{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:HHM3VY5LMRAGI6WLERX73A5RFQ","short_pith_number":"pith:HHM3VY5L","schema_version":"1.0","canonical_sha256":"39d9bae3ab6440647acb246ffd83b12c277659c8450521ecf5f0ab77b7a1719f","source":{"kind":"arxiv","id":"2606.04190","version":1},"attestation_state":"computed","paper":{"title":"Sampling and reconstruction of convex functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Albert Cohen, Andrea Bonito, Guergana Petrova, Jonathan W. Siegel, Ronald DeVore, Wolfgang Dahmen","submitted_at":"2026-06-02T20:19:38Z","abstract_excerpt":"We discuss optimal recovery for classes of multivariate convex functions from given point samples, as well as the sampling numbers of these classes, corresponding to optimal sample choices. Upper and lower bounds for either variant are established when the reconstruction error is measured in $L_p$ for $1\\leq p\\leq \\infty$. These bounds match, sometimes up to logarithmic factors, and therefore characterize the respective optimal rate of decay. For classical smoothness classes such as Sobolev, H\\\"older or Besov spaces, it is well known that the optimal decay rate of sampling numbers can be achie"},"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":"2606.04190","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-02T20:19:38Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"1d3029fe05bfa113f99b7e61cc4a35b47ddf1298bd5588075944e56abd8bb8b3","abstract_canon_sha256":"7f6be3ec6a7b024eb781d748f0ede22148cbce9a6c451705faffcaeed456c905"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:19.734492Z","signature_b64":"wCcGFIXfrOnX2Dl4y3gSV2klgLaTHxzK4Ea4T5HI6fgAaCkHgyLRG0nORrk/7vEtd9rW9pEf25+gG6/WVzEuDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39d9bae3ab6440647acb246ffd83b12c277659c8450521ecf5f0ab77b7a1719f","last_reissued_at":"2026-06-04T01:08:19.733776Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:19.733776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sampling and reconstruction of convex functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Albert Cohen, Andrea Bonito, Guergana Petrova, Jonathan W. Siegel, Ronald DeVore, Wolfgang Dahmen","submitted_at":"2026-06-02T20:19:38Z","abstract_excerpt":"We discuss optimal recovery for classes of multivariate convex functions from given point samples, as well as the sampling numbers of these classes, corresponding to optimal sample choices. Upper and lower bounds for either variant are established when the reconstruction error is measured in $L_p$ for $1\\leq p\\leq \\infty$. These bounds match, sometimes up to logarithmic factors, and therefore characterize the respective optimal rate of decay. For classical smoothness classes such as Sobolev, H\\\"older or Besov spaces, it is well known that the optimal decay rate of sampling numbers can be achie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04190","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04190/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.04190","created_at":"2026-06-04T01:08:19.733876+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.04190v1","created_at":"2026-06-04T01:08:19.733876+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04190","created_at":"2026-06-04T01:08:19.733876+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHM3VY5LMRAG","created_at":"2026-06-04T01:08:19.733876+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHM3VY5LMRAGI6WL","created_at":"2026-06-04T01:08:19.733876+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHM3VY5L","created_at":"2026-06-04T01:08:19.733876+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/HHM3VY5LMRAGI6WLERX73A5RFQ","json":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ.json","graph_json":"https://pith.science/api/pith-number/HHM3VY5LMRAGI6WLERX73A5RFQ/graph.json","events_json":"https://pith.science/api/pith-number/HHM3VY5LMRAGI6WLERX73A5RFQ/events.json","paper":"https://pith.science/paper/HHM3VY5L"},"agent_actions":{"view_html":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ","download_json":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ.json","view_paper":"https://pith.science/paper/HHM3VY5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.04190&json=true","fetch_graph":"https://pith.science/api/pith-number/HHM3VY5LMRAGI6WLERX73A5RFQ/graph.json","fetch_events":"https://pith.science/api/pith-number/HHM3VY5LMRAGI6WLERX73A5RFQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ/action/storage_attestation","attest_author":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ/action/author_attestation","sign_citation":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ/action/citation_signature","submit_replication":"https://pith.science/pith/HHM3VY5LMRAGI6WLERX73A5RFQ/action/replication_record"}},"created_at":"2026-06-04T01:08:19.733876+00:00","updated_at":"2026-06-04T01:08:19.733876+00:00"}