{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AXOHQ3NUG5VK2RSKT3OUGOQ2AK","short_pith_number":"pith:AXOHQ3NU","canonical_record":{"source":{"id":"1502.04590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-16T16:03:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"eb4cb4480fcd8c2153034f62d6f58909b28ca493b7811b12b0336cbdfaa5240e","abstract_canon_sha256":"5858c4a2012f0551396742efcaa6e4ec594dcc7e27ef3985ffe9342a760f0841"},"schema_version":"1.0"},"canonical_sha256":"05dc786db4376aad464a9edd433a1a02896ff9684e7897dc53a941efef0bd8c0","source":{"kind":"arxiv","id":"1502.04590","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04590","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04590v3","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04590","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"AXOHQ3NUG5VK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AXOHQ3NUG5VK2RSK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AXOHQ3NU","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AXOHQ3NUG5VK2RSKT3OUGOQ2AK","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04590","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-16T16:03:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"eb4cb4480fcd8c2153034f62d6f58909b28ca493b7811b12b0336cbdfaa5240e","abstract_canon_sha256":"5858c4a2012f0551396742efcaa6e4ec594dcc7e27ef3985ffe9342a760f0841"},"schema_version":"1.0"},"canonical_sha256":"05dc786db4376aad464a9edd433a1a02896ff9684e7897dc53a941efef0bd8c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.423912Z","signature_b64":"1SZb0OTffWeh+xIKJyQ12hEMsvtFNlsJX4MdVSL5J581dx9cy0vKSOlnxCbDl6WC22ogrMXApX8C3x2AilgNCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05dc786db4376aad464a9edd433a1a02896ff9684e7897dc53a941efef0bd8c0","last_reissued_at":"2026-05-18T01:05:46.423427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.423427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04590","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9/lXsfS5g94pwikGwtyADgyte7Np/M92gHjCEZlBAjmf9xoKxSZGpmU15vOMUwHGw1Glg3k+HtSmFxZL4xdPCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T22:28:25.515767Z"},"content_sha256":"47790b0b406848052caa983f20d8916bd5694c94dfc3983defd36c5279b0f957","schema_version":"1.0","event_id":"sha256:47790b0b406848052caa983f20d8916bd5694c94dfc3983defd36c5279b0f957"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AXOHQ3NUG5VK2RSKT3OUGOQ2AK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerate flag varieties and Schubert varieties: a characteristic free approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Giovanni Cerulli Irelli, Martina Lanini, Peter Littelmann","submitted_at":"2015-02-16T16:03:54Z","abstract_excerpt":"We consider the PBW filtrations over the integers of the irreducible highest weight modules in type A and C. We show that the associated graded modules can be realized as Demazure modules for group schemes of the same type and doubled rank. We deduce that the corresponding degenerate flag varieties are isomorphic to Schubert varieties in any characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04590","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pp5Md3EIDx4tXUOxoxOfT7kp/apR511ptx5mH5WoHLPBqGWVZL4pN42eI0lToHxI8YZ4YoBSqJ1xAevdAiCPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T22:28:25.516226Z"},"content_sha256":"970cd583c6b768bd9ff7f234b1eda28869a2ff24e73b0b03e5342ee4cf08342d","schema_version":"1.0","event_id":"sha256:970cd583c6b768bd9ff7f234b1eda28869a2ff24e73b0b03e5342ee4cf08342d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/bundle.json","state_url":"https://pith.science/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/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":"2026-05-22T22:28:25Z","links":{"resolver":"https://pith.science/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK","bundle":"https://pith.science/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/bundle.json","state":"https://pith.science/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXOHQ3NUG5VK2RSKT3OUGOQ2AK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AXOHQ3NUG5VK2RSKT3OUGOQ2AK","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":"5858c4a2012f0551396742efcaa6e4ec594dcc7e27ef3985ffe9342a760f0841","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-16T16:03:54Z","title_canon_sha256":"eb4cb4480fcd8c2153034f62d6f58909b28ca493b7811b12b0336cbdfaa5240e"},"schema_version":"1.0","source":{"id":"1502.04590","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04590","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04590v3","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04590","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"AXOHQ3NUG5VK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AXOHQ3NUG5VK2RSK","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AXOHQ3NU","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:970cd583c6b768bd9ff7f234b1eda28869a2ff24e73b0b03e5342ee4cf08342d","target":"graph","created_at":"2026-05-18T01:05:46Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the PBW filtrations over the integers of the irreducible highest weight modules in type A and C. We show that the associated graded modules can be realized as Demazure modules for group schemes of the same type and doubled rank. We deduce that the corresponding degenerate flag varieties are isomorphic to Schubert varieties in any characteristic.","authors_text":"Giovanni Cerulli Irelli, Martina Lanini, Peter Littelmann","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-16T16:03:54Z","title":"Degenerate flag varieties and Schubert varieties: a characteristic free approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04590","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47790b0b406848052caa983f20d8916bd5694c94dfc3983defd36c5279b0f957","target":"record","created_at":"2026-05-18T01:05:46Z","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":"5858c4a2012f0551396742efcaa6e4ec594dcc7e27ef3985ffe9342a760f0841","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-16T16:03:54Z","title_canon_sha256":"eb4cb4480fcd8c2153034f62d6f58909b28ca493b7811b12b0336cbdfaa5240e"},"schema_version":"1.0","source":{"id":"1502.04590","kind":"arxiv","version":3}},"canonical_sha256":"05dc786db4376aad464a9edd433a1a02896ff9684e7897dc53a941efef0bd8c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05dc786db4376aad464a9edd433a1a02896ff9684e7897dc53a941efef0bd8c0","first_computed_at":"2026-05-18T01:05:46.423427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.423427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1SZb0OTffWeh+xIKJyQ12hEMsvtFNlsJX4MdVSL5J581dx9cy0vKSOlnxCbDl6WC22ogrMXApX8C3x2AilgNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.423912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04590","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47790b0b406848052caa983f20d8916bd5694c94dfc3983defd36c5279b0f957","sha256:970cd583c6b768bd9ff7f234b1eda28869a2ff24e73b0b03e5342ee4cf08342d"],"state_sha256":"9ad5d38ecbca363f7165b7f19c8e665b3ca5958be70c7ffa8f69b1dd68be750b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QOEVKPYjkFWzPc8OIaarKUrymuKfkkACLx+6iN9OeBAGBUDniVhqOjR4lpxBu3hSKZn/DVhLEIIXWx2jC6Y1Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T22:28:25.520024Z","bundle_sha256":"664326c5d91f092f226c596316e7d5e10470b49b1330f285a6a64a925353ff85"}}