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.09573","created_at":"2026-05-17T23:45:16.679526+00:00"},{"alias_kind":"pith_short_12","alias_value":"D2NX627FWAWD","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"D2NX627FWAWD2KJJ","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"D2NX627F","created_at":"2026-05-18T12:33:15.570797+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/D2NX627FWAWD2KJJZLLNQN7W7Z","json":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z.json","graph_json":"https://pith.science/api/pith-number/D2NX627FWAWD2KJJZLLNQN7W7Z/graph.json","events_json":"https://pith.science/api/pith-number/D2NX627FWAWD2KJJZLLNQN7W7Z/events.json","paper":"https://pith.science/paper/D2NX627F"},"agent_actions":{"view_html":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z","download_json":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z.json","view_paper":"https://pith.science/paper/D2NX627F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.09573&json=true","fetch_graph":"https://pith.science/api/pith-number/D2NX627FWAWD2KJJZLLNQN7W7Z/graph.json","fetch_events":"https://pith.science/api/pith-number/D2NX627FWAWD2KJJZLLNQN7W7Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z/action/storage_attestation","attest_author":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z/action/author_attestation","sign_citation":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z/action/citation_signature","submit_replication":"https://pith.science/pith/D2NX627FWAWD2KJJZLLNQN7W7Z/action/replication_record"}},"created_at":"2026-05-17T23:45:16.679526+00:00","updated_at":"2026-05-17T23:45:16.679526+00:00"}