{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CLDRERW6E26HPI3PEHDG3NGOXY","short_pith_number":"pith:CLDRERW6","canonical_record":{"source":{"id":"1506.07263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-24T07:25:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7dc140951d3c24279bdd8367c609d430013bf1f10e900646ec6d65e8aa44215c","abstract_canon_sha256":"3eebef704b779d5bc56df854faf0af2487ccf96b6d10d9f4158c9cd7bb06eba9"},"schema_version":"1.0"},"canonical_sha256":"12c71246de26bc77a36f21c66db4cebe23086fda6982d1f9aeed59c9785d8cf9","source":{"kind":"arxiv","id":"1506.07263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07263","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07263v2","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07263","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"CLDRERW6E26H","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CLDRERW6E26HPI3P","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CLDRERW6","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CLDRERW6E26HPI3PEHDG3NGOXY","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-24T07:25:12Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"7dc140951d3c24279bdd8367c609d430013bf1f10e900646ec6d65e8aa44215c","abstract_canon_sha256":"3eebef704b779d5bc56df854faf0af2487ccf96b6d10d9f4158c9cd7bb06eba9"},"schema_version":"1.0"},"canonical_sha256":"12c71246de26bc77a36f21c66db4cebe23086fda6982d1f9aeed59c9785d8cf9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:35.662569Z","signature_b64":"MtqWXAfWbhX/L+J0cKgZ/jugXaqJyWCOA3rqcsjYuhE9X2MAlEJRRP32eByvpdLb5cJUUA1AtEmd+lQWUNVxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12c71246de26bc77a36f21c66db4cebe23086fda6982d1f9aeed59c9785d8cf9","last_reissued_at":"2026-05-18T00:24:35.662133Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:35.662133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07263","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c89Cej0XdSW/gQcGWns0ZKIlelUfrNhOP4X7HpXRh9rEZ3JxLLkGl4HERDfocdGIWPDJxrWzq1ccK6eEBTngCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:49:03.048036Z"},"content_sha256":"978534a7697565a24a17948f130f48ad23cc86c09acf1c34ce5ec4cbb83c9a6b","schema_version":"1.0","event_id":"sha256:978534a7697565a24a17948f130f48ad23cc86c09acf1c34ce5ec4cbb83c9a6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CLDRERW6E26HPI3PEHDG3NGOXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An elementary construction of monomial bases of modified quantum affine $\\mathfrak{gl}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Chun-Ju Lai, Li Luo","submitted_at":"2015-06-24T07:25:12Z","abstract_excerpt":"In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of modified quantum $\\mathfrak{gl}_n$ and its canonical basis. A key step of their work is a construction of a monomial basis. Recently, Du and Fu provided an algebraic construction of the canonical basis for modified quantum affine $\\mathfrak{gl}_n$, which among other results used an earlier construction of monomial bases using Ringel-Hall algebra of the cyclic quiver. In this paper, we give an elementary algebraic construction of a monomial basis for affine Schur algebras and modified quantum affine $\\mathfrak{gl}_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07263","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4I94OleqqW9uiNgUrxgf+fuqmsfNGGFR1ypQIFYUwSr2si2/hbAF1yUR9w6URInxyUZbrUcZSp2AuWyho9TOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:49:03.048412Z"},"content_sha256":"d90d08785a8e5ad1b9d76c793550e2feb78f619a919c47504cfe3260e324b962","schema_version":"1.0","event_id":"sha256:d90d08785a8e5ad1b9d76c793550e2feb78f619a919c47504cfe3260e324b962"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLDRERW6E26HPI3PEHDG3NGOXY/bundle.json","state_url":"https://pith.science/pith/CLDRERW6E26HPI3PEHDG3NGOXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLDRERW6E26HPI3PEHDG3NGOXY/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":"2026-06-12T09:49:03Z","links":{"resolver":"https://pith.science/pith/CLDRERW6E26HPI3PEHDG3NGOXY","bundle":"https://pith.science/pith/CLDRERW6E26HPI3PEHDG3NGOXY/bundle.json","state":"https://pith.science/pith/CLDRERW6E26HPI3PEHDG3NGOXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLDRERW6E26HPI3PEHDG3NGOXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CLDRERW6E26HPI3PEHDG3NGOXY","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":"3eebef704b779d5bc56df854faf0af2487ccf96b6d10d9f4158c9cd7bb06eba9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-24T07:25:12Z","title_canon_sha256":"7dc140951d3c24279bdd8367c609d430013bf1f10e900646ec6d65e8aa44215c"},"schema_version":"1.0","source":{"id":"1506.07263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07263","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07263v2","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07263","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"CLDRERW6E26H","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CLDRERW6E26HPI3P","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CLDRERW6","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:d90d08785a8e5ad1b9d76c793550e2feb78f619a919c47504cfe3260e324b962","target":"graph","created_at":"2026-05-18T00:24:35Z","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":"In 1990 Beilinson, Lusztig and MacPherson provided a geometric realization of modified quantum $\\mathfrak{gl}_n$ and its canonical basis. A key step of their work is a construction of a monomial basis. Recently, Du and Fu provided an algebraic construction of the canonical basis for modified quantum affine $\\mathfrak{gl}_n$, which among other results used an earlier construction of monomial bases using Ringel-Hall algebra of the cyclic quiver. In this paper, we give an elementary algebraic construction of a monomial basis for affine Schur algebras and modified quantum affine $\\mathfrak{gl}_n$.","authors_text":"Chun-Ju Lai, Li Luo","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-24T07:25:12Z","title":"An elementary construction of monomial bases of modified quantum affine $\\mathfrak{gl}_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07263","kind":"arxiv","version":2},"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":"sha256:978534a7697565a24a17948f130f48ad23cc86c09acf1c34ce5ec4cbb83c9a6b","target":"record","created_at":"2026-05-18T00:24:35Z","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":"3eebef704b779d5bc56df854faf0af2487ccf96b6d10d9f4158c9cd7bb06eba9","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-06-24T07:25:12Z","title_canon_sha256":"7dc140951d3c24279bdd8367c609d430013bf1f10e900646ec6d65e8aa44215c"},"schema_version":"1.0","source":{"id":"1506.07263","kind":"arxiv","version":2}},"canonical_sha256":"12c71246de26bc77a36f21c66db4cebe23086fda6982d1f9aeed59c9785d8cf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12c71246de26bc77a36f21c66db4cebe23086fda6982d1f9aeed59c9785d8cf9","first_computed_at":"2026-05-18T00:24:35.662133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:35.662133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MtqWXAfWbhX/L+J0cKgZ/jugXaqJyWCOA3rqcsjYuhE9X2MAlEJRRP32eByvpdLb5cJUUA1AtEmd+lQWUNVxCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:35.662569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:978534a7697565a24a17948f130f48ad23cc86c09acf1c34ce5ec4cbb83c9a6b","sha256:d90d08785a8e5ad1b9d76c793550e2feb78f619a919c47504cfe3260e324b962"],"state_sha256":"8d2d0b2b20e35f7f0f38174a981f9ad48e55babd9e3cd1ba003abc92f624cf29"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbvO95tArQ6sjq/unCRrrE6Ja4K9rOGo+owVEe0Ilc1YR/grKq/eKzrGT5sH6tFaxmCoGnjjn9HFqpStmBhnDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:49:03.050471Z","bundle_sha256":"dca3585dd6d7b37ed0cf36d8b7823a97da0a0541771bd34997295348c042cda1"}}