{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JDPGC7JZ4E2N7NSTIBGBBL7Y4P","short_pith_number":"pith:JDPGC7JZ","canonical_record":{"source":{"id":"1403.0602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-03T21:31:10Z","cross_cats_sorted":["math.NT","math.QA"],"title_canon_sha256":"9a09c1fc8fb40a02b3b97dee6c3912f2dff4d66eba02c85412a4ca5a2b7aa3a7","abstract_canon_sha256":"28521320cba4a349a6e5919db6a12fe4be5536c4f6d1f3256b8ebeda07f7e97f"},"schema_version":"1.0"},"canonical_sha256":"48de617d39e134dfb653404c10aff8e3cee699328037256c0f352b6b891b22fe","source":{"kind":"arxiv","id":"1403.0602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0602","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0602v1","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0602","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"JDPGC7JZ4E2N","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDPGC7JZ4E2N7NST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDPGC7JZ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JDPGC7JZ4E2N7NSTIBGBBL7Y4P","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-03T21:31:10Z","cross_cats_sorted":["math.NT","math.QA"],"title_canon_sha256":"9a09c1fc8fb40a02b3b97dee6c3912f2dff4d66eba02c85412a4ca5a2b7aa3a7","abstract_canon_sha256":"28521320cba4a349a6e5919db6a12fe4be5536c4f6d1f3256b8ebeda07f7e97f"},"schema_version":"1.0"},"canonical_sha256":"48de617d39e134dfb653404c10aff8e3cee699328037256c0f352b6b891b22fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:16.169568Z","signature_b64":"TXEBEgIC35gCA/6rmBEpHMmK872e/b6ydqXa/m82qthP30lrTfMYcoS7FmBKq8SM99owgMkorjzdldkwqIR8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48de617d39e134dfb653404c10aff8e3cee699328037256c0f352b6b891b22fe","last_reissued_at":"2026-05-18T02:57:16.168999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:16.168999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0602","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMFPCKXuHzoHGAiTZjwwiV/C2nJKGWvtZaQETBN3gkAuPxN3SQh25Yd5TmE9clh9tGklNtVPMDIfFB5oHgEyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:50:55.944874Z"},"content_sha256":"a66a9eecac4e5ba3ef4ed6cc3956bd3a8ab432b6f79b8e99709f533753cf97d2","schema_version":"1.0","event_id":"sha256:a66a9eecac4e5ba3ef4ed6cc3956bd3a8ab432b6f79b8e99709f533753cf97d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JDPGC7JZ4E2N7NSTIBGBBL7Y4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Iwahori-Hecke algebras for p-adic loop groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.QA"],"primary_cat":"math.RT","authors_text":"Alexander Braverman, David Kazhdan, Manish Patnaik","submitted_at":"2014-03-03T21:31:10Z","abstract_excerpt":"This paper is a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik's double affine Hecke algebra. Furthermore, using these results, we give an explicit description of the affine Satake isomorphism, generalizing Macdonald's formula for the spherical function in the finite-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0602","kind":"arxiv","version":1},"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":"2026-05-18T02:57:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xe8dxXiSyiQuQVI3KWBC8hnlRnRW2jaj42/lWIfAXae0mjnp3wuBLdfdTm4WHaxslSxbiosth3dG4Un2bWcxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:50:55.945567Z"},"content_sha256":"3fdd92713a32c7a54dfd48871167095eee2107637cde5190f375b534700d9351","schema_version":"1.0","event_id":"sha256:3fdd92713a32c7a54dfd48871167095eee2107637cde5190f375b534700d9351"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/bundle.json","state_url":"https://pith.science/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/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":"2026-05-26T02:50:55Z","links":{"resolver":"https://pith.science/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P","bundle":"https://pith.science/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/bundle.json","state":"https://pith.science/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDPGC7JZ4E2N7NSTIBGBBL7Y4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JDPGC7JZ4E2N7NSTIBGBBL7Y4P","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":"28521320cba4a349a6e5919db6a12fe4be5536c4f6d1f3256b8ebeda07f7e97f","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-03T21:31:10Z","title_canon_sha256":"9a09c1fc8fb40a02b3b97dee6c3912f2dff4d66eba02c85412a4ca5a2b7aa3a7"},"schema_version":"1.0","source":{"id":"1403.0602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0602","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0602v1","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0602","created_at":"2026-05-18T02:57:16Z"},{"alias_kind":"pith_short_12","alias_value":"JDPGC7JZ4E2N","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDPGC7JZ4E2N7NST","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDPGC7JZ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:3fdd92713a32c7a54dfd48871167095eee2107637cde5190f375b534700d9351","target":"graph","created_at":"2026-05-18T02:57:16Z","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 a continuation of a previous paper in which the first two authors have introduced the spherical Hecke algebra and the Satake isomorphism for an untwisted affine Kac-Moody group over a non-archimedian local field. In this paper we develop the theory of the Iwahori-Hecke algebra associated to these same groups. The resulting algebra is shown to be closely related to Cherednik's double affine Hecke algebra. Furthermore, using these results, we give an explicit description of the affine Satake isomorphism, generalizing Macdonald's formula for the spherical function in the finite-dime","authors_text":"Alexander Braverman, David Kazhdan, Manish Patnaik","cross_cats":["math.NT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-03T21:31:10Z","title":"Iwahori-Hecke algebras for p-adic loop groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0602","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:a66a9eecac4e5ba3ef4ed6cc3956bd3a8ab432b6f79b8e99709f533753cf97d2","target":"record","created_at":"2026-05-18T02:57:16Z","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":"28521320cba4a349a6e5919db6a12fe4be5536c4f6d1f3256b8ebeda07f7e97f","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-03-03T21:31:10Z","title_canon_sha256":"9a09c1fc8fb40a02b3b97dee6c3912f2dff4d66eba02c85412a4ca5a2b7aa3a7"},"schema_version":"1.0","source":{"id":"1403.0602","kind":"arxiv","version":1}},"canonical_sha256":"48de617d39e134dfb653404c10aff8e3cee699328037256c0f352b6b891b22fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48de617d39e134dfb653404c10aff8e3cee699328037256c0f352b6b891b22fe","first_computed_at":"2026-05-18T02:57:16.168999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:16.168999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TXEBEgIC35gCA/6rmBEpHMmK872e/b6ydqXa/m82qthP30lrTfMYcoS7FmBKq8SM99owgMkorjzdldkwqIR8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:16.169568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a66a9eecac4e5ba3ef4ed6cc3956bd3a8ab432b6f79b8e99709f533753cf97d2","sha256:3fdd92713a32c7a54dfd48871167095eee2107637cde5190f375b534700d9351"],"state_sha256":"2bf677d0fb7f24cc21fa12dbf9e1254c7bbb6026c67732f996501cf898c9e548"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QtJOMTwxW6se4XScbZCCbzl93SRsDyg5REkfvdL6wofYjqDtAdxbiTbkHRK2ItiLccJJSL8SDhsKiaCN+2YXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:50:55.949601Z","bundle_sha256":"5edde56c76aa8e8b8ea1d6684ea6fb3c37892fa848afd52df7766e0618993a8a"}}