{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:X7HWAJSCZYAEH4I5J2FUUGOSNV","short_pith_number":"pith:X7HWAJSC","canonical_record":{"source":{"id":"1606.02913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-09T11:25:57Z","cross_cats_sorted":[],"title_canon_sha256":"0c01f2e825344803f1f04f2a2a01267bf613ea9120b1448174937e4ebd0dde27","abstract_canon_sha256":"d59c423509afb99fe6534bffcf9c7d52cbf5e9ddd7acce1306c0522309bfd4ff"},"schema_version":"1.0"},"canonical_sha256":"bfcf602642ce0043f11d4e8b4a19d26d4f697d9f312a04d5e9a50afe04a10675","source":{"kind":"arxiv","id":"1606.02913","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02913","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02913v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02913","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"X7HWAJSCZYAE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X7HWAJSCZYAEH4I5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X7HWAJSC","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:X7HWAJSCZYAEH4I5J2FUUGOSNV","target":"record","payload":{"canonical_record":{"source":{"id":"1606.02913","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-09T11:25:57Z","cross_cats_sorted":[],"title_canon_sha256":"0c01f2e825344803f1f04f2a2a01267bf613ea9120b1448174937e4ebd0dde27","abstract_canon_sha256":"d59c423509afb99fe6534bffcf9c7d52cbf5e9ddd7acce1306c0522309bfd4ff"},"schema_version":"1.0"},"canonical_sha256":"bfcf602642ce0043f11d4e8b4a19d26d4f697d9f312a04d5e9a50afe04a10675","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:59.127160Z","signature_b64":"w0nWlujnt3V8gps7PwIoOOHR4/74httcyQDisrfHBoc5lhV9fvqlC0QJZ4qRVwN5DxK6jT9vREX34hx2ShbcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfcf602642ce0043f11d4e8b4a19d26d4f697d9f312a04d5e9a50afe04a10675","last_reissued_at":"2026-05-18T00:31:59.126805Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:59.126805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.02913","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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNK5DUSu2Uv/lSZFW1pEfCYXM72B3Z/2SXLCqBaf8jhl6SmrYV9jgXy+67C8bz25rOz69aGmTXTU7V1TS3ZsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:14:26.604133Z"},"content_sha256":"a67073ece90f10fb15664b12e290bbdcc1b13fbc5535af81bd1f67d7a22056e5","schema_version":"1.0","event_id":"sha256:a67073ece90f10fb15664b12e290bbdcc1b13fbc5535af81bd1f67d7a22056e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:X7HWAJSCZYAEH4I5J2FUUGOSNV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Zhi Qi","submitted_at":"2016-06-09T11:25:57Z","abstract_excerpt":"In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation theoretic motivations in the Waldspurger correspondence over the complex field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02913","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":""},"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":"2026-05-18T00:31:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xoOQmaAzKRmY2WR8Zf9/PlJqh3HJVkA2qcLCOwc1iK9ySQdljGPnoNcWYAeXaa6FdZU8P46cNqMu492rWIsuBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T05:14:26.604486Z"},"content_sha256":"8cf95ae21d44635a04e889ee7b76a5b986bd1fac6486d8ea92841a3817e1fdbd","schema_version":"1.0","event_id":"sha256:8cf95ae21d44635a04e889ee7b76a5b986bd1fac6486d8ea92841a3817e1fdbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/bundle.json","state_url":"https://pith.science/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/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":"2026-07-02T05:14:26Z","links":{"resolver":"https://pith.science/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV","bundle":"https://pith.science/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/bundle.json","state":"https://pith.science/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7HWAJSCZYAEH4I5J2FUUGOSNV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X7HWAJSCZYAEH4I5J2FUUGOSNV","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":"d59c423509afb99fe6534bffcf9c7d52cbf5e9ddd7acce1306c0522309bfd4ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-09T11:25:57Z","title_canon_sha256":"0c01f2e825344803f1f04f2a2a01267bf613ea9120b1448174937e4ebd0dde27"},"schema_version":"1.0","source":{"id":"1606.02913","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02913","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02913v2","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02913","created_at":"2026-05-18T00:31:59Z"},{"alias_kind":"pith_short_12","alias_value":"X7HWAJSCZYAE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X7HWAJSCZYAEH4I5","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X7HWAJSC","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:8cf95ae21d44635a04e889ee7b76a5b986bd1fac6486d8ea92841a3817e1fdbd","target":"graph","created_at":"2026-05-18T00:31:59Z","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":"In this note, we shall prove a formula for the Fourier transform of spherical Bessel functions over complex numbers, viewed as the complex analogue of the classical formulae of Hardy and Weber. The formula has strong representation theoretic motivations in the Waldspurger correspondence over the complex field.","authors_text":"Zhi Qi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-09T11:25:57Z","title":"On the Fourier Transform of Bessel Functions over Complex Numbers---I: the Spherical Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02913","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:a67073ece90f10fb15664b12e290bbdcc1b13fbc5535af81bd1f67d7a22056e5","target":"record","created_at":"2026-05-18T00:31:59Z","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":"d59c423509afb99fe6534bffcf9c7d52cbf5e9ddd7acce1306c0522309bfd4ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-06-09T11:25:57Z","title_canon_sha256":"0c01f2e825344803f1f04f2a2a01267bf613ea9120b1448174937e4ebd0dde27"},"schema_version":"1.0","source":{"id":"1606.02913","kind":"arxiv","version":2}},"canonical_sha256":"bfcf602642ce0043f11d4e8b4a19d26d4f697d9f312a04d5e9a50afe04a10675","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfcf602642ce0043f11d4e8b4a19d26d4f697d9f312a04d5e9a50afe04a10675","first_computed_at":"2026-05-18T00:31:59.126805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:59.126805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w0nWlujnt3V8gps7PwIoOOHR4/74httcyQDisrfHBoc5lhV9fvqlC0QJZ4qRVwN5DxK6jT9vREX34hx2ShbcCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:59.127160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02913","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a67073ece90f10fb15664b12e290bbdcc1b13fbc5535af81bd1f67d7a22056e5","sha256:8cf95ae21d44635a04e889ee7b76a5b986bd1fac6486d8ea92841a3817e1fdbd"],"state_sha256":"cb6b57c6862300cf81f63b8d1c1f9cdf8860e44768843cbb3dbdd3e4fc3b85ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCMK1v423E8bvINVRjgBj4gYV1EuR/TcyYVzP1i+Xvzse+qAKAfgivmqUkYOHEcStdbLzSxKdq5bO5WMw9nWBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T05:14:26.606284Z","bundle_sha256":"98718f47312814869fb28c690e2acca4284cd169340479428da54617c7547c0f"}}