{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:KRCB663JWYWLVYWP3U2RFVGDKL","short_pith_number":"pith:KRCB663J","schema_version":"1.0","canonical_sha256":"54441f7b69b62cbae2cfdd3512d4c352f16bb41b199e5c7249627badda66aa32","source":{"kind":"arxiv","id":"2203.16750","version":3},"attestation_state":"computed","paper":{"title":"Torus orbit closures in the flag variety","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.AG","authors_text":"Eunjeong Lee, Mikiya Masuda, Seonjeong Park","submitted_at":"2022-03-31T02:12:32Z","abstract_excerpt":"The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand--Serganova in the mid-1980s, but it seems that not much has been done since then. In this chapter, we present some of the work by Klyachko and Gelfand--Serganova and our recent work on the topology, geometry, and combinatorics of torus orbit closures in the flag variety."},"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":"2203.16750","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-03-31T02:12:32Z","cross_cats_sorted":["math.AT","math.CO"],"title_canon_sha256":"a46c9f0f83724804591df7a8329b7120b3111d57be9a7bad5067cee871b5eb37","abstract_canon_sha256":"e60dbd9237531b5e001f41407efee39ebd71b13a55425be5049d50c848e5585e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:24:35.145201Z","signature_b64":"3WG2S5Y/djzYGfYZ31PLupKuKqAQO6/Kz4TDdDgbItjAgFPeW+2XgbqyJK7NeXiebLntN8TKVeA656UcM7BgAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54441f7b69b62cbae2cfdd3512d4c352f16bb41b199e5c7249627badda66aa32","last_reissued_at":"2026-07-05T08:24:35.144736Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:24:35.144736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Torus orbit closures in the flag variety","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AT","math.CO"],"primary_cat":"math.AG","authors_text":"Eunjeong Lee, Mikiya Masuda, Seonjeong Park","submitted_at":"2022-03-31T02:12:32Z","abstract_excerpt":"The study of torus orbit closures in the (complete) flag variety was initiated by Klyachko and Gelfand--Serganova in the mid-1980s, but it seems that not much has been done since then. In this chapter, we present some of the work by Klyachko and Gelfand--Serganova and our recent work on the topology, geometry, and combinatorics of torus orbit closures in the flag variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.16750","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.16750/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2203.16750","created_at":"2026-07-05T08:24:35.144792+00:00"},{"alias_kind":"arxiv_version","alias_value":"2203.16750v3","created_at":"2026-07-05T08:24:35.144792+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.16750","created_at":"2026-07-05T08:24:35.144792+00:00"},{"alias_kind":"pith_short_12","alias_value":"KRCB663JWYWL","created_at":"2026-07-05T08:24:35.144792+00:00"},{"alias_kind":"pith_short_16","alias_value":"KRCB663JWYWLVYWP","created_at":"2026-07-05T08:24:35.144792+00:00"},{"alias_kind":"pith_short_8","alias_value":"KRCB663J","created_at":"2026-07-05T08:24:35.144792+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/KRCB663JWYWLVYWP3U2RFVGDKL","json":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL.json","graph_json":"https://pith.science/api/pith-number/KRCB663JWYWLVYWP3U2RFVGDKL/graph.json","events_json":"https://pith.science/api/pith-number/KRCB663JWYWLVYWP3U2RFVGDKL/events.json","paper":"https://pith.science/paper/KRCB663J"},"agent_actions":{"view_html":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL","download_json":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL.json","view_paper":"https://pith.science/paper/KRCB663J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2203.16750&json=true","fetch_graph":"https://pith.science/api/pith-number/KRCB663JWYWLVYWP3U2RFVGDKL/graph.json","fetch_events":"https://pith.science/api/pith-number/KRCB663JWYWLVYWP3U2RFVGDKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL/action/storage_attestation","attest_author":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL/action/author_attestation","sign_citation":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL/action/citation_signature","submit_replication":"https://pith.science/pith/KRCB663JWYWLVYWP3U2RFVGDKL/action/replication_record"}},"created_at":"2026-07-05T08:24:35.144792+00:00","updated_at":"2026-07-05T08:24:35.144792+00:00"}