{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:D7ICQV3RCNBE4QYBYCT3LQWVZJ","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":"2c6bddff452715ec22854211079b35306e8829c0baa25b6c2ea2c99a28119f5f","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-07T17:51:40Z","title_canon_sha256":"d8f132bfaeb77e7c55b5df45bd917f76b9be09269393f992da95151e3381d1f6"},"schema_version":"1.0","source":{"id":"2211.03724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.03724","created_at":"2026-07-05T05:13:52Z"},{"alias_kind":"arxiv_version","alias_value":"2211.03724v1","created_at":"2026-07-05T05:13:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.03724","created_at":"2026-07-05T05:13:52Z"},{"alias_kind":"pith_short_12","alias_value":"D7ICQV3RCNBE","created_at":"2026-07-05T05:13:52Z"},{"alias_kind":"pith_short_16","alias_value":"D7ICQV3RCNBE4QYB","created_at":"2026-07-05T05:13:52Z"},{"alias_kind":"pith_short_8","alias_value":"D7ICQV3R","created_at":"2026-07-05T05:13:52Z"}],"graph_snapshots":[{"event_id":"sha256:58cb678bb3c8a0d35a98f5096ee3ee4da925275644c05cd4b5f2f408f58a8cee","target":"graph","created_at":"2026-07-05T05:13:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.03724/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe the structure of the Whittaker or Gelfand-Graev module on a $n$-fold metaplectic cover of a $p$-adic group $G$ at both the Iwahori and spherical level. We express our answer in terms of the representation theory of a quantum group at a root of unity attached to the Langlands dual group of $G$. To do so, we introduce an algebro-combinatorial model for these modules and develop for them a Kazhdan-Lusztig theory involving new generic parameters. These parameters can either be specialized to Gauss sums to recover the $p$-adic theory or to the natural grading parameter in the representa","authors_text":"Manish M. Patnaik, Valentin Buciumas","cross_cats":["math.NT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-07T17:51:40Z","title":"Metaplectic Covers of $p$-adic Groups and Quantum Groups at Roots of Unity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.03724","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:f2ed16ee04b75d37764c149a487ecea7a8f5c7966ee50541774505c0021b5277","target":"record","created_at":"2026-07-05T05:13:52Z","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":"2c6bddff452715ec22854211079b35306e8829c0baa25b6c2ea2c99a28119f5f","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2022-11-07T17:51:40Z","title_canon_sha256":"d8f132bfaeb77e7c55b5df45bd917f76b9be09269393f992da95151e3381d1f6"},"schema_version":"1.0","source":{"id":"2211.03724","kind":"arxiv","version":1}},"canonical_sha256":"1fd028577113424e4301c0a7b5c2d5ca453ec70d80d30f416b3dc784b1ba0b71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fd028577113424e4301c0a7b5c2d5ca453ec70d80d30f416b3dc784b1ba0b71","first_computed_at":"2026-07-05T05:13:52.083427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:52.083427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YhhCkV35jnvcE0KtACdiB89LCkjzHIUdW7yNLDVZgE9klPgFBVT05srKn91evDDREol20cuBRVlgz+yZZGCaCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:52.083772Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.03724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2ed16ee04b75d37764c149a487ecea7a8f5c7966ee50541774505c0021b5277","sha256:58cb678bb3c8a0d35a98f5096ee3ee4da925275644c05cd4b5f2f408f58a8cee"],"state_sha256":"9964e4d4d3909d1cea3f1b53ab27ad743cee9dbff048ef04960e90add45bd06e"}