{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MRIOSACHNPCUVFFADD7AOZQSXS","short_pith_number":"pith:MRIOSACH","canonical_record":{"source":{"id":"1104.3918","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-04-20T01:58:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2f2d57d305b82f8a88e5c5e08551f787188fdc9424871e1d2d5592653f7c8935","abstract_canon_sha256":"c20deca41fe5b46e14594103ac00a9146138ec7f5f55c934012ef76d74d74c2a"},"schema_version":"1.0"},"canonical_sha256":"6450e900476bc54a94a018fe076612bcad2c3f8cff922b538cdf2aef34c17216","source":{"kind":"arxiv","id":"1104.3918","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3918","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3918v3","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3918","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"MRIOSACHNPCU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MRIOSACHNPCUVFFA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MRIOSACH","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MRIOSACHNPCUVFFADD7AOZQSXS","target":"record","payload":{"canonical_record":{"source":{"id":"1104.3918","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-04-20T01:58:43Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"2f2d57d305b82f8a88e5c5e08551f787188fdc9424871e1d2d5592653f7c8935","abstract_canon_sha256":"c20deca41fe5b46e14594103ac00a9146138ec7f5f55c934012ef76d74d74c2a"},"schema_version":"1.0"},"canonical_sha256":"6450e900476bc54a94a018fe076612bcad2c3f8cff922b538cdf2aef34c17216","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:07.707547Z","signature_b64":"Z4033R3SIW9Tdt51TBAOXua6GZLsMBzWONZQ4zf2eCUAe2gC+AM0lm9zDO0bm1kz00HLE2YPU04crFkXSf4vAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6450e900476bc54a94a018fe076612bcad2c3f8cff922b538cdf2aef34c17216","last_reissued_at":"2026-05-18T03:43:07.706815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:07.706815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.3918","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++cVp0e8ql6MXXysON312cm6wG/raWcdqFPGkK3LzuELj5+chiRh9P8yU43cuM0UAIWkCNjNntLHfGJqTQiWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:25.269967Z"},"content_sha256":"66a8aff96cc6c11db577227f59a86a23d5fcc2332e279ffaa2e265fc901b8272","schema_version":"1.0","event_id":"sha256:66a8aff96cc6c11db577227f59a86a23d5fcc2332e279ffaa2e265fc901b8272"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MRIOSACHNPCUVFFADD7AOZQSXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-dimensional nil-DAHA and Whittaker functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Daniel Orr, Ivan Cherednik","submitted_at":"2011-04-20T01:58:43Z","abstract_excerpt":"This work, to be published in Transformation Groups in two parts, is devoted to the theory of nil-DAHA for the root system A_1 and its applications to symmetric and nonsymmetric (spinor) global q-Whittaker functions. These functions integrate the q-Toda eigenvalue problem and its Dunkl-type nonsymmetric version.\n  The global symmetric function can be interpreted as the generating function of the Demazure characters for dominant weights, which describe the algebraic-geometric properties of the corresponding affine Schubert varieties. Its Harish-Chandra-type asymptotic expansion appeared directl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3918","kind":"arxiv","version":3},"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":"2026-05-18T03:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Knw/76B4XDBifStx/POitmrAbYQxveHVmkGB0zrF6HclTSUsdF9FCnTB2pa6vDiLtn665OsPgN2k+kt/gYCXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:26:25.270385Z"},"content_sha256":"3ed7b92b2dcfa6b0a6f346ca054b8d50386c84de557563e48c0e27d446741537","schema_version":"1.0","event_id":"sha256:3ed7b92b2dcfa6b0a6f346ca054b8d50386c84de557563e48c0e27d446741537"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRIOSACHNPCUVFFADD7AOZQSXS/bundle.json","state_url":"https://pith.science/pith/MRIOSACHNPCUVFFADD7AOZQSXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRIOSACHNPCUVFFADD7AOZQSXS/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":"2026-05-27T10:26:25Z","links":{"resolver":"https://pith.science/pith/MRIOSACHNPCUVFFADD7AOZQSXS","bundle":"https://pith.science/pith/MRIOSACHNPCUVFFADD7AOZQSXS/bundle.json","state":"https://pith.science/pith/MRIOSACHNPCUVFFADD7AOZQSXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRIOSACHNPCUVFFADD7AOZQSXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MRIOSACHNPCUVFFADD7AOZQSXS","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":"c20deca41fe5b46e14594103ac00a9146138ec7f5f55c934012ef76d74d74c2a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-04-20T01:58:43Z","title_canon_sha256":"2f2d57d305b82f8a88e5c5e08551f787188fdc9424871e1d2d5592653f7c8935"},"schema_version":"1.0","source":{"id":"1104.3918","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3918","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3918v3","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3918","created_at":"2026-05-18T03:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"MRIOSACHNPCU","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MRIOSACHNPCUVFFA","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MRIOSACH","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:3ed7b92b2dcfa6b0a6f346ca054b8d50386c84de557563e48c0e27d446741537","target":"graph","created_at":"2026-05-18T03:43:07Z","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 work, to be published in Transformation Groups in two parts, is devoted to the theory of nil-DAHA for the root system A_1 and its applications to symmetric and nonsymmetric (spinor) global q-Whittaker functions. These functions integrate the q-Toda eigenvalue problem and its Dunkl-type nonsymmetric version.\n  The global symmetric function can be interpreted as the generating function of the Demazure characters for dominant weights, which describe the algebraic-geometric properties of the corresponding affine Schubert varieties. Its Harish-Chandra-type asymptotic expansion appeared directl","authors_text":"Daniel Orr, Ivan Cherednik","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-04-20T01:58:43Z","title":"One-dimensional nil-DAHA and Whittaker functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3918","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":"sha256:66a8aff96cc6c11db577227f59a86a23d5fcc2332e279ffaa2e265fc901b8272","target":"record","created_at":"2026-05-18T03:43:07Z","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":"c20deca41fe5b46e14594103ac00a9146138ec7f5f55c934012ef76d74d74c2a","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-04-20T01:58:43Z","title_canon_sha256":"2f2d57d305b82f8a88e5c5e08551f787188fdc9424871e1d2d5592653f7c8935"},"schema_version":"1.0","source":{"id":"1104.3918","kind":"arxiv","version":3}},"canonical_sha256":"6450e900476bc54a94a018fe076612bcad2c3f8cff922b538cdf2aef34c17216","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6450e900476bc54a94a018fe076612bcad2c3f8cff922b538cdf2aef34c17216","first_computed_at":"2026-05-18T03:43:07.706815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:07.706815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z4033R3SIW9Tdt51TBAOXua6GZLsMBzWONZQ4zf2eCUAe2gC+AM0lm9zDO0bm1kz00HLE2YPU04crFkXSf4vAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:07.707547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3918","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66a8aff96cc6c11db577227f59a86a23d5fcc2332e279ffaa2e265fc901b8272","sha256:3ed7b92b2dcfa6b0a6f346ca054b8d50386c84de557563e48c0e27d446741537"],"state_sha256":"06cc4d1c2d2551b8fbb11c052e5ae516f8137abbea781602dafbd156a3a46bc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BxE00OCmx5Rw1VS+VSFyqIE1tGh6KMVJm0I1ubYSUCF2H5auLSoTaFFaPWlw18YCGSIHdTFS+sm+Mw1lZGSBDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:26:25.272709Z","bundle_sha256":"cdad21e17bdf58971ef192bba8c090e3bf07afbd06f1509684191035c95c668a"}}