{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ITI5XKWAH4E74LP6XHYL4CLEV5","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":"6001d2559345eccc6d6cd91081ca7b1b97f16db4fe972323c141d0a406d57fe3","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-23T08:07:47Z","title_canon_sha256":"2c830a7c3cdce236c35dafe57c3717786f97a4d438f87af3a1f8d205a3d30e7c"},"schema_version":"1.0","source":{"id":"2409.14791","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.14791","created_at":"2026-07-05T10:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"2409.14791v2","created_at":"2026-07-05T10:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.14791","created_at":"2026-07-05T10:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"ITI5XKWAH4E7","created_at":"2026-07-05T10:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"ITI5XKWAH4E74LP6","created_at":"2026-07-05T10:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"ITI5XKWA","created_at":"2026-07-05T10:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:290f4f974da9d510e2a416b326cd8accaa58e04092728dc2fd43fedda7e91914","target":"graph","created_at":"2026-07-05T10:31:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.14791/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study multiscale scattered data interpolation schemes for globally supported radial basis functions with focus on the Mat\\'ern class. The multiscale approximation is constructed through a sequence of residual corrections, where radial basis functions with different lengthscale parameters are combined to capture varying levels of detail. We prove that the condition numbers of the the diagonal blocks of the corresponding multiscale system remain bounded independently of the particular level, allowing us to use an iterative solver with a bounded number of iterations for the numerical solution.","authors_text":"Holger Wendland, Michael Multerer, R\\\"udiger Kempf, Sara Avesani","cross_cats":["cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-23T08:07:47Z","title":"Multiscale scattered data analysis in samplet coordinates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.14791","kind":"arxiv","version":2},"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":"sha256:11b9920f7dbcb16d879dc940a9be50ab12960574b7eda16b89480a92ead7614d","target":"record","created_at":"2026-07-05T10:31:46Z","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":"6001d2559345eccc6d6cd91081ca7b1b97f16db4fe972323c141d0a406d57fe3","cross_cats_sorted":["cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-09-23T08:07:47Z","title_canon_sha256":"2c830a7c3cdce236c35dafe57c3717786f97a4d438f87af3a1f8d205a3d30e7c"},"schema_version":"1.0","source":{"id":"2409.14791","kind":"arxiv","version":2}},"canonical_sha256":"44d1dbaac03f09fe2dfeb9f0be0964af5b10ff77d278cca58959befc04a18cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44d1dbaac03f09fe2dfeb9f0be0964af5b10ff77d278cca58959befc04a18cdf","first_computed_at":"2026-07-05T10:31:46.976619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:31:46.976619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yh2JJjPthdLMCgdjWqHb/YKmkObL4L9+nV5MbXuncBDOK58migzE1oAhpjCADckQJisN3fmVhr1yd4qds5YdBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:31:46.977126Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.14791","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11b9920f7dbcb16d879dc940a9be50ab12960574b7eda16b89480a92ead7614d","sha256:290f4f974da9d510e2a416b326cd8accaa58e04092728dc2fd43fedda7e91914"],"state_sha256":"1249a60ca6665793075f22064f72c37eb4750f5cf0ee7d9bf4a517cfa1732057"}