{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5PY4FFKBK72AWJG6QTAPKTLU5D","short_pith_number":"pith:5PY4FFKB","canonical_record":{"source":{"id":"1405.4320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-16T22:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"99712261985ca8c594db99603ef2f7bb7d55eacf15896b70907b21677c1370ae","abstract_canon_sha256":"18c9dd446d2ff05eeafc67a41b937177e98aab4697c102380fc9845307a845d0"},"schema_version":"1.0"},"canonical_sha256":"ebf1c2954157f40b24de84c0f54d74e8fd661f96943ad99144e9575952edfe71","source":{"kind":"arxiv","id":"1405.4320","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4320","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4320v1","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4320","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"pith_short_12","alias_value":"5PY4FFKBK72A","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PY4FFKBK72AWJG6","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PY4FFKB","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5PY4FFKBK72AWJG6QTAPKTLU5D","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-16T22:02:29Z","cross_cats_sorted":[],"title_canon_sha256":"99712261985ca8c594db99603ef2f7bb7d55eacf15896b70907b21677c1370ae","abstract_canon_sha256":"18c9dd446d2ff05eeafc67a41b937177e98aab4697c102380fc9845307a845d0"},"schema_version":"1.0"},"canonical_sha256":"ebf1c2954157f40b24de84c0f54d74e8fd661f96943ad99144e9575952edfe71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:11.473154Z","signature_b64":"kR+BmU/AcCcHdxvWApNH/wybcDIfNgqF6Jlh+8RWl18eYITtY/Pidf+BBi4+eiXIxZJzDuDcWcL42LYUquBFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebf1c2954157f40b24de84c0f54d74e8fd661f96943ad99144e9575952edfe71","last_reissued_at":"2026-05-18T01:43:11.472591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:11.472591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4320","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":"2026-05-18T01:43:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obw8NoTkVVH2dTXdNWrFh6PSx8w9nlTL2+NWTHyp1f9XHPsVxTrf6AxVD84mXn4t1NHo8tH2NjgCBeOa69uVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:57.848156Z"},"content_sha256":"aea807415f193335514600dc0cafb9caa94c36da1c8c15b635cb6a3b8f8dfb89","schema_version":"1.0","event_id":"sha256:aea807415f193335514600dc0cafb9caa94c36da1c8c15b635cb6a3b8f8dfb89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5PY4FFKBK72AWJG6QTAPKTLU5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameter selection and numerical approximation properties of Fourier extensions from fixed data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ben Adcock, Joseph Ruan","submitted_at":"2014-05-16T22:02:29Z","abstract_excerpt":"Fourier extensions have been shown to be an effective means for the approximation of smooth, nonperiodic functions on bounded intervals given their values on an equispaced, or in general, scattered grid. Related to this method are two parameters. These are the extension parameter $T$ (the ratio of the size of the extended domain to the physical domain) and the oversampling ratio $\\eta$ (the number of sampling nodes per Fourier mode). The purpose of this paper is to investigate how the choice of these parameters affects the accuracy and stability of the approximation. Our main contribution is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4320","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":"2026-05-18T01:43:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0OGV03j7Jk9fu5Op7cZXEhYLg+9OzhkrNlPsw+nCBtWy2Etz50HQyzYiZ66V2Xm0WoO/71pa6U5FSZVIU+PAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:33:57.848846Z"},"content_sha256":"348aa862a6ad7c203a1a753af591b21c0ca9b2bab82b66150019e7d42f11efca","schema_version":"1.0","event_id":"sha256:348aa862a6ad7c203a1a753af591b21c0ca9b2bab82b66150019e7d42f11efca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/bundle.json","state_url":"https://pith.science/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/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":"2026-06-10T23:33:57Z","links":{"resolver":"https://pith.science/pith/5PY4FFKBK72AWJG6QTAPKTLU5D","bundle":"https://pith.science/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/bundle.json","state":"https://pith.science/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PY4FFKBK72AWJG6QTAPKTLU5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5PY4FFKBK72AWJG6QTAPKTLU5D","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":"18c9dd446d2ff05eeafc67a41b937177e98aab4697c102380fc9845307a845d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-16T22:02:29Z","title_canon_sha256":"99712261985ca8c594db99603ef2f7bb7d55eacf15896b70907b21677c1370ae"},"schema_version":"1.0","source":{"id":"1405.4320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4320","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4320v1","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4320","created_at":"2026-05-18T01:43:11Z"},{"alias_kind":"pith_short_12","alias_value":"5PY4FFKBK72A","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5PY4FFKBK72AWJG6","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5PY4FFKB","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:348aa862a6ad7c203a1a753af591b21c0ca9b2bab82b66150019e7d42f11efca","target":"graph","created_at":"2026-05-18T01:43:11Z","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":"Fourier extensions have been shown to be an effective means for the approximation of smooth, nonperiodic functions on bounded intervals given their values on an equispaced, or in general, scattered grid. Related to this method are two parameters. These are the extension parameter $T$ (the ratio of the size of the extended domain to the physical domain) and the oversampling ratio $\\eta$ (the number of sampling nodes per Fourier mode). The purpose of this paper is to investigate how the choice of these parameters affects the accuracy and stability of the approximation. Our main contribution is t","authors_text":"Ben Adcock, Joseph Ruan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-16T22:02:29Z","title":"Parameter selection and numerical approximation properties of Fourier extensions from fixed data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4320","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:aea807415f193335514600dc0cafb9caa94c36da1c8c15b635cb6a3b8f8dfb89","target":"record","created_at":"2026-05-18T01:43:11Z","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":"18c9dd446d2ff05eeafc67a41b937177e98aab4697c102380fc9845307a845d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-16T22:02:29Z","title_canon_sha256":"99712261985ca8c594db99603ef2f7bb7d55eacf15896b70907b21677c1370ae"},"schema_version":"1.0","source":{"id":"1405.4320","kind":"arxiv","version":1}},"canonical_sha256":"ebf1c2954157f40b24de84c0f54d74e8fd661f96943ad99144e9575952edfe71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebf1c2954157f40b24de84c0f54d74e8fd661f96943ad99144e9575952edfe71","first_computed_at":"2026-05-18T01:43:11.472591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:11.472591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kR+BmU/AcCcHdxvWApNH/wybcDIfNgqF6Jlh+8RWl18eYITtY/Pidf+BBi4+eiXIxZJzDuDcWcL42LYUquBFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:11.473154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aea807415f193335514600dc0cafb9caa94c36da1c8c15b635cb6a3b8f8dfb89","sha256:348aa862a6ad7c203a1a753af591b21c0ca9b2bab82b66150019e7d42f11efca"],"state_sha256":"078aed01dfbdd33354b1c466f687cc60c650d3af205e217d6513b132aa011077"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uunj3KAOVm+9V2fEJf3HZyIj13VaQV7FR3N6br5ssCzR1aaGJZB8XWIHTszFGhounX/lUIj+scdYJiwCN/efAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:33:57.852705Z","bundle_sha256":"be85a497d10a34eb9bbaae54217a17bcdc44d417858b94c5d99de4b301bf56af"}}