{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:W7EONXGI7RGFLM5DXA5T64GGT6","short_pith_number":"pith:W7EONXGI","canonical_record":{"source":{"id":"math/0110024","kind":"arxiv","version":10},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-10-01T21:47:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4de39af61929b4434fabb9e2783dcd3ec5ea2f316c2e89d3fb5444482d39225d","abstract_canon_sha256":"079f52d2e7cc8b7618fc9c3032c6d0f2d8205f11701c1506deedb978e2bcfadf"},"schema_version":"1.0"},"canonical_sha256":"b7c8e6dcc8fc4c55b3a3b83b3f70c69f9fa7d67fcaa043fcf3a47716a79a965b","source":{"kind":"arxiv","id":"math/0110024","version":10},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110024","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110024v10","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110024","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_12","alias_value":"W7EONXGI7RGF","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_16","alias_value":"W7EONXGI7RGFLM5D","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_8","alias_value":"W7EONXGI","created_at":"2026-07-04T14:35:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:W7EONXGI7RGFLM5DXA5T64GGT6","target":"record","payload":{"canonical_record":{"source":{"id":"math/0110024","kind":"arxiv","version":10},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-10-01T21:47:16Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"4de39af61929b4434fabb9e2783dcd3ec5ea2f316c2e89d3fb5444482d39225d","abstract_canon_sha256":"079f52d2e7cc8b7618fc9c3032c6d0f2d8205f11701c1506deedb978e2bcfadf"},"schema_version":"1.0"},"canonical_sha256":"b7c8e6dcc8fc4c55b3a3b83b3f70c69f9fa7d67fcaa043fcf3a47716a79a965b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:32.622894Z","signature_b64":"GOsRHs1EH68z7gS+CBDK0cI1onCzdj3F9k1zq2vEkcu1vwSg3Dn8vWojrhukvJVSJdN5fkHGQE4qMjPD1LjdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7c8e6dcc8fc4c55b3a3b83b3f70c69f9fa7d67fcaa043fcf3a47716a79a965b","last_reissued_at":"2026-07-04T14:35:32.622532Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:32.622532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0110024","source_version":10,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:35:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywL7NEq5s34V2PoaMCg7y7VMWL6uvP9itoIJzj+OZm3Dj8z2fVHQUKlfNiHrszQTVFoHh6WRr2GxoFW1oEumBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:13:05.786379Z"},"content_sha256":"962354cee4a49e88754ca97dadb46bd07bde0b194650e0d9055d1a8ad3f8d67f","schema_version":"1.0","event_id":"sha256:962354cee4a49e88754ca97dadb46bd07bde0b194650e0d9055d1a8ad3f8d67f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:W7EONXGI7RGFLM5DXA5T64GGT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Double Affine Hecke Algebras and Difference Fourier Transforms","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ivan Cherednik","submitted_at":"2001-10-01T21:47:16Z","abstract_excerpt":"In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including finite-dimensional ones, give a general description of the semisimple representations with a special consideration of the GL-case, and then gradually restrict ourselves with spherical, pseudo-unitary, and Fourier-invariant representations. The latter generalize the Verlinde algebras and lead to new Gauss-Selberg sums and Macdonald's eta-type identities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110024","kind":"arxiv","version":10},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0110024/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:35:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cQPNLJlaKJsBp+pK+YjCLeMKnMKvLXWWZlogxDVBWrsRH0iV2GUbjJ4JGX+w9gAKKBu8LvZ+yZ1TzDxL+atABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:13:05.787238Z"},"content_sha256":"4582460c86bf1be66e13aae3a49ae032996a8af58e9816dcdc968f9d1e0b190b","schema_version":"1.0","event_id":"sha256:4582460c86bf1be66e13aae3a49ae032996a8af58e9816dcdc968f9d1e0b190b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7EONXGI7RGFLM5DXA5T64GGT6/bundle.json","state_url":"https://pith.science/pith/W7EONXGI7RGFLM5DXA5T64GGT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7EONXGI7RGFLM5DXA5T64GGT6/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":"2026-08-03T21:13:05Z","links":{"resolver":"https://pith.science/pith/W7EONXGI7RGFLM5DXA5T64GGT6","bundle":"https://pith.science/pith/W7EONXGI7RGFLM5DXA5T64GGT6/bundle.json","state":"https://pith.science/pith/W7EONXGI7RGFLM5DXA5T64GGT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7EONXGI7RGFLM5DXA5T64GGT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:W7EONXGI7RGFLM5DXA5T64GGT6","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":"079f52d2e7cc8b7618fc9c3032c6d0f2d8205f11701c1506deedb978e2bcfadf","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2001-10-01T21:47:16Z","title_canon_sha256":"4de39af61929b4434fabb9e2783dcd3ec5ea2f316c2e89d3fb5444482d39225d"},"schema_version":"1.0","source":{"id":"math/0110024","kind":"arxiv","version":10}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110024","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110024v10","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110024","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_12","alias_value":"W7EONXGI7RGF","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_16","alias_value":"W7EONXGI7RGFLM5D","created_at":"2026-07-04T14:35:32Z"},{"alias_kind":"pith_short_8","alias_value":"W7EONXGI","created_at":"2026-07-04T14:35:32Z"}],"graph_snapshots":[{"event_id":"sha256:4582460c86bf1be66e13aae3a49ae032996a8af58e9816dcdc968f9d1e0b190b","target":"graph","created_at":"2026-07-04T14:35:32Z","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/0110024/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including finite-dimensional ones, give a general description of the semisimple representations with a special consideration of the GL-case, and then gradually restrict ourselves with spherical, pseudo-unitary, and Fourier-invariant representations. The latter generalize the Verlinde algebras and lead to new Gauss-Selberg sums and Macdonald's eta-type identities.","authors_text":"Ivan Cherednik","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2001-10-01T21:47:16Z","title":"Double Affine Hecke Algebras and Difference Fourier Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110024","kind":"arxiv","version":10},"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":"sha256:962354cee4a49e88754ca97dadb46bd07bde0b194650e0d9055d1a8ad3f8d67f","target":"record","created_at":"2026-07-04T14:35:32Z","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":"079f52d2e7cc8b7618fc9c3032c6d0f2d8205f11701c1506deedb978e2bcfadf","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2001-10-01T21:47:16Z","title_canon_sha256":"4de39af61929b4434fabb9e2783dcd3ec5ea2f316c2e89d3fb5444482d39225d"},"schema_version":"1.0","source":{"id":"math/0110024","kind":"arxiv","version":10}},"canonical_sha256":"b7c8e6dcc8fc4c55b3a3b83b3f70c69f9fa7d67fcaa043fcf3a47716a79a965b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7c8e6dcc8fc4c55b3a3b83b3f70c69f9fa7d67fcaa043fcf3a47716a79a965b","first_computed_at":"2026-07-04T14:35:32.622532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:32.622532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GOsRHs1EH68z7gS+CBDK0cI1onCzdj3F9k1zq2vEkcu1vwSg3Dn8vWojrhukvJVSJdN5fkHGQE4qMjPD1LjdDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:32.622894Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110024","source_kind":"arxiv","source_version":10}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:962354cee4a49e88754ca97dadb46bd07bde0b194650e0d9055d1a8ad3f8d67f","sha256:4582460c86bf1be66e13aae3a49ae032996a8af58e9816dcdc968f9d1e0b190b"],"state_sha256":"919d0f04b415755fad8e6b609fc4fbec0c6be104084dc428722a29c3e9ac2982"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6OE0wfpFmGD3QFlUkxdQD2X41s9RZ+1o3Ze4XcDukSvB37xfcFQud3mJ/wAYAjb27tU7C8OpKee1KdKz/Ve/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:13:05.793750Z","bundle_sha256":"94818e5f864c6b79802c9fd21a7a1e10a4097bfe593cc66f8553cde4d3bc77fd"}}