{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:MHAHUNSUEZI2Y3PQMTC3NBVMLZ","short_pith_number":"pith:MHAHUNSU","canonical_record":{"source":{"id":"0904.4324","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-04-28T07:45:14Z","cross_cats_sorted":[],"title_canon_sha256":"5ae59687ee71af9bc6590e353ce59578746cac56914871b101fcfee1445cfb41","abstract_canon_sha256":"5e8743c6f7188434f9c01e55d76dbd6d401a894087440e101e5cdb90f02de9ca"},"schema_version":"1.0"},"canonical_sha256":"61c07a36542651ac6df064c5b686ac5e7dd8a739a5418dac8deede628d1caabb","source":{"kind":"arxiv","id":"0904.4324","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4324","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4324v6","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4324","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"MHAHUNSUEZI2","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MHAHUNSUEZI2Y3PQ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MHAHUNSU","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:MHAHUNSUEZI2Y3PQMTC3NBVMLZ","target":"record","payload":{"canonical_record":{"source":{"id":"0904.4324","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-04-28T07:45:14Z","cross_cats_sorted":[],"title_canon_sha256":"5ae59687ee71af9bc6590e353ce59578746cac56914871b101fcfee1445cfb41","abstract_canon_sha256":"5e8743c6f7188434f9c01e55d76dbd6d401a894087440e101e5cdb90f02de9ca"},"schema_version":"1.0"},"canonical_sha256":"61c07a36542651ac6df064c5b686ac5e7dd8a739a5418dac8deede628d1caabb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:12.286363Z","signature_b64":"f18AbioSPkOf60J2mC1GTmOy6mAZrGOU2oGr8piW1424blt0wFx9MLfMB0hV4pr42iu/RmiPpDYouyZUoHFGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61c07a36542651ac6df064c5b686ac5e7dd8a739a5418dac8deede628d1caabb","last_reissued_at":"2026-05-18T03:42:12.285551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:12.285551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.4324","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:42:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qPZJeqQYmTGz2nIat7GZyvvdev1meBOcUITbxuZku9DyB6Hzm9AwyBjmkv+WYdZhUTojX2cDkBXzK7kQZLmnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:15:58.871965Z"},"content_sha256":"a15d610e4edf59049ad7c34a6436d6bc24ee1cb6ff9004822246f360d766e74e","schema_version":"1.0","event_id":"sha256:a15d610e4edf59049ad7c34a6436d6bc24ee1cb6ff9004822246f360d766e74e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:MHAHUNSUEZI2Y3PQMTC3NBVMLZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ivan Cherednik, Xiaoguang Ma","submitted_at":"2009-04-28T07:45:14Z","abstract_excerpt":"This paper is based on the lectures given by the first author at Harvard in February and March, 2009. It begins with an introduction to the classical p-adic theory of the Macdonald, Matsumoto and Whittaker functions. Its major directions are as follows: 1) extending the theory of DAHA to arbitrary levels; 2) the affine Satake isomorphism and Hall functions via DAHA; 3) the spinor Dunkl operators for the Q-Toda equation; 4) applications to the nil-DAHA and q-Whittaker functions; 5) the technique of spinors in the differential theory and its applications to the AKZ-QMBP isomorphism theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4324","kind":"arxiv","version":6},"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":"2026-05-18T03:42:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZDUE3M4c72zDyMYNAufU3zgunLpv6DRAHnmBPLyzruE+O/pHYVWeHih0jo45IDMzsWSHud/932LOtJ9Qo+9rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T22:15:58.872603Z"},"content_sha256":"af54ad9caacc351fcc3664fe18148718c469c31e39e4cbac9b04b097573625bd","schema_version":"1.0","event_id":"sha256:af54ad9caacc351fcc3664fe18148718c469c31e39e4cbac9b04b097573625bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/bundle.json","state_url":"https://pith.science/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/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":"2026-05-27T22:15:58Z","links":{"resolver":"https://pith.science/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ","bundle":"https://pith.science/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/bundle.json","state":"https://pith.science/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MHAHUNSUEZI2Y3PQMTC3NBVMLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MHAHUNSUEZI2Y3PQMTC3NBVMLZ","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":"5e8743c6f7188434f9c01e55d76dbd6d401a894087440e101e5cdb90f02de9ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-04-28T07:45:14Z","title_canon_sha256":"5ae59687ee71af9bc6590e353ce59578746cac56914871b101fcfee1445cfb41"},"schema_version":"1.0","source":{"id":"0904.4324","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.4324","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"arxiv_version","alias_value":"0904.4324v6","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.4324","created_at":"2026-05-18T03:42:12Z"},{"alias_kind":"pith_short_12","alias_value":"MHAHUNSUEZI2","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MHAHUNSUEZI2Y3PQ","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MHAHUNSU","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:af54ad9caacc351fcc3664fe18148718c469c31e39e4cbac9b04b097573625bd","target":"graph","created_at":"2026-05-18T03:42:12Z","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":"This paper is based on the lectures given by the first author at Harvard in February and March, 2009. It begins with an introduction to the classical p-adic theory of the Macdonald, Matsumoto and Whittaker functions. Its major directions are as follows: 1) extending the theory of DAHA to arbitrary levels; 2) the affine Satake isomorphism and Hall functions via DAHA; 3) the spinor Dunkl operators for the Q-Toda equation; 4) applications to the nil-DAHA and q-Whittaker functions; 5) the technique of spinors in the differential theory and its applications to the AKZ-QMBP isomorphism theorem.","authors_text":"Ivan Cherednik, Xiaoguang Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-04-28T07:45:14Z","title":"A new take on spherical, Whittaker and Bessel functions (Spherical and Whittaker functions via DAHA I,II)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.4324","kind":"arxiv","version":6},"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:a15d610e4edf59049ad7c34a6436d6bc24ee1cb6ff9004822246f360d766e74e","target":"record","created_at":"2026-05-18T03:42:12Z","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":"5e8743c6f7188434f9c01e55d76dbd6d401a894087440e101e5cdb90f02de9ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-04-28T07:45:14Z","title_canon_sha256":"5ae59687ee71af9bc6590e353ce59578746cac56914871b101fcfee1445cfb41"},"schema_version":"1.0","source":{"id":"0904.4324","kind":"arxiv","version":6}},"canonical_sha256":"61c07a36542651ac6df064c5b686ac5e7dd8a739a5418dac8deede628d1caabb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61c07a36542651ac6df064c5b686ac5e7dd8a739a5418dac8deede628d1caabb","first_computed_at":"2026-05-18T03:42:12.285551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:12.285551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f18AbioSPkOf60J2mC1GTmOy6mAZrGOU2oGr8piW1424blt0wFx9MLfMB0hV4pr42iu/RmiPpDYouyZUoHFGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:12.286363Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.4324","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a15d610e4edf59049ad7c34a6436d6bc24ee1cb6ff9004822246f360d766e74e","sha256:af54ad9caacc351fcc3664fe18148718c469c31e39e4cbac9b04b097573625bd"],"state_sha256":"6f719e457fa63ed0ee0b8c9efdf486c708f9fc825654d9fd0a1a3fe091754283"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iHJTibsofvjr+1lVnVmvayz49rh0l26jUs/QmUXOQ/2JP8ZBqo3T405zk70ul9YNvRpduFYuVXYDgeEdyhcTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T22:15:58.875259Z","bundle_sha256":"34c677e2d05139e7c2704ccd6b94c5938bc575f8c90f629323dbd5b3d6aaf5d2"}}