{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:3Q74PDJ5TCDHIPUIZGXZDT57A3","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":"3bba2381185505ebac4a05a1823ed65a7780678178badc1ab6b96371d38ff641","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2004-06-03T12:46:16Z","title_canon_sha256":"b0f57dbf89893bdf076d03673eb700dfed4477725478590b8cd2cca28f2759fc"},"schema_version":"1.0","source":{"id":"math/0406060","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406060","created_at":"2026-07-04T14:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406060v3","created_at":"2026-07-04T14:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406060","created_at":"2026-07-04T14:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"3Q74PDJ5TCDH","created_at":"2026-07-04T14:49:47Z"},{"alias_kind":"pith_short_16","alias_value":"3Q74PDJ5TCDHIPUI","created_at":"2026-07-04T14:49:47Z"},{"alias_kind":"pith_short_8","alias_value":"3Q74PDJ5","created_at":"2026-07-04T14:49:47Z"}],"graph_snapshots":[{"event_id":"sha256:b0d4849c6318f4f8e9a15975b77be710a7a7fb3246b7ecb34ccf42bb9a07ba2c","target":"graph","created_at":"2026-07-04T14:49:47Z","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/math/0406060/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a connection between (degenerate) nonsymmetric Macdonald polynomials and standard bases and dual standard bases of maximal parabolic modules of affine Hecke algebras. Along the way we prove a (weak) polynomiality result for coefficients of symmetric and nonsymmetric Macdonald polynomials.","authors_text":"Bogdan Ion","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2004-06-03T12:46:16Z","title":"Standard bases for affine parabolic modules and nonsymmetric Macdonald polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406060","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:c7527446b8b937bbf5a869da88c816b65fa1246aea9879fc00ceca205178aa18","target":"record","created_at":"2026-07-04T14:49:47Z","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":"3bba2381185505ebac4a05a1823ed65a7780678178badc1ab6b96371d38ff641","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2004-06-03T12:46:16Z","title_canon_sha256":"b0f57dbf89893bdf076d03673eb700dfed4477725478590b8cd2cca28f2759fc"},"schema_version":"1.0","source":{"id":"math/0406060","kind":"arxiv","version":3}},"canonical_sha256":"dc3fc78d3d9886743e88c9af91cfbf06f4b45d3b0695459a857289cc357ce699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc3fc78d3d9886743e88c9af91cfbf06f4b45d3b0695459a857289cc357ce699","first_computed_at":"2026-07-04T14:49:47.823066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:49:47.823066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGofSwOPkp5gB2+zAhVEdDpK8wWriEDbguCziCzZ29vv8h21GwOP8NtroJFg0Lwc+vFvSEdmcLGo7n1PbsiiCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:49:47.823428Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406060","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7527446b8b937bbf5a869da88c816b65fa1246aea9879fc00ceca205178aa18","sha256:b0d4849c6318f4f8e9a15975b77be710a7a7fb3246b7ecb34ccf42bb9a07ba2c"],"state_sha256":"13d7b96a005f3de4da73c6d36e9f2fd547d140329ec590c99c4d02eab73d62d1"}