{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FL2V6YKE2LFCFRCCMMJAE3YGUQ","short_pith_number":"pith:FL2V6YKE","canonical_record":{"source":{"id":"1710.06841","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","cross_cats_sorted":[],"title_canon_sha256":"c545b0fd7c530299c7734648041490eadc627e4daa3f9f364f2e27ae7bc13460","abstract_canon_sha256":"a5fb0afa2b43f40b03548782bd6ff271c7c2d366f7c5f25e98babdccc1c1563b"},"schema_version":"1.0"},"canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","source":{"kind":"arxiv","id":"1710.06841","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06841","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06841v3","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06841","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"FL2V6YKE2LFC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FL2V6YKE2LFCFRCC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FL2V6YKE","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FL2V6YKE2LFCFRCCMMJAE3YGUQ","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06841","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","cross_cats_sorted":[],"title_canon_sha256":"c545b0fd7c530299c7734648041490eadc627e4daa3f9f364f2e27ae7bc13460","abstract_canon_sha256":"a5fb0afa2b43f40b03548782bd6ff271c7c2d366f7c5f25e98babdccc1c1563b"},"schema_version":"1.0"},"canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:46.160242Z","signature_b64":"QWmocjNI4c2i2gwPbwz7Sjsj/Ft5GF5E3Ke5x1AmUK4YnEbufqO7AVDbZG+jJ7uyiKmvdWoZy0dxulCYmwSCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","last_reissued_at":"2026-05-18T00:18:46.159484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:46.159484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06841","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":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Z5ABtVd51Gd4HItVKrHPVbo9hOcotjH6Oc8P5x3rvLlzwN9IRGgw+I/UBPz+stZ8R51P9ixfdbS6rAalawEBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:26:23.381690Z"},"content_sha256":"d2f104d344fa772d994c827ce54a00a194e37e0a75af2459360ca4988475757a","schema_version":"1.0","event_id":"sha256:d2f104d344fa772d994c827ce54a00a194e37e0a75af2459360ca4988475757a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FL2V6YKE2LFCFRCCMMJAE3YGUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalized Fourier Transforms for standard L-functions (with an appendix by Wen-Wei Li)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Freydoon Shahidi","submitted_at":"2017-10-18T17:48:16Z","abstract_excerpt":"Any generalization of the method of Godement-Jacquet on principal L-functions for GL(n) to other groups as perceived by Braverman-Kazhdan and Ngo requires a Fourier transform on a space of Schwartz functions. In the case of standard L-functions for classical groups, a theory of this nature was developed by Piatetski-Shapiro and Rallis, called the doubling method. It was later that Braverman and Kazhdan, using an algebro-geometric approach, different from doubling method, introduced a space of Schwartz functions and a Fourier transform, which projected onto those from doubling method. In both m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06841","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":"2026-05-18T00:18:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TUcnfhGYg+r9901iKDyJZsHSPQ0Mg6kUeGyA3eJfsl8SDVENXz6lD+X2JRbPOB5uH/cL2V+egMY/3p+ZSK+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T13:26:23.382041Z"},"content_sha256":"fef7e9c47646d1d36cd0477cb80907c4ca809d904e8c35bca5c843c4439b7ba8","schema_version":"1.0","event_id":"sha256:fef7e9c47646d1d36cd0477cb80907c4ca809d904e8c35bca5c843c4439b7ba8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/bundle.json","state_url":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/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":"2026-06-01T13:26:23Z","links":{"resolver":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ","bundle":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/bundle.json","state":"https://pith.science/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FL2V6YKE2LFCFRCCMMJAE3YGUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FL2V6YKE2LFCFRCCMMJAE3YGUQ","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":"a5fb0afa2b43f40b03548782bd6ff271c7c2d366f7c5f25e98babdccc1c1563b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","title_canon_sha256":"c545b0fd7c530299c7734648041490eadc627e4daa3f9f364f2e27ae7bc13460"},"schema_version":"1.0","source":{"id":"1710.06841","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06841","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06841v3","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06841","created_at":"2026-05-18T00:18:46Z"},{"alias_kind":"pith_short_12","alias_value":"FL2V6YKE2LFC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FL2V6YKE2LFCFRCC","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FL2V6YKE","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:fef7e9c47646d1d36cd0477cb80907c4ca809d904e8c35bca5c843c4439b7ba8","target":"graph","created_at":"2026-05-18T00:18:46Z","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":"Any generalization of the method of Godement-Jacquet on principal L-functions for GL(n) to other groups as perceived by Braverman-Kazhdan and Ngo requires a Fourier transform on a space of Schwartz functions. In the case of standard L-functions for classical groups, a theory of this nature was developed by Piatetski-Shapiro and Rallis, called the doubling method. It was later that Braverman and Kazhdan, using an algebro-geometric approach, different from doubling method, introduced a space of Schwartz functions and a Fourier transform, which projected onto those from doubling method. In both m","authors_text":"Freydoon Shahidi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","title":"On generalized Fourier Transforms for standard L-functions (with an appendix by Wen-Wei Li)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06841","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:d2f104d344fa772d994c827ce54a00a194e37e0a75af2459360ca4988475757a","target":"record","created_at":"2026-05-18T00:18:46Z","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":"a5fb0afa2b43f40b03548782bd6ff271c7c2d366f7c5f25e98babdccc1c1563b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-18T17:48:16Z","title_canon_sha256":"c545b0fd7c530299c7734648041490eadc627e4daa3f9f364f2e27ae7bc13460"},"schema_version":"1.0","source":{"id":"1710.06841","kind":"arxiv","version":3}},"canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2af55f6144d2ca22c4426312026f06a421e07bd064e9ef2e64eb3f67f6cdf781","first_computed_at":"2026-05-18T00:18:46.159484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:46.159484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QWmocjNI4c2i2gwPbwz7Sjsj/Ft5GF5E3Ke5x1AmUK4YnEbufqO7AVDbZG+jJ7uyiKmvdWoZy0dxulCYmwSCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:46.160242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06841","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2f104d344fa772d994c827ce54a00a194e37e0a75af2459360ca4988475757a","sha256:fef7e9c47646d1d36cd0477cb80907c4ca809d904e8c35bca5c843c4439b7ba8"],"state_sha256":"fba16c081c95a9b60ccc3143339d43a0c5e1baf2ae7468115642a0e93fa257a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+X+cyqVCnGxyIEn54Wsg7p7g2jQ2TEnWQVkR0qMNEVsEezXzAvCxJAIbgZBgdGPGgrq566jyQD1+Hx4fmH2mDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T13:26:23.384073Z","bundle_sha256":"81f4396ed759ac7272616dbba597b4e96bf86a289fad8b6f0fd58604fa559858"}}