{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:CMYMOJRZ4LEZQRSC2OBI25IO27","short_pith_number":"pith:CMYMOJRZ","schema_version":"1.0","canonical_sha256":"1330c72639e2c9984642d3828d750ed7d4176d45b6e3905893f498cd330f99ef","source":{"kind":"arxiv","id":"0909.0564","version":2},"attestation_state":"computed","paper":{"title":"A Gr\\\"{o}bner basis for Kazhdan-Lusztig ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Alexander Woo, Alexander Yong","submitted_at":"2009-09-03T03:41:37Z","abstract_excerpt":"Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. Our main result is a Grobner basis for these ideals. This provides a single geometric setting to transparently explain the naturality of pipe dreams on the Rothe diagram of a permutation, and their appearance in:\n  * combinatorial formulas [Fomin-Kirillov '94] for Schubert and Grothendieck polynomials of [Lascoux-Schutzenberger '82];\n  * the equ"},"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":"0909.0564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-09-03T03:41:37Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"db26d4ef43fe866a4f341fb3d9b81017abcc9a033bbe3b242f0316d4d4307453","abstract_canon_sha256":"406f877ce01860ef3de6dda53b1c6b6be34f72f71a4aef52a3a555a09ae7a81e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:58.737268Z","signature_b64":"0FISyO7GnNLzvIImCETnofhVoa3xz4tbZBitDAMdF9bEXY6Cnjk5mQfxpc9KmTH6+nxEOx5n3MxCyr/IbQBiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1330c72639e2c9984642d3828d750ed7d4176d45b6e3905893f498cd330f99ef","last_reissued_at":"2026-05-18T03:49:58.736793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:58.736793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Gr\\\"{o}bner basis for Kazhdan-Lusztig ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CO","authors_text":"Alexander Woo, Alexander Yong","submitted_at":"2009-09-03T03:41:37Z","abstract_excerpt":"Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. Our main result is a Grobner basis for these ideals. This provides a single geometric setting to transparently explain the naturality of pipe dreams on the Rothe diagram of a permutation, and their appearance in:\n  * combinatorial formulas [Fomin-Kirillov '94] for Schubert and Grothendieck polynomials of [Lascoux-Schutzenberger '82];\n  * the equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0564","kind":"arxiv","version":2},"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":"0909.0564","created_at":"2026-05-18T03:49:58.736871+00:00"},{"alias_kind":"arxiv_version","alias_value":"0909.0564v2","created_at":"2026-05-18T03:49:58.736871+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0564","created_at":"2026-05-18T03:49:58.736871+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMYMOJRZ4LEZ","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMYMOJRZ4LEZQRSC","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMYMOJRZ","created_at":"2026-05-18T12:25:59.703012+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/CMYMOJRZ4LEZQRSC2OBI25IO27","json":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27.json","graph_json":"https://pith.science/api/pith-number/CMYMOJRZ4LEZQRSC2OBI25IO27/graph.json","events_json":"https://pith.science/api/pith-number/CMYMOJRZ4LEZQRSC2OBI25IO27/events.json","paper":"https://pith.science/paper/CMYMOJRZ"},"agent_actions":{"view_html":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27","download_json":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27.json","view_paper":"https://pith.science/paper/CMYMOJRZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0909.0564&json=true","fetch_graph":"https://pith.science/api/pith-number/CMYMOJRZ4LEZQRSC2OBI25IO27/graph.json","fetch_events":"https://pith.science/api/pith-number/CMYMOJRZ4LEZQRSC2OBI25IO27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27/action/storage_attestation","attest_author":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27/action/author_attestation","sign_citation":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27/action/citation_signature","submit_replication":"https://pith.science/pith/CMYMOJRZ4LEZQRSC2OBI25IO27/action/replication_record"}},"created_at":"2026-05-18T03:49:58.736871+00:00","updated_at":"2026-05-18T03:49:58.736871+00:00"}