{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV","short_pith_number":"pith:KEUFKEQZ","schema_version":"1.0","canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","source":{"kind":"arxiv","id":"2605.13091","version":1},"attestation_state":"computed","paper":{"title":"Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\\text{SL}_2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claude Eicher","submitted_at":"2026-05-13T07:01:53Z","abstract_excerpt":"We describe how each finite dimensional Schubert cell in the affine flag variety of $\\text{SL}_2$ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group."},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.13091","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-13T07:01:53Z","cross_cats_sorted":[],"title_canon_sha256":"898aff74c9b24b67ff8f38812c6600142dc68bfb779daecad73b51bda5fe2ea1","abstract_canon_sha256":"8560eaa77d916c4359e9dac4a60eda05f887c260ef43d010121e497c51a2e86f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:58.445637Z","signature_b64":"PmHuSTEkhi56c8z1rN1mMrgIyE+k9t52Yczb8Bs4hG/S4AgQUZrMMDXyQlyhZOTIhPatOM1gFSDdpNL3ZnxaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","last_reissued_at":"2026-05-18T03:08:58.445137Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:58.445137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\\text{SL}_2$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claude Eicher","submitted_at":"2026-05-13T07:01:53Z","abstract_excerpt":"We describe how each finite dimensional Schubert cell in the affine flag variety of $\\text{SL}_2$ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We describe how each finite dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The subgroups of the Iwahori group form a well-defined chain of codimensions one to four for which an explicit orbit decomposition exists on every finite-dimensional Schubert cell.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f7621ad141f374b708bcdc9477539c019f1ec531d28d3b366fefc1acf2d87e00"},"source":{"id":"2605.13091","kind":"arxiv","version":1},"verdict":{"id":"c146002a-c7c5-4ca9-b2bd-e866848a7cff","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:37:20.281751Z","strongest_claim":"We describe how each finite dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits for a chain of subgroups of codimension one to four of the Iwahori group.","one_line_summary":"Each finite-dimensional Schubert cell in the affine flag variety of SL₂ decomposes into orbits under a chain of Iwahori subgroups of codimension one to four.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The subgroups of the Iwahori group form a well-defined chain of codimensions one to four for which an explicit orbit decomposition exists on every finite-dimensional Schubert cell.","pith_extraction_headline":"Finite-dimensional Schubert cells in the affine flag variety of SL₂ decompose into orbits under a chain of Iwahori subgroups of codimensions one to four."},"references":{"count":3,"sample":[{"doi":"","year":null,"title":"A. Beilinson and V. Drinfeld. Quantization of Hitchin 's integrable system and Hecke eigensheaves . Unpublished","work_id":"a5c2f8a0-040f-4da3-8366-cb0dd3fcf88b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2016,"title":"C. Eicher. Relaxed highest weight modules from D -modules on the Kashiwara flag scheme. https://arxiv.org/abs/1607.06342 arXiv:1607.06342 [math.RT] , 2016","work_id":"2021aae7-11d0-485a-81f9-271e03f7d0e0","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"C. Eicher. Twisted D -module extensions of local systems on a certain subvariety isomorphic to G _ m ^2 of the affine flag variety of SL _2 . https://arxiv.org/abs/2011.03764 arXiv:2011.03764 [math.AG","work_id":"dbcea37d-1f88-439e-af25-44215b8a607f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":3,"snapshot_sha256":"71cb863591769176cee557b5478687b5ae21f0834381e8f8fcdae63feb32847a","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":"2605.13091","created_at":"2026-05-18T03:08:58.445202+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13091v1","created_at":"2026-05-18T03:08:58.445202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13091","created_at":"2026-05-18T03:08:58.445202+00:00"},{"alias_kind":"pith_short_12","alias_value":"KEUFKEQZLFSF","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"KEUFKEQZLFSF6HES","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"KEUFKEQZ","created_at":"2026-05-18T12:33:37.589309+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/KEUFKEQZLFSF6HESMJZ4OEKBHV","json":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV.json","graph_json":"https://pith.science/api/pith-number/KEUFKEQZLFSF6HESMJZ4OEKBHV/graph.json","events_json":"https://pith.science/api/pith-number/KEUFKEQZLFSF6HESMJZ4OEKBHV/events.json","paper":"https://pith.science/paper/KEUFKEQZ"},"agent_actions":{"view_html":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV","download_json":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV.json","view_paper":"https://pith.science/paper/KEUFKEQZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13091&json=true","fetch_graph":"https://pith.science/api/pith-number/KEUFKEQZLFSF6HESMJZ4OEKBHV/graph.json","fetch_events":"https://pith.science/api/pith-number/KEUFKEQZLFSF6HESMJZ4OEKBHV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/action/storage_attestation","attest_author":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/action/author_attestation","sign_citation":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/action/citation_signature","submit_replication":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/action/replication_record"}},"created_at":"2026-05-18T03:08:58.445202+00:00","updated_at":"2026-05-18T03:08:58.445202+00:00"}