{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KFSKPL2YLBF33N3LFZHVJ22LA3","short_pith_number":"pith:KFSKPL2Y","canonical_record":{"source":{"id":"1502.07734","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2015-02-12T04:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"573080b33cf7fa6dd0a7ef7f2d05157937c1743a414adbf390ae76e511882c48","abstract_canon_sha256":"105569cb459d47c751c4384fc3fb61af5eb86483bb19905dc31723aa163ae727"},"schema_version":"1.0"},"canonical_sha256":"5164a7af58584bbdb76b2e4f54eb4b06debacbad2bc800be2811a25750fce972","source":{"kind":"arxiv","id":"1502.07734","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07734","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07734v4","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07734","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"KFSKPL2YLBF3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KFSKPL2YLBF33N3L","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KFSKPL2Y","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KFSKPL2YLBF33N3LFZHVJ22LA3","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07734","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2015-02-12T04:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"573080b33cf7fa6dd0a7ef7f2d05157937c1743a414adbf390ae76e511882c48","abstract_canon_sha256":"105569cb459d47c751c4384fc3fb61af5eb86483bb19905dc31723aa163ae727"},"schema_version":"1.0"},"canonical_sha256":"5164a7af58584bbdb76b2e4f54eb4b06debacbad2bc800be2811a25750fce972","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:18.976851Z","signature_b64":"5e9y9vKGfj0xTjQgaVjtwdxfNREGRRV/zvPzsH0YENEZVboRxChLeyaIWchXhlQr7HFeOv3vNZVP4xMqCHwvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5164a7af58584bbdb76b2e4f54eb4b06debacbad2bc800be2811a25750fce972","last_reissued_at":"2026-05-18T01:23:18.976158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:18.976158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07734","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+YdfxwXfhj5vapM8MnGWGjAsjJplFB20uE5pQ5dCdYi75dRyvM176AC3VQM3/PlQAgIef56v5coeCHeSbvSUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:24:06.766189Z"},"content_sha256":"265738b8a3912495e5bac0da41e5be6497d943191d4604e114eadcce1f37495c","schema_version":"1.0","event_id":"sha256:265738b8a3912495e5bac0da41e5be6497d943191d4604e114eadcce1f37495c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KFSKPL2YLBF33N3LFZHVJ22LA3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Weierstrass Fourier Transform and Experiments","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Brendan Harding, Sheng Zhang","submitted_at":"2015-02-12T04:44:16Z","abstract_excerpt":"We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this paper. In some examples, this method has a faster convergent speed than Discrete Fourier Transform."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07734","kind":"arxiv","version":4},"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":"2026-05-18T01:23:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9lrI+Qe3pltz2FNUr2g/lVbP87lSQZrOsCrDOfrEauHiLOkpr5xkyv4fI/LXFTjupAaPg+6EiS0bV8hfvzK6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:24:06.766548Z"},"content_sha256":"0b179b3546480b27f69adb1646cf580f954567eb2fa436430aae60c0f10cfc3f","schema_version":"1.0","event_id":"sha256:0b179b3546480b27f69adb1646cf580f954567eb2fa436430aae60c0f10cfc3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/bundle.json","state_url":"https://pith.science/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/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":"2026-06-03T03:24:06Z","links":{"resolver":"https://pith.science/pith/KFSKPL2YLBF33N3LFZHVJ22LA3","bundle":"https://pith.science/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/bundle.json","state":"https://pith.science/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFSKPL2YLBF33N3LFZHVJ22LA3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KFSKPL2YLBF33N3LFZHVJ22LA3","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":"105569cb459d47c751c4384fc3fb61af5eb86483bb19905dc31723aa163ae727","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2015-02-12T04:44:16Z","title_canon_sha256":"573080b33cf7fa6dd0a7ef7f2d05157937c1743a414adbf390ae76e511882c48"},"schema_version":"1.0","source":{"id":"1502.07734","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07734","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07734v4","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07734","created_at":"2026-05-18T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"KFSKPL2YLBF3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KFSKPL2YLBF33N3L","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KFSKPL2Y","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:0b179b3546480b27f69adb1646cf580f954567eb2fa436430aae60c0f10cfc3f","target":"graph","created_at":"2026-05-18T01:23:18Z","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":"We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this paper. In some examples, this method has a faster convergent speed than Discrete Fourier Transform.","authors_text":"Brendan Harding, Sheng Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2015-02-12T04:44:16Z","title":"Discrete Weierstrass Fourier Transform and Experiments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07734","kind":"arxiv","version":4},"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":"sha256:265738b8a3912495e5bac0da41e5be6497d943191d4604e114eadcce1f37495c","target":"record","created_at":"2026-05-18T01:23:18Z","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":"105569cb459d47c751c4384fc3fb61af5eb86483bb19905dc31723aa163ae727","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2015-02-12T04:44:16Z","title_canon_sha256":"573080b33cf7fa6dd0a7ef7f2d05157937c1743a414adbf390ae76e511882c48"},"schema_version":"1.0","source":{"id":"1502.07734","kind":"arxiv","version":4}},"canonical_sha256":"5164a7af58584bbdb76b2e4f54eb4b06debacbad2bc800be2811a25750fce972","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5164a7af58584bbdb76b2e4f54eb4b06debacbad2bc800be2811a25750fce972","first_computed_at":"2026-05-18T01:23:18.976158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:18.976158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5e9y9vKGfj0xTjQgaVjtwdxfNREGRRV/zvPzsH0YENEZVboRxChLeyaIWchXhlQr7HFeOv3vNZVP4xMqCHwvDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:18.976851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07734","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:265738b8a3912495e5bac0da41e5be6497d943191d4604e114eadcce1f37495c","sha256:0b179b3546480b27f69adb1646cf580f954567eb2fa436430aae60c0f10cfc3f"],"state_sha256":"5566ebcb4cdb99ee890cb992cf82f5e7dd0d3594322f0a952a72e073005df4b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRtya3KZzSEBO2N/4PP8FR469qPvuVsVBqy4zmBqOqTnfT+I9n530wkEjycyWiKxMf+jpR6rne5YC0JlydvhDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:24:06.768901Z","bundle_sha256":"b99805912840137350364061233552d1cf982cfcdf7fa6264ab9c4dea8b9f7aa"}}