{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:25GO2RAYXR5BAJXB5MDP5EMUVQ","short_pith_number":"pith:25GO2RAY","canonical_record":{"source":{"id":"2110.05696","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-12T02:31:26Z","cross_cats_sorted":["math.FA","math.RT"],"title_canon_sha256":"fa03b8f744c52a66eebf1810490286b0ec4a0abade5ee44990ed163d343141a3","abstract_canon_sha256":"18a051dd8ccc8948f621d603eff271bb91bac8ad60fe663fc5e5ce577ad44d74"},"schema_version":"1.0"},"canonical_sha256":"d74ced4418bc7a1026e1eb06fe9194ac28c2c0beeb2293cb5e41b06a476365e4","source":{"kind":"arxiv","id":"2110.05696","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05696","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05696v2","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05696","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"25GO2RAYXR5B","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_16","alias_value":"25GO2RAYXR5BAJXB","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_8","alias_value":"25GO2RAY","created_at":"2026-07-05T03:25:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:25GO2RAYXR5BAJXB5MDP5EMUVQ","target":"record","payload":{"canonical_record":{"source":{"id":"2110.05696","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-12T02:31:26Z","cross_cats_sorted":["math.FA","math.RT"],"title_canon_sha256":"fa03b8f744c52a66eebf1810490286b0ec4a0abade5ee44990ed163d343141a3","abstract_canon_sha256":"18a051dd8ccc8948f621d603eff271bb91bac8ad60fe663fc5e5ce577ad44d74"},"schema_version":"1.0"},"canonical_sha256":"d74ced4418bc7a1026e1eb06fe9194ac28c2c0beeb2293cb5e41b06a476365e4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:25:34.802291Z","signature_b64":"ShsYBSUAWAebZZX1M6lhANqlHer6hLrXet5xcnNiX4OBtIoCyhLNJvKHZKR9ISlKP1Gra9F6LAslZLKSqfLyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d74ced4418bc7a1026e1eb06fe9194ac28c2c0beeb2293cb5e41b06a476365e4","last_reissued_at":"2026-07-05T03:25:34.801904Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:25:34.801904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.05696","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/53lzZvnJWdau574a3cqJbZ8iYAgO8PR9JaUNKDggzgXRIdmrxxE8JHpktARmkCdC0iPLKSdYML+vrzwqBGFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:31:27.780464Z"},"content_sha256":"a3ab4ce54b52d1e5c0b8242500882f9a8a4088cc0377e28b689d3614f25bd411","schema_version":"1.0","event_id":"sha256:a3ab4ce54b52d1e5c0b8242500882f9a8a4088cc0377e28b689d3614f25bd411"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:25GO2RAYXR5BAJXB5MDP5EMUVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Poisson summation for Hankel transforms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.RT"],"primary_cat":"math.NT","authors_text":"Taiwang Deng","submitted_at":"2021-10-12T02:31:26Z","abstract_excerpt":"In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\\rho: GL_1\\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05696","kind":"arxiv","version":2},"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/2110.05696/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":"2026-07-05T03:25:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJbZKpvnP8a29N/LUxMZz2xsCf/BY1X9uKmh1OdWG70NNOPGwDQG8ZGs6SmMS50V6ttOU2O7FXbj5dfguvuPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T21:31:27.785488Z"},"content_sha256":"dd5cf18af5a8bf6f168e1fa219e42cad6c1a283fb89998266de724423e99e331","schema_version":"1.0","event_id":"sha256:dd5cf18af5a8bf6f168e1fa219e42cad6c1a283fb89998266de724423e99e331"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/bundle.json","state_url":"https://pith.science/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/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":"2026-08-17T21:31:27Z","links":{"resolver":"https://pith.science/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ","bundle":"https://pith.science/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/bundle.json","state":"https://pith.science/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25GO2RAYXR5BAJXB5MDP5EMUVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:25GO2RAYXR5BAJXB5MDP5EMUVQ","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":"18a051dd8ccc8948f621d603eff271bb91bac8ad60fe663fc5e5ce577ad44d74","cross_cats_sorted":["math.FA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-12T02:31:26Z","title_canon_sha256":"fa03b8f744c52a66eebf1810490286b0ec4a0abade5ee44990ed163d343141a3"},"schema_version":"1.0","source":{"id":"2110.05696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.05696","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"arxiv_version","alias_value":"2110.05696v2","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.05696","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_12","alias_value":"25GO2RAYXR5B","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_16","alias_value":"25GO2RAYXR5BAJXB","created_at":"2026-07-05T03:25:34Z"},{"alias_kind":"pith_short_8","alias_value":"25GO2RAY","created_at":"2026-07-05T03:25:34Z"}],"graph_snapshots":[{"event_id":"sha256:dd5cf18af5a8bf6f168e1fa219e42cad6c1a283fb89998266de724423e99e331","target":"graph","created_at":"2026-07-05T03:25:34Z","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/2110.05696/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\\rho: GL_1\\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula.","authors_text":"Taiwang Deng","cross_cats":["math.FA","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-12T02:31:26Z","title":"Poisson summation for Hankel transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.05696","kind":"arxiv","version":2},"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:a3ab4ce54b52d1e5c0b8242500882f9a8a4088cc0377e28b689d3614f25bd411","target":"record","created_at":"2026-07-05T03:25:34Z","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":"18a051dd8ccc8948f621d603eff271bb91bac8ad60fe663fc5e5ce577ad44d74","cross_cats_sorted":["math.FA","math.RT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2021-10-12T02:31:26Z","title_canon_sha256":"fa03b8f744c52a66eebf1810490286b0ec4a0abade5ee44990ed163d343141a3"},"schema_version":"1.0","source":{"id":"2110.05696","kind":"arxiv","version":2}},"canonical_sha256":"d74ced4418bc7a1026e1eb06fe9194ac28c2c0beeb2293cb5e41b06a476365e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d74ced4418bc7a1026e1eb06fe9194ac28c2c0beeb2293cb5e41b06a476365e4","first_computed_at":"2026-07-05T03:25:34.801904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:25:34.801904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ShsYBSUAWAebZZX1M6lhANqlHer6hLrXet5xcnNiX4OBtIoCyhLNJvKHZKR9ISlKP1Gra9F6LAslZLKSqfLyDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:25:34.802291Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.05696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3ab4ce54b52d1e5c0b8242500882f9a8a4088cc0377e28b689d3614f25bd411","sha256:dd5cf18af5a8bf6f168e1fa219e42cad6c1a283fb89998266de724423e99e331"],"state_sha256":"10e64e79d313e8b760132522221fa435ddfaa0f5e0844d07791bda9322c3ecdc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kn6Es4aNs88bAbkuG8f+wB6dfcYCjPiK9HGGawfhl73fetwrYu4zkPqFnyfcDd0ioSyA3l4S51kw6du2ZMubDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T21:31:27.861311Z","bundle_sha256":"b1b2b82f65e4e0942144725a1566dd19fc2e1338912323813e59dc857421c71a"}}