{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:O4YXQPJJDB67X7NFVVT5V7LXI7","short_pith_number":"pith:O4YXQPJJ","schema_version":"1.0","canonical_sha256":"7731783d29187dfbfda5ad67dafd7747e2b9a595eae3415027b2889801607e7c","source":{"kind":"arxiv","id":"1205.5961","version":2},"attestation_state":"computed","paper":{"title":"Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Dmitry Yarotsky","submitted_at":"2012-05-27T12:43:04Z","abstract_excerpt":"We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the Harish-Chandra-Itzykson-Zuber formula. We then prove the exponential convergence of interpolation for functions analytic in a sufficiently large domain. As an application, we prove the global exponential convergence of optimization by expected improvement for such functions."},"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":"1205.5961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-05-27T12:43:04Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"999d8081572fccdd7a2a752a584a046ddf9010d73617bca9a28b231b36941888","abstract_canon_sha256":"504bc6c25a91d3019c83fe8211767381a599b40a35780bc12ddebfe3d3513cbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:23.508526Z","signature_b64":"RNm7XTqjo2xzhK3qMyVct0FITlv/xdquwdeV+RavLtBWLk87/DcZsatnVC5nbBVNsKDpPC8tXx5m1d0v6yJ/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7731783d29187dfbfda5ad67dafd7747e2b9a595eae3415027b2889801607e7c","last_reissued_at":"2026-05-18T03:38:23.507726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:23.507726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Univariate interpolation by exponential functions and gaussian RBFs for generic sets of nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Dmitry Yarotsky","submitted_at":"2012-05-27T12:43:04Z","abstract_excerpt":"We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the Harish-Chandra-Itzykson-Zuber formula. We then prove the exponential convergence of interpolation for functions analytic in a sufficiently large domain. As an application, we prove the global exponential convergence of optimization by expected improvement for such functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5961","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":"1205.5961","created_at":"2026-05-18T03:38:23.507862+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.5961v2","created_at":"2026-05-18T03:38:23.507862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5961","created_at":"2026-05-18T03:38:23.507862+00:00"},{"alias_kind":"pith_short_12","alias_value":"O4YXQPJJDB67","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"O4YXQPJJDB67X7NF","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"O4YXQPJJ","created_at":"2026-05-18T12:27:16.716162+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/O4YXQPJJDB67X7NFVVT5V7LXI7","json":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7.json","graph_json":"https://pith.science/api/pith-number/O4YXQPJJDB67X7NFVVT5V7LXI7/graph.json","events_json":"https://pith.science/api/pith-number/O4YXQPJJDB67X7NFVVT5V7LXI7/events.json","paper":"https://pith.science/paper/O4YXQPJJ"},"agent_actions":{"view_html":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7","download_json":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7.json","view_paper":"https://pith.science/paper/O4YXQPJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.5961&json=true","fetch_graph":"https://pith.science/api/pith-number/O4YXQPJJDB67X7NFVVT5V7LXI7/graph.json","fetch_events":"https://pith.science/api/pith-number/O4YXQPJJDB67X7NFVVT5V7LXI7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7/action/storage_attestation","attest_author":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7/action/author_attestation","sign_citation":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7/action/citation_signature","submit_replication":"https://pith.science/pith/O4YXQPJJDB67X7NFVVT5V7LXI7/action/replication_record"}},"created_at":"2026-05-18T03:38:23.507862+00:00","updated_at":"2026-05-18T03:38:23.507862+00:00"}