{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XUXOJI4KQMML2E35QEU6S46ZUU","short_pith_number":"pith:XUXOJI4K","canonical_record":{"source":{"id":"1605.01560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-05T11:46:48Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"63986974ea8021d3425f3fcf4a307fa51effd840bd89aed9b39d25c9e1e2dd5d","abstract_canon_sha256":"5be3df801fe692c65e2e1f87376c259439f7e616556a265059a11df5d511bb6c"},"schema_version":"1.0"},"canonical_sha256":"bd2ee4a38a8318bd137d8129e973d9a50d0218f9e5e802599cb14895453ece18","source":{"kind":"arxiv","id":"1605.01560","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01560","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01560v1","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01560","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"XUXOJI4KQMML","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XUXOJI4KQMML2E35","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XUXOJI4K","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XUXOJI4KQMML2E35QEU6S46ZUU","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-05T11:46:48Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"63986974ea8021d3425f3fcf4a307fa51effd840bd89aed9b39d25c9e1e2dd5d","abstract_canon_sha256":"5be3df801fe692c65e2e1f87376c259439f7e616556a265059a11df5d511bb6c"},"schema_version":"1.0"},"canonical_sha256":"bd2ee4a38a8318bd137d8129e973d9a50d0218f9e5e802599cb14895453ece18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:33.348612Z","signature_b64":"Ts1L11QrRDBX3W/EYCzefQNGGLR4spODIdtZW49+LZtJYX2Rd2+jBHfG5KdKjt77A+hzHTJ3fxUeudNAyQ88Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd2ee4a38a8318bd137d8129e973d9a50d0218f9e5e802599cb14895453ece18","last_reissued_at":"2026-05-18T01:15:33.347975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:33.347975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01560","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":"2026-05-18T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvL8jKDDBcD6i70kCiUNVd/h3t40p3PiBmbUUoQYrhXZ16DZ/AHpbaNYtJV4ewE/6bAAO6Yb1p+dOKgXYvg5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:51:18.380592Z"},"content_sha256":"823aa67188159247d50edc3b3c7d2fc63ea8355448a5a15da5175fecb458cc0a","schema_version":"1.0","event_id":"sha256:823aa67188159247d50edc3b3c7d2fc63ea8355448a5a15da5175fecb458cc0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XUXOJI4KQMML2E35QEU6S46ZUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Weyl modules and nonsymmetric $q$-Whittaker functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.RT","authors_text":"Daniel Orr, Evgeny Feigin, Ievgen Makedonskyi","submitted_at":"2016-05-05T11:46:48Z","abstract_excerpt":"We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker function is a generating function for the graded characters of generalized global Weyl modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01560","kind":"arxiv","version":1},"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":"2026-05-18T01:15:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMOZTqmvjI2QCTnLsv+/apfkRvD1tqJFPr50wuV794Xbi1+JFu0K+NYPVstTAWdl1vc7lMj9QssTu/3yvciEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T19:51:18.381208Z"},"content_sha256":"ce71c402de0e0461029fc56ee0e39d5a5b7ef12685236f9db3bc80b5ddf511f2","schema_version":"1.0","event_id":"sha256:ce71c402de0e0461029fc56ee0e39d5a5b7ef12685236f9db3bc80b5ddf511f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUXOJI4KQMML2E35QEU6S46ZUU/bundle.json","state_url":"https://pith.science/pith/XUXOJI4KQMML2E35QEU6S46ZUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUXOJI4KQMML2E35QEU6S46ZUU/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":"2026-05-27T19:51:18Z","links":{"resolver":"https://pith.science/pith/XUXOJI4KQMML2E35QEU6S46ZUU","bundle":"https://pith.science/pith/XUXOJI4KQMML2E35QEU6S46ZUU/bundle.json","state":"https://pith.science/pith/XUXOJI4KQMML2E35QEU6S46ZUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUXOJI4KQMML2E35QEU6S46ZUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XUXOJI4KQMML2E35QEU6S46ZUU","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":"5be3df801fe692c65e2e1f87376c259439f7e616556a265059a11df5d511bb6c","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-05T11:46:48Z","title_canon_sha256":"63986974ea8021d3425f3fcf4a307fa51effd840bd89aed9b39d25c9e1e2dd5d"},"schema_version":"1.0","source":{"id":"1605.01560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01560","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01560v1","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01560","created_at":"2026-05-18T01:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"XUXOJI4KQMML","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XUXOJI4KQMML2E35","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XUXOJI4K","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:ce71c402de0e0461029fc56ee0e39d5a5b7ef12685236f9db3bc80b5ddf511f2","target":"graph","created_at":"2026-05-18T01:15:33Z","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 introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric $q$-Whittaker functions. In particular, we show that the series part of the nonsymmetric $q$-Whittaker function is a generating function for the graded characters of generalized global Weyl modules.","authors_text":"Daniel Orr, Evgeny Feigin, Ievgen Makedonskyi","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-05T11:46:48Z","title":"Generalized Weyl modules and nonsymmetric $q$-Whittaker functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01560","kind":"arxiv","version":1},"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":"sha256:823aa67188159247d50edc3b3c7d2fc63ea8355448a5a15da5175fecb458cc0a","target":"record","created_at":"2026-05-18T01:15:33Z","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":"5be3df801fe692c65e2e1f87376c259439f7e616556a265059a11df5d511bb6c","cross_cats_sorted":["math.CO","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-05-05T11:46:48Z","title_canon_sha256":"63986974ea8021d3425f3fcf4a307fa51effd840bd89aed9b39d25c9e1e2dd5d"},"schema_version":"1.0","source":{"id":"1605.01560","kind":"arxiv","version":1}},"canonical_sha256":"bd2ee4a38a8318bd137d8129e973d9a50d0218f9e5e802599cb14895453ece18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd2ee4a38a8318bd137d8129e973d9a50d0218f9e5e802599cb14895453ece18","first_computed_at":"2026-05-18T01:15:33.347975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:33.347975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ts1L11QrRDBX3W/EYCzefQNGGLR4spODIdtZW49+LZtJYX2Rd2+jBHfG5KdKjt77A+hzHTJ3fxUeudNAyQ88Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:33.348612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:823aa67188159247d50edc3b3c7d2fc63ea8355448a5a15da5175fecb458cc0a","sha256:ce71c402de0e0461029fc56ee0e39d5a5b7ef12685236f9db3bc80b5ddf511f2"],"state_sha256":"05306e03c910a7a6e43b9a650cd3c08a88e92a3bc059797c79ca094d3113b9fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5iQvdyj1xtaYT+oR1RF5XrUzw4e39wPXu/1glH+PULQd7A+H+asobYGFDHuWv16VURdf32gjQ0J/8xLCm6OAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T19:51:18.384732Z","bundle_sha256":"9d08d0fdfaf5c976e5c39d5dd7fc4b83ee8e3d0a36df5543294d614eccad87fb"}}