{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FCSOELAVEW5NYDFFYHIHA5DHMC","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":"af600b4bfcd57b8349f11c3647ccabb3026f4062795f310420a87b9ef459584a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T23:07:01Z","title_canon_sha256":"06c6daf2878a21522edaebcd23e1b0f555da024bebcc8187770752927cab0d88"},"schema_version":"1.0","source":{"id":"1610.05374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.05374","created_at":"2026-05-18T00:53:25Z"},{"alias_kind":"arxiv_version","alias_value":"1610.05374v1","created_at":"2026-05-18T00:53:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05374","created_at":"2026-05-18T00:53:25Z"},{"alias_kind":"pith_short_12","alias_value":"FCSOELAVEW5N","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FCSOELAVEW5NYDFF","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FCSOELAV","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:0a506db421d7d7b81ce141fb7571a2f355f7285fe43e2fe85f39e04a7373b9a1","target":"graph","created_at":"2026-05-18T00:53:25Z","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":"One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Cont","authors_text":"Bengt Fornberg, Grady B. Wright","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T23:07:01Z","title":"Stable computations with flat radial basis functions using vector-valued rational approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05374","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":"sha256:28998d4ef0203adfa4430e480dae07a67deecb2d2219a8ba495493d1eaedd651","target":"record","created_at":"2026-05-18T00:53:25Z","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":"af600b4bfcd57b8349f11c3647ccabb3026f4062795f310420a87b9ef459584a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-17T23:07:01Z","title_canon_sha256":"06c6daf2878a21522edaebcd23e1b0f555da024bebcc8187770752927cab0d88"},"schema_version":"1.0","source":{"id":"1610.05374","kind":"arxiv","version":1}},"canonical_sha256":"28a4e22c1525badc0ca5c1d070746760bf0f0c34ccc6d8ad973232040b2fc99e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28a4e22c1525badc0ca5c1d070746760bf0f0c34ccc6d8ad973232040b2fc99e","first_computed_at":"2026-05-18T00:53:25.197131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:25.197131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jf3Ky7m0u1FY16T6cBayz27GpFxUKsDQhMP7ZphPjW6LvP3Do6v+h9fjWXxstgecnKxYyABYNUf4jP0U13onBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:25.197485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.05374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28998d4ef0203adfa4430e480dae07a67deecb2d2219a8ba495493d1eaedd651","sha256:0a506db421d7d7b81ce141fb7571a2f355f7285fe43e2fe85f39e04a7373b9a1"],"state_sha256":"cec2f2ef2efb9898a6f83c97f90c99974e5a7361dae6d3f51a4e572fb1e71a63"}