{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4XLNVIX3YR4POK3AKUGLBSAFAH","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":"ef5146124f86985d63e4c1f081b711d359736633aa58c15a03a993eea1b065d0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-12-13T18:14:34Z","title_canon_sha256":"ddfe8527cd0ac65ad085aeb57426056803471df9d075b17b1b57bfb6b33ab1ce"},"schema_version":"1.0","source":{"id":"1412.4265","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4265","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4265v3","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4265","created_at":"2026-05-18T02:30:46Z"},{"alias_kind":"pith_short_12","alias_value":"4XLNVIX3YR4P","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4XLNVIX3YR4POK3A","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4XLNVIX3","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:de8269f7eabd716abffa0b53a3fa18af55a68bf06f27db6d213c39035d612884","target":"graph","created_at":"2026-05-18T02:30:46Z","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":"Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an exponentially-decaying approximation error to reconstruct a multivariate bandlimited function from its finite average oversampling data. The key problem in our analysis is how to extend a function so that its Fourier transform decays at an optimal rate to zero at infinity.","authors_text":"Haizhang Zhang, Wenjian Chen","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-12-13T18:14:34Z","title":"Exponential Approximation of Multivariate Bandlimited Functions from Average Oversampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4265","kind":"arxiv","version":3},"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":"sha256:8ec81df8749b5d4a5f845c32bc6cc346e45f7254d7f412da4fa7858e2204231e","target":"record","created_at":"2026-05-18T02:30:46Z","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":"ef5146124f86985d63e4c1f081b711d359736633aa58c15a03a993eea1b065d0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-12-13T18:14:34Z","title_canon_sha256":"ddfe8527cd0ac65ad085aeb57426056803471df9d075b17b1b57bfb6b33ab1ce"},"schema_version":"1.0","source":{"id":"1412.4265","kind":"arxiv","version":3}},"canonical_sha256":"e5d6daa2fbc478f72b60550cb0c80501cb181200745dc7e81fad94a6119f0f33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5d6daa2fbc478f72b60550cb0c80501cb181200745dc7e81fad94a6119f0f33","first_computed_at":"2026-05-18T02:30:46.730259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:46.730259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g4zG2v/CvfZnNTYJ8Nz5pRmApICTb0kP3OCgqW1L0fHZWb4giXBlLdhMU5/Bym0o0XCRmq6f3ikuncUWyDlFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:46.730685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4265","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec81df8749b5d4a5f845c32bc6cc346e45f7254d7f412da4fa7858e2204231e","sha256:de8269f7eabd716abffa0b53a3fa18af55a68bf06f27db6d213c39035d612884"],"state_sha256":"60792e9446ccd9b5c3607e20948481dbc78dc7a431d91f762bef9d4db99aeede"}