{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV","short_pith_number":"pith:KEUFKEQZ","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"},"canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","source":{"kind":"arxiv","id":"2605.13091","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13091","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13091v1","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13091","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"KEUFKEQZLFSF","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KEUFKEQZLFSF6HES","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KEUFKEQZ","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV","target":"record","payload":{"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"},"canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","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"},"source_kind":"arxiv","source_id":"2605.13091","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGbJ+0nFPy1Q6iVoJxeTXs4vB4BEazxbq4AZiEv7M2hIspMDUZYFJ1glgI3fsZTTZ0yM/68Z1Zlx/nGKg0smCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:25:22.132050Z"},"content_sha256":"9e341dbb0543bffa13fbd0a85b1df73f027abf9ba6ced1bc07451bdcb9b72dc6","schema_version":"1.0","event_id":"sha256:9e341dbb0543bffa13fbd0a85b1df73f027abf9ba6ced1bc07451bdcb9b72dc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV","target":"graph","payload":{"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"},"verdict_id":"c146002a-c7c5-4ca9-b2bd-e866848a7cff"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSIR6hD95tlRy2R4AlraD2cizDDoya+97V7SpQuCde2OBj9AFD5CbrHHNOoyJs5xHHEjKV4SGas2aU82GUx4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:25:22.132641Z"},"content_sha256":"8d8540fd1549b6952af7d228b901551ddfecaf586b5b32f073f98a8d3383a77f","schema_version":"1.0","event_id":"sha256:8d8540fd1549b6952af7d228b901551ddfecaf586b5b32f073f98a8d3383a77f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/bundle.json","state_url":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T16:25:22Z","links":{"resolver":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV","bundle":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/bundle.json","state":"https://pith.science/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEUFKEQZLFSF6HESMJZ4OEKBHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KEUFKEQZLFSF6HESMJZ4OEKBHV","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":"8560eaa77d916c4359e9dac4a60eda05f887c260ef43d010121e497c51a2e86f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-13T07:01:53Z","title_canon_sha256":"898aff74c9b24b67ff8f38812c6600142dc68bfb779daecad73b51bda5fe2ea1"},"schema_version":"1.0","source":{"id":"2605.13091","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13091","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13091v1","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13091","created_at":"2026-05-18T03:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"KEUFKEQZLFSF","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"KEUFKEQZLFSF6HES","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"KEUFKEQZ","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:8d8540fd1549b6952af7d228b901551ddfecaf586b5b32f073f98a8d3383a77f","target":"graph","created_at":"2026-05-18T03:08:58Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","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."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","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."}],"snapshot_sha256":"f7621ad141f374b708bcdc9477539c019f1ec531d28d3b366fefc1acf2d87e00"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Claude Eicher","cross_cats":[],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-13T07:01:53Z","title":"Orbits of subgroups of codimension one to four of the Iwahori group in the affine flag variety of $\\text{SL}_2$"},"references":{"count":3,"internal_anchors":0,"resolved_work":3,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A. Beilinson and V. Drinfeld. Quantization of Hitchin 's integrable system and Hecke eigensheaves . Unpublished","work_id":"a5c2f8a0-040f-4da3-8366-cb0dd3fcf88b","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"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","year":2016},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"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","year":2011}],"snapshot_sha256":"71cb863591769176cee557b5478687b5ae21f0834381e8f8fcdae63feb32847a"},"source":{"id":"2605.13091","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:37:20.281751Z","id":"c146002a-c7c5-4ca9-b2bd-e866848a7cff","model_set":{"reader":"grok-4.3"},"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","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.","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.","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."}},"verdict_id":"c146002a-c7c5-4ca9-b2bd-e866848a7cff"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9e341dbb0543bffa13fbd0a85b1df73f027abf9ba6ced1bc07451bdcb9b72dc6","target":"record","created_at":"2026-05-18T03:08:58Z","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":"8560eaa77d916c4359e9dac4a60eda05f887c260ef43d010121e497c51a2e86f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2026-05-13T07:01:53Z","title_canon_sha256":"898aff74c9b24b67ff8f38812c6600142dc68bfb779daecad73b51bda5fe2ea1"},"schema_version":"1.0","source":{"id":"2605.13091","kind":"arxiv","version":1}},"canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"512855121959645f1c926273c711413d5081a7aade8f2dcf717fcc0dffe34602","first_computed_at":"2026-05-18T03:08:58.445137Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:58.445137Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PmHuSTEkhi56c8z1rN1mMrgIyE+k9t52Yczb8Bs4hG/S4AgQUZrMMDXyQlyhZOTIhPatOM1gFSDdpNL3ZnxaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:58.445637Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13091","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e341dbb0543bffa13fbd0a85b1df73f027abf9ba6ced1bc07451bdcb9b72dc6","sha256:8d8540fd1549b6952af7d228b901551ddfecaf586b5b32f073f98a8d3383a77f"],"state_sha256":"909d5759a8c7cbc25c332bc38296f390306dda71b145e30952f7db22490f0fb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7PplWT47jHe47QlZhXOdWB9Rj7ErSAfYMbWWjC1M9zC6qR9X5qt+VU0bC6AqhYz/GEls/73XjFiwof689dQtAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:25:22.135362Z","bundle_sha256":"f19862e02a3cd84e65b0db3e617c7b22d9f40850ebe68df3ea7e7067a608f8e5"}}