{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D5OPUHNKXKA3A26KJAI6G5D3U2","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":"08b9ba719985c22575679c7d8ddd4bf7a975c10dde720c396250eed3f1d635ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-14T14:27:37Z","title_canon_sha256":"4a57618b9e21f5212bf5364690a3d6c003fb0c14f6c40cc0d25f7ec18c10dfc4"},"schema_version":"1.0","source":{"id":"1710.05192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05192","created_at":"2026-05-18T00:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05192v1","created_at":"2026-05-18T00:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05192","created_at":"2026-05-18T00:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"D5OPUHNKXKA3","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D5OPUHNKXKA3A26K","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D5OPUHNK","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:91b444ad82b79725e0c686b3af0097822d39acd97c7ecbad5200013cf1643e61","target":"graph","created_at":"2026-05-18T00:32:54Z","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":"In this article, we solve a deterministically generalized interpolation problem by a stochastic approach. We introduce a kernel-based probability measure on a Banach space by a covariance kernel which is defined on the dual space of the Banach space. The kernel-based probability measure provides a numerical tool to construct and analyze the kernel-based estimators conditioned on non-noise data or noisy data including algorithms and error analysis. Same as meshfree methods, we can also obtain the kernel-based approximate solutions of elliptic partial differential equations by the kernel-based p","authors_text":"Qi Ye","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-14T14:27:37Z","title":"Kernel-based Approximation Methods for Generalized Interpolations: A Deterministic or Stochastic Problem?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05192","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:d6600d693a1379fa8dbd0130684790e513eec2aab1132ea4cd85a6c9769c94a2","target":"record","created_at":"2026-05-18T00:32:54Z","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":"08b9ba719985c22575679c7d8ddd4bf7a975c10dde720c396250eed3f1d635ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-14T14:27:37Z","title_canon_sha256":"4a57618b9e21f5212bf5364690a3d6c003fb0c14f6c40cc0d25f7ec18c10dfc4"},"schema_version":"1.0","source":{"id":"1710.05192","kind":"arxiv","version":1}},"canonical_sha256":"1f5cfa1daaba81b06bca4811e3747ba6a669aa44a1170472354bed19784a9634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5cfa1daaba81b06bca4811e3747ba6a669aa44a1170472354bed19784a9634","first_computed_at":"2026-05-18T00:32:54.109264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:54.109264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QFh8T2H1BfNbCRh3lwF0vZBEaPjiLLRIqv/RuKoVlITdFwbQC/6qlsohtSGoDzGWB4+oydI7ujqOxYhA8Qt/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:54.109965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6600d693a1379fa8dbd0130684790e513eec2aab1132ea4cd85a6c9769c94a2","sha256:91b444ad82b79725e0c686b3af0097822d39acd97c7ecbad5200013cf1643e61"],"state_sha256":"b7eb0590448448f691183dcf34fca034bdb9169327d32d1e76996de471e165ca"}