{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WJPW5XX6L4J5XDG7QPV3SKEUQY","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":"1fd0627de1483e57ddd67a752e20c504b295546e198cdc056282f2fd5d870788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-10T17:20:59Z","title_canon_sha256":"62c399077c5ff76fbd4e814ca05c13ee7d7cc49879aaa9b22eb71bb0457b1f5c"},"schema_version":"1.0","source":{"id":"1310.2892","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2892","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2892v3","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2892","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"WJPW5XX6L4J5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WJPW5XX6L4J5XDG7","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WJPW5XX6","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:3caa3cc634f6410056e0f4a3c1698dacb011ed1597419a04f8a4e1d685254f36","target":"graph","created_at":"2026-05-18T01:23:29Z","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":"A \\Riesz-basis sequence for $L_2[-\\pi,\\pi]$ is a strictly increasing sequence $X:=(x_j)_{j\\in\\mathbb{Z}}$ in $\\mathbb{R}$ such that the set of functions $\\left(e^{-ix_j(\\cdot)}\\right)_{j\\in\\mathbb{Z}}$ is a Riesz basis for $L_2[-\\pi,\\pi]$. Given such a sequence and a parameter $0<h\\leq1$, we consider interpolation of functions $g\\in W_2^k(\\mathbb{R})$ at the set $(hx_j)_{j\\in\\mathbb{Z}}$ via translates of the Gaussian kernel. Existence is shown of an interpolant of the form $$I^{hX}(g)(x):=\\underset{j\\in\\mathbb{Z}}{\\sum}a_je^{-(x-hx_j)^2},\\quad x\\in\\mathbb{R},$$ which is continuous and square-","authors_text":"Keaton Hamm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-10T17:20:59Z","title":"Approximation Rates for Interpolation of Sobolev Functions via Gaussians and Allied Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2892","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":"sha256:6e28206b841cf3b656f6ed409c1b56ba1ec267db282a9b7fb9a8894c6c41a775","target":"record","created_at":"2026-05-18T01:23:29Z","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":"1fd0627de1483e57ddd67a752e20c504b295546e198cdc056282f2fd5d870788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-10T17:20:59Z","title_canon_sha256":"62c399077c5ff76fbd4e814ca05c13ee7d7cc49879aaa9b22eb71bb0457b1f5c"},"schema_version":"1.0","source":{"id":"1310.2892","kind":"arxiv","version":3}},"canonical_sha256":"b25f6edefe5f13db8cdf83ebb928948616fd5700b5deb87adfb6a4f6bf98e276","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b25f6edefe5f13db8cdf83ebb928948616fd5700b5deb87adfb6a4f6bf98e276","first_computed_at":"2026-05-18T01:23:29.984288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:29.984288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wdois/bbtgZXmbqtBYNIH4XLoLwgTX9PneWJ37Vhx1C7QXjJis8UHKEmy0yc1zgAFz+F68RRTHOpg4wFsJYcAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:29.984833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2892","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e28206b841cf3b656f6ed409c1b56ba1ec267db282a9b7fb9a8894c6c41a775","sha256:3caa3cc634f6410056e0f4a3c1698dacb011ed1597419a04f8a4e1d685254f36"],"state_sha256":"0f9e398593740d8c714adaaef9276727efa01117b3c93a59997aa6ddf97d13f5"}