{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WGUMLSL2FPLL25AY4HNYGSJUMB","short_pith_number":"pith:WGUMLSL2","schema_version":"1.0","canonical_sha256":"b1a8c5c97a2bd6bd7418e1db834934604fb7c53aed42150d8137a3e1d2c2c7ba","source":{"kind":"arxiv","id":"1307.8408","version":1},"attestation_state":"computed","paper":{"title":"The Fourier transform of multiradial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Frederic Bernicot (LMJL), Loukas Grafakos (MU Mathematics), Yandan Zhang","submitted_at":"2013-07-31T18:06:10Z","abstract_excerpt":"We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\\Phi(x)=\\phi(|x_1|, \\dots, |x_m|)$, $x_i\\in \\mathbf R^{n_i}$, in terms of the Fourier transform of the function $\\phi$ on $\\mathbf R^{r_1}\\times \\cdots \\times \\mathbf R^{r_m}$, where $r_i$ is either 1 or 2."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.8408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-31T18:06:10Z","cross_cats_sorted":[],"title_canon_sha256":"834b4adf8b4c5335f63e513470b0266995d206305106cbdd4033f48ad8fad4ce","abstract_canon_sha256":"6dde7d791850cd2340af62ea4577bdb467f03ff831e5228d6eaf230ff3729ae1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:01.243219Z","signature_b64":"fRXOZo4AT4vMAxn4UQaA4khdUhLdpbwg0K4drNfzwg2RFZPF4wcCxX6RdtwSRuFDOLiiMD1yuzReGQbtfs/eBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1a8c5c97a2bd6bd7418e1db834934604fb7c53aed42150d8137a3e1d2c2c7ba","last_reissued_at":"2026-05-18T03:17:01.242519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:01.242519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fourier transform of multiradial functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Frederic Bernicot (LMJL), Loukas Grafakos (MU Mathematics), Yandan Zhang","submitted_at":"2013-07-31T18:06:10Z","abstract_excerpt":"We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\\Phi(x)=\\phi(|x_1|, \\dots, |x_m|)$, $x_i\\in \\mathbf R^{n_i}$, in terms of the Fourier transform of the function $\\phi$ on $\\mathbf R^{r_1}\\times \\cdots \\times \\mathbf R^{r_m}$, where $r_i$ is either 1 or 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8408","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.8408","created_at":"2026-05-18T03:17:01.242631+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.8408v1","created_at":"2026-05-18T03:17:01.242631+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8408","created_at":"2026-05-18T03:17:01.242631+00:00"},{"alias_kind":"pith_short_12","alias_value":"WGUMLSL2FPLL","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WGUMLSL2FPLL25AY","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WGUMLSL2","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB","json":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB.json","graph_json":"https://pith.science/api/pith-number/WGUMLSL2FPLL25AY4HNYGSJUMB/graph.json","events_json":"https://pith.science/api/pith-number/WGUMLSL2FPLL25AY4HNYGSJUMB/events.json","paper":"https://pith.science/paper/WGUMLSL2"},"agent_actions":{"view_html":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB","download_json":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB.json","view_paper":"https://pith.science/paper/WGUMLSL2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.8408&json=true","fetch_graph":"https://pith.science/api/pith-number/WGUMLSL2FPLL25AY4HNYGSJUMB/graph.json","fetch_events":"https://pith.science/api/pith-number/WGUMLSL2FPLL25AY4HNYGSJUMB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB/action/storage_attestation","attest_author":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB/action/author_attestation","sign_citation":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB/action/citation_signature","submit_replication":"https://pith.science/pith/WGUMLSL2FPLL25AY4HNYGSJUMB/action/replication_record"}},"created_at":"2026-05-18T03:17:01.242631+00:00","updated_at":"2026-05-18T03:17:01.242631+00:00"}