{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TNYQFIBCXF7W6UDUUWNJ4H6YIW","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":"da500bd885c070a57442832b6b1209966678581888bc0b94fd51cee000bbb0f5","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-28T07:20:35Z","title_canon_sha256":"90c6310c8c01cb877f7bf59b4e424eda60fdb86252e67ec1edfa5f3fa36fed0d"},"schema_version":"1.0","source":{"id":"2412.00116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.00116","created_at":"2026-07-05T09:42:36Z"},{"alias_kind":"arxiv_version","alias_value":"2412.00116v1","created_at":"2026-07-05T09:42:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.00116","created_at":"2026-07-05T09:42:36Z"},{"alias_kind":"pith_short_12","alias_value":"TNYQFIBCXF7W","created_at":"2026-07-05T09:42:36Z"},{"alias_kind":"pith_short_16","alias_value":"TNYQFIBCXF7W6UDU","created_at":"2026-07-05T09:42:36Z"},{"alias_kind":"pith_short_8","alias_value":"TNYQFIBC","created_at":"2026-07-05T09:42:36Z"}],"graph_snapshots":[{"event_id":"sha256:dff2720bae8faf828e7176fa383633b3dd5d52084ac6ab807cdf28fce162ebd9","target":"graph","created_at":"2026-07-05T09:42:36Z","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/2412.00116/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study $q$-Whittaker polynomials and their monomial expansions given by the fermionic formula, the inv statistic of Haglund-Haiman-Loehr and the quinv statistic of Ayyer-Mandelshtam-Martin. The combinatorial models underlying these expansions are partition overlaid patterns and column strict fillings. The former model is closely tied to representations of the affine Lie algebra $\\widehat{\\mathfrak{sl}_n}$ and admits projections, branching maps and direct limits that mirror these structures in the Chari-Loktev basis of local Weyl modules. We formulate novel versions of these notions in the co","authors_text":"Aritra Bhattacharya, Sankaran Viswanath, T V Ratheesh","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-28T07:20:35Z","title":"$q$-Whittaker polynomials: bases, branching and direct limits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.00116","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:c1f69ed878cea35772a818a18429f091353f7890adf269044183316500130043","target":"record","created_at":"2026-07-05T09:42:36Z","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":"da500bd885c070a57442832b6b1209966678581888bc0b94fd51cee000bbb0f5","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-28T07:20:35Z","title_canon_sha256":"90c6310c8c01cb877f7bf59b4e424eda60fdb86252e67ec1edfa5f3fa36fed0d"},"schema_version":"1.0","source":{"id":"2412.00116","kind":"arxiv","version":1}},"canonical_sha256":"9b7102a022b97f6f5074a59a9e1fd845b9bad5915365c8a12c89ed8d8eb1807f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b7102a022b97f6f5074a59a9e1fd845b9bad5915365c8a12c89ed8d8eb1807f","first_computed_at":"2026-07-05T09:42:36.493122Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:42:36.493122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tv2+9g3Ac3LKqRRkPxDumiIQ+hQHBbfNxXOyCLawXXSirbTUWhdEhf1ObDeLf69Iqe42qEjIWCR/WwqiKOEjDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:42:36.493690Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.00116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1f69ed878cea35772a818a18429f091353f7890adf269044183316500130043","sha256:dff2720bae8faf828e7176fa383633b3dd5d52084ac6ab807cdf28fce162ebd9"],"state_sha256":"63b8f47ec9bcd6a53fefbcf0c73c9cb239f6bf29e874045b3301a3274a66fc29"}