{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CW5WX4AWDNMPCDGX5VCLC6TR6A","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":"24428ccdb78c1aebfa01c08be6e9315872f81696ec5331a0a055c7b5f829a422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-13T16:10:01Z","title_canon_sha256":"d69fff8c2e57833720be478d50543c2788f21b75f6477575e4962beacfa250b4"},"schema_version":"1.0","source":{"id":"1401.2893","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.2893","created_at":"2026-05-18T03:02:31Z"},{"alias_kind":"arxiv_version","alias_value":"1401.2893v1","created_at":"2026-05-18T03:02:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.2893","created_at":"2026-05-18T03:02:31Z"},{"alias_kind":"pith_short_12","alias_value":"CW5WX4AWDNMP","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CW5WX4AWDNMPCDGX","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CW5WX4AW","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:cc0bcdd143c7481f38dde5024fcfa020a299dbeb23033d6b6ce3d4a64ca3e89a","target":"graph","created_at":"2026-05-18T03:02:31Z","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":"This paper continues the study of interpolation operators on scattered data. We introduce the Poisson interpolation operator and prove various properties. The main result concerns functions in the Paley-Wiener space $PW_{B_\\beta}$, and shows that one may recover these functions from their samples on a complete interpolating sequence for $[-\\delta,\\delta]^2$ by using the Poisson interpolation operator, provided that $0<\\beta < (3-\\sqrt{8})\\delta$.","authors_text":"Jeff Ledford","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-13T16:10:01Z","title":"Recovery of bivariate band limited functions using scattered translates of the Poisson kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2893","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":"sha256:4ff6fe1d88c9810b4cfe2b272906ff428860732007f69703fcbf73b7091c3abf","target":"record","created_at":"2026-05-18T03:02:31Z","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":"24428ccdb78c1aebfa01c08be6e9315872f81696ec5331a0a055c7b5f829a422","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-13T16:10:01Z","title_canon_sha256":"d69fff8c2e57833720be478d50543c2788f21b75f6477575e4962beacfa250b4"},"schema_version":"1.0","source":{"id":"1401.2893","kind":"arxiv","version":1}},"canonical_sha256":"15bb6bf0161b58f10cd7ed44b17a71f014e048b26558cbb20e948f1eebba05d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15bb6bf0161b58f10cd7ed44b17a71f014e048b26558cbb20e948f1eebba05d5","first_computed_at":"2026-05-18T03:02:31.591232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:31.591232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gKH/4cyYXJ1j6q9mXEulK47QuYC3XI6noj/Ip754e0sxI5RApHulyjcq740FtknZnrSiNObHRhGhNJIib75jDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:31.591891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.2893","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff6fe1d88c9810b4cfe2b272906ff428860732007f69703fcbf73b7091c3abf","sha256:cc0bcdd143c7481f38dde5024fcfa020a299dbeb23033d6b6ce3d4a64ca3e89a"],"state_sha256":"c28dd72d288199b8cb861b18f3c5d92e8f0841fba4c227ca2f746a8b96b607d4"}