{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:AVWVWX6UM6UDMS532FORULPB5D","short_pith_number":"pith:AVWVWX6U","canonical_record":{"source":{"id":"0902.0943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T17:18:52Z","cross_cats_sorted":[],"title_canon_sha256":"6243fec09f9c1af853b8a0e6346dc3a36ce18bb127fc05629000e121ebd50fb6","abstract_canon_sha256":"642553a528c62bb2c79635b061f67c7a3e6e6172173b82ae4160928e1df910f8"},"schema_version":"1.0"},"canonical_sha256":"056d5b5fd467a8364bbbd15d1a2de1e8e2f159f9028e8dd01ac4e7a2d31b48f3","source":{"kind":"arxiv","id":"0902.0943","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0943","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0943v2","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0943","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"AVWVWX6UM6UD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AVWVWX6UM6UDMS53","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AVWVWX6U","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:AVWVWX6UM6UDMS532FORULPB5D","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T17:18:52Z","cross_cats_sorted":[],"title_canon_sha256":"6243fec09f9c1af853b8a0e6346dc3a36ce18bb127fc05629000e121ebd50fb6","abstract_canon_sha256":"642553a528c62bb2c79635b061f67c7a3e6e6172173b82ae4160928e1df910f8"},"schema_version":"1.0"},"canonical_sha256":"056d5b5fd467a8364bbbd15d1a2de1e8e2f159f9028e8dd01ac4e7a2d31b48f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.793537Z","signature_b64":"UiF1f8Y9lnpAZIFWVyEJFrTGJ3qxPpCOxDHnSb32eZv8kcm1iJqqiyBtDFCzdCCdzNMXEaBhbo25+WOYk9NhDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"056d5b5fd467a8364bbbd15d1a2de1e8e2f159f9028e8dd01ac4e7a2d31b48f3","last_reissued_at":"2026-05-18T03:59:49.793048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.793048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0943","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/jtkgExt+vxxmTTKpDOwmo+Ws46liFf2SrGxr4GZL/6xntH3738HhzzCrnVgm0XSdEVU86RgEjZPQ10zTa0sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T06:57:17.618368Z"},"content_sha256":"fcde2019bc94fd4f3eea1bbe915068e6a739c58cf64dc8c20a139f82ca012273","schema_version":"1.0","event_id":"sha256:fcde2019bc94fd4f3eea1bbe915068e6a739c58cf64dc8c20a139f82ca012273"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:AVWVWX6UM6UDMS532FORULPB5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Radial Fourier multipliers in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andreas Seeger, Fedor Nazarov, Yaryong Heo","submitted_at":"2009-02-05T17:18:52Z","abstract_excerpt":"Given a fixed $p\\neq 2$, we prove a simple and effective characterization of all radial multipliers of $\\cF L^p(\\Bbb R^d)$, provided that the dimension $d$ is sufficiently large. The method also yields new $L^q$ space-time regularity results for solutions of the wave equation in high dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0943","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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n6BAt+V9z9nD3H9YHXMUnOUpKciswYEDeWtChEOAJEF5tL5JiulF/L8XqI+Z62gFyQWDHx/H8Wi3Bjuyejc3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T06:57:17.618715Z"},"content_sha256":"e8c6da63cd5a037a9a8b06912dd70c96a99ed34bebd48da9e43441199e968105","schema_version":"1.0","event_id":"sha256:e8c6da63cd5a037a9a8b06912dd70c96a99ed34bebd48da9e43441199e968105"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVWVWX6UM6UDMS532FORULPB5D/bundle.json","state_url":"https://pith.science/pith/AVWVWX6UM6UDMS532FORULPB5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVWVWX6UM6UDMS532FORULPB5D/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":"2026-05-20T06:57:17Z","links":{"resolver":"https://pith.science/pith/AVWVWX6UM6UDMS532FORULPB5D","bundle":"https://pith.science/pith/AVWVWX6UM6UDMS532FORULPB5D/bundle.json","state":"https://pith.science/pith/AVWVWX6UM6UDMS532FORULPB5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVWVWX6UM6UDMS532FORULPB5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AVWVWX6UM6UDMS532FORULPB5D","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":"642553a528c62bb2c79635b061f67c7a3e6e6172173b82ae4160928e1df910f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T17:18:52Z","title_canon_sha256":"6243fec09f9c1af853b8a0e6346dc3a36ce18bb127fc05629000e121ebd50fb6"},"schema_version":"1.0","source":{"id":"0902.0943","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0943","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0943v2","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0943","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"AVWVWX6UM6UD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AVWVWX6UM6UDMS53","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AVWVWX6U","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:e8c6da63cd5a037a9a8b06912dd70c96a99ed34bebd48da9e43441199e968105","target":"graph","created_at":"2026-05-18T03:59:49Z","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":"Given a fixed $p\\neq 2$, we prove a simple and effective characterization of all radial multipliers of $\\cF L^p(\\Bbb R^d)$, provided that the dimension $d$ is sufficiently large. The method also yields new $L^q$ space-time regularity results for solutions of the wave equation in high dimensions.","authors_text":"Andreas Seeger, Fedor Nazarov, Yaryong Heo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T17:18:52Z","title":"Radial Fourier multipliers in high dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0943","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:fcde2019bc94fd4f3eea1bbe915068e6a739c58cf64dc8c20a139f82ca012273","target":"record","created_at":"2026-05-18T03:59:49Z","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":"642553a528c62bb2c79635b061f67c7a3e6e6172173b82ae4160928e1df910f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-02-05T17:18:52Z","title_canon_sha256":"6243fec09f9c1af853b8a0e6346dc3a36ce18bb127fc05629000e121ebd50fb6"},"schema_version":"1.0","source":{"id":"0902.0943","kind":"arxiv","version":2}},"canonical_sha256":"056d5b5fd467a8364bbbd15d1a2de1e8e2f159f9028e8dd01ac4e7a2d31b48f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"056d5b5fd467a8364bbbd15d1a2de1e8e2f159f9028e8dd01ac4e7a2d31b48f3","first_computed_at":"2026-05-18T03:59:49.793048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.793048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UiF1f8Y9lnpAZIFWVyEJFrTGJ3qxPpCOxDHnSb32eZv8kcm1iJqqiyBtDFCzdCCdzNMXEaBhbo25+WOYk9NhDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.793537Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0943","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcde2019bc94fd4f3eea1bbe915068e6a739c58cf64dc8c20a139f82ca012273","sha256:e8c6da63cd5a037a9a8b06912dd70c96a99ed34bebd48da9e43441199e968105"],"state_sha256":"b4726b9078859e5502274f45bd006d0d78954d18b7f928a98ef2a54e2827be54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rs47aaJDEW0UTf04Cs5Bs33S/2VIb/BG+zKKJUo31cEGclIcD43cTy0VqhKtvZR4RI9lKgZy8Q7hEln7EPEaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T06:57:17.620790Z","bundle_sha256":"eb69225566f342114b1ada2d55254485aaee83e80694f545576fbef4fae2c7fd"}}