{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:HMAMO5RBWUMD4VKOORCVQ5OMDP","short_pith_number":"pith:HMAMO5RB","schema_version":"1.0","canonical_sha256":"3b00c77621b5183e554e74455875cc1bd938eb77b6527f0257bd61c15a2676c3","source":{"kind":"arxiv","id":"1310.7820","version":2},"attestation_state":"computed","paper":{"title":"On stable reconstructions from nonuniform Fourier measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anders C. Hansen, Ben Adcock, Milana Gataric","submitted_at":"2013-10-29T14:43:33Z","abstract_excerpt":"We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies - specifically, their density and bandwidth - it is possible to recover any such function $f$ in a stable and accurate manner in any given finite-dimensional subspace; in particular, one which is well suited for approximating $f$. In practice, this is carried out using so-called nonuniform generalized sampling (NUGS). Second, we consider approximation spaces in o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.7820","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-29T14:43:33Z","cross_cats_sorted":[],"title_canon_sha256":"99e02f6b7da5038368497eee6994466bd5319220a722478f8f38d471425e72ef","abstract_canon_sha256":"6c83c0e48c1b548035e67703386d76a2223d12abc51559a4400dfc8e920dbd7e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.773754Z","signature_b64":"T9CTEqUiQWi29w0OTEXd4kWWH3YdY0UXlUKW22zDLR3LpIIw8vo0XPZ6u6rKKZ000EdOd6+XbOlU6YVaqFWoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b00c77621b5183e554e74455875cc1bd938eb77b6527f0257bd61c15a2676c3","last_reissued_at":"2026-05-18T02:54:46.773373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.773373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On stable reconstructions from nonuniform Fourier measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Anders C. Hansen, Ben Adcock, Milana Gataric","submitted_at":"2013-10-29T14:43:33Z","abstract_excerpt":"We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies - specifically, their density and bandwidth - it is possible to recover any such function $f$ in a stable and accurate manner in any given finite-dimensional subspace; in particular, one which is well suited for approximating $f$. In practice, this is carried out using so-called nonuniform generalized sampling (NUGS). Second, we consider approximation spaces in o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7820","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.7820","created_at":"2026-05-18T02:54:46.773430+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.7820v2","created_at":"2026-05-18T02:54:46.773430+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7820","created_at":"2026-05-18T02:54:46.773430+00:00"},{"alias_kind":"pith_short_12","alias_value":"HMAMO5RBWUMD","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"HMAMO5RBWUMD4VKO","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"HMAMO5RB","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP","json":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP.json","graph_json":"https://pith.science/api/pith-number/HMAMO5RBWUMD4VKOORCVQ5OMDP/graph.json","events_json":"https://pith.science/api/pith-number/HMAMO5RBWUMD4VKOORCVQ5OMDP/events.json","paper":"https://pith.science/paper/HMAMO5RB"},"agent_actions":{"view_html":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP","download_json":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP.json","view_paper":"https://pith.science/paper/HMAMO5RB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.7820&json=true","fetch_graph":"https://pith.science/api/pith-number/HMAMO5RBWUMD4VKOORCVQ5OMDP/graph.json","fetch_events":"https://pith.science/api/pith-number/HMAMO5RBWUMD4VKOORCVQ5OMDP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP/action/storage_attestation","attest_author":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP/action/author_attestation","sign_citation":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP/action/citation_signature","submit_replication":"https://pith.science/pith/HMAMO5RBWUMD4VKOORCVQ5OMDP/action/replication_record"}},"created_at":"2026-05-18T02:54:46.773430+00:00","updated_at":"2026-05-18T02:54:46.773430+00:00"}