{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JNI5N4YBXDHW3SZOWZIFBFJJRW","short_pith_number":"pith:JNI5N4YB","canonical_record":{"source":{"id":"1403.3332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-13T17:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"41ed9171223b6665669eb84e8c3bb6483a506687bdeb61f0aec18cd2733c91b5","abstract_canon_sha256":"4596fb84fb7e0ba068143cd25d29e526702a597dea5adc8673e1aef1da5fdd12"},"schema_version":"1.0"},"canonical_sha256":"4b51d6f301b8cf6dcb2eb6505095298dab918c941119a10a088ec24966e0a279","source":{"kind":"arxiv","id":"1403.3332","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3332","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3332v1","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3332","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"JNI5N4YBXDHW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JNI5N4YBXDHW3SZO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JNI5N4YB","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JNI5N4YBXDHW3SZOWZIFBFJJRW","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-13T17:17:51Z","cross_cats_sorted":[],"title_canon_sha256":"41ed9171223b6665669eb84e8c3bb6483a506687bdeb61f0aec18cd2733c91b5","abstract_canon_sha256":"4596fb84fb7e0ba068143cd25d29e526702a597dea5adc8673e1aef1da5fdd12"},"schema_version":"1.0"},"canonical_sha256":"4b51d6f301b8cf6dcb2eb6505095298dab918c941119a10a088ec24966e0a279","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:24.293745Z","signature_b64":"3IFIBmZonH1R0CiJgbRcpQleQUfuWOgihunOSNvtAeOZP3wg/5E4vz6bB7KKP7Uf1v7VOjzBQtQfJ9RV3TtVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b51d6f301b8cf6dcb2eb6505095298dab918c941119a10a088ec24966e0a279","last_reissued_at":"2026-05-18T01:03:24.293153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:24.293153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3332","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f5sZcFwHqhDIMl2PdI7VlWx1G7sEI4RDD+xJZRqkjnaENuW+JBi5QtCMcOLT64mS/+f7Wtpgm37ddt1TsV/kDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:30:32.038447Z"},"content_sha256":"4847bd6796794952d62958d348c284d09b7af7203fe17bdc0e7eb3f97c9b5992","schema_version":"1.0","event_id":"sha256:4847bd6796794952d62958d348c284d09b7af7203fe17bdc0e7eb3f97c9b5992"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JNI5N4YBXDHW3SZOWZIFBFJJRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A frame theoretic approach to the Non-Uniform Fast Fourier Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anne Gelb, Guohui Song","submitted_at":"2014-03-13T17:17:51Z","abstract_excerpt":"Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse process, the non-uniform fast Fourier transform (NFFT), also called convolutional gridding, is frequently employed. While various investigations have led to improvements in accuracy, efficiency, and robustness of the NFFT, not much attention has been paid to the fundamental analysis of the scheme, and in particular its convergence properties. This paper ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3332","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1b/JfZYuF9Esy0tgBGwc8GG4jGkfiDK+isE/tcfie9Q5o18ZQ/Hmen8MKQgbFl1ETMAuXUsmrIG+iUWJIyNIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:30:32.039155Z"},"content_sha256":"21b222802c36a943dbb7377c53ba25ad1ee7eb8e662afb5781272b00b53622f2","schema_version":"1.0","event_id":"sha256:21b222802c36a943dbb7377c53ba25ad1ee7eb8e662afb5781272b00b53622f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/bundle.json","state_url":"https://pith.science/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/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":"2026-06-06T04:30:32Z","links":{"resolver":"https://pith.science/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW","bundle":"https://pith.science/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/bundle.json","state":"https://pith.science/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JNI5N4YBXDHW3SZOWZIFBFJJRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JNI5N4YBXDHW3SZOWZIFBFJJRW","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":"4596fb84fb7e0ba068143cd25d29e526702a597dea5adc8673e1aef1da5fdd12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-13T17:17:51Z","title_canon_sha256":"41ed9171223b6665669eb84e8c3bb6483a506687bdeb61f0aec18cd2733c91b5"},"schema_version":"1.0","source":{"id":"1403.3332","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3332","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3332v1","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3332","created_at":"2026-05-18T01:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"JNI5N4YBXDHW","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JNI5N4YBXDHW3SZO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JNI5N4YB","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:21b222802c36a943dbb7377c53ba25ad1ee7eb8e662afb5781272b00b53622f2","target":"graph","created_at":"2026-05-18T01:03:24Z","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":"Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse process, the non-uniform fast Fourier transform (NFFT), also called convolutional gridding, is frequently employed. While various investigations have led to improvements in accuracy, efficiency, and robustness of the NFFT, not much attention has been paid to the fundamental analysis of the scheme, and in particular its convergence properties. This paper ana","authors_text":"Anne Gelb, Guohui Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-13T17:17:51Z","title":"A frame theoretic approach to the Non-Uniform Fast Fourier Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3332","kind":"arxiv","version":1},"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":"sha256:4847bd6796794952d62958d348c284d09b7af7203fe17bdc0e7eb3f97c9b5992","target":"record","created_at":"2026-05-18T01:03:24Z","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":"4596fb84fb7e0ba068143cd25d29e526702a597dea5adc8673e1aef1da5fdd12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-13T17:17:51Z","title_canon_sha256":"41ed9171223b6665669eb84e8c3bb6483a506687bdeb61f0aec18cd2733c91b5"},"schema_version":"1.0","source":{"id":"1403.3332","kind":"arxiv","version":1}},"canonical_sha256":"4b51d6f301b8cf6dcb2eb6505095298dab918c941119a10a088ec24966e0a279","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b51d6f301b8cf6dcb2eb6505095298dab918c941119a10a088ec24966e0a279","first_computed_at":"2026-05-18T01:03:24.293153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:24.293153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3IFIBmZonH1R0CiJgbRcpQleQUfuWOgihunOSNvtAeOZP3wg/5E4vz6bB7KKP7Uf1v7VOjzBQtQfJ9RV3TtVDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:24.293745Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3332","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4847bd6796794952d62958d348c284d09b7af7203fe17bdc0e7eb3f97c9b5992","sha256:21b222802c36a943dbb7377c53ba25ad1ee7eb8e662afb5781272b00b53622f2"],"state_sha256":"f93b3672633c326813091e5e8b4e6d2feb4d478bd34b92bbc8034e812777f705"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E7ffTYMEdzS+CYav/MXTwX+oKAFJ/MhXcy0/aaP/Nim/Ww6QIkoNSOsiVViFrhbna/q/mLuuIW94h2529n9bAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:30:32.043447Z","bundle_sha256":"c06726b30a43f85903d0d0617e9dd70974e19ca6847aaa20604fb525344c3077"}}