{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4CAJ34DIL5Z3EAOZDBOSTXL5AG","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":"979f20e91a232f22db659e286c70779fec414854563343d877b0ea44e1702507","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-03-03T00:23:15Z","title_canon_sha256":"8530d09ec12ab0dd44f4b0ce51f81763e7695b18f36de9be8f704d493d1c4c12"},"schema_version":"1.0","source":{"id":"2003.01263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.01263","created_at":"2026-07-05T00:45:26Z"},{"alias_kind":"arxiv_version","alias_value":"2003.01263v1","created_at":"2026-07-05T00:45:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.01263","created_at":"2026-07-05T00:45:26Z"},{"alias_kind":"pith_short_12","alias_value":"4CAJ34DIL5Z3","created_at":"2026-07-05T00:45:26Z"},{"alias_kind":"pith_short_16","alias_value":"4CAJ34DIL5Z3EAOZ","created_at":"2026-07-05T00:45:26Z"},{"alias_kind":"pith_short_8","alias_value":"4CAJ34DI","created_at":"2026-07-05T00:45:26Z"}],"graph_snapshots":[{"event_id":"sha256:1f63bf1d66b5c7521a515d9c25f5a4ce35ba722078febf56a6b0b64bca0dedf0","target":"graph","created_at":"2026-07-05T00:45:26Z","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/2003.01263/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differentiation operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.","authors_text":"Bishnu Lamichhane, Elizabeth Harris, Quoc Thong Le Gia","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-03-03T00:23:15Z","title":"Approximation of noisy data using multivariate splines and finite element methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.01263","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":"sha256:8c5f5cd7a933e06faa3110470bbed49fcff3e055f7b0610691870d25f9d2f953","target":"record","created_at":"2026-07-05T00:45:26Z","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":"979f20e91a232f22db659e286c70779fec414854563343d877b0ea44e1702507","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-03-03T00:23:15Z","title_canon_sha256":"8530d09ec12ab0dd44f4b0ce51f81763e7695b18f36de9be8f704d493d1c4c12"},"schema_version":"1.0","source":{"id":"2003.01263","kind":"arxiv","version":1}},"canonical_sha256":"e0809df0685f73b201d9185d29dd7d018c3bfc9eada210e8b024d0b24ba27e91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0809df0685f73b201d9185d29dd7d018c3bfc9eada210e8b024d0b24ba27e91","first_computed_at":"2026-07-05T00:45:26.683136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:45:26.683136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpKAyJA67rrpBpfngcFPY8/PYmaIx0Gc/it4msucseibbhP4bVpVGdEm5YfDS3Zxyh8XuujbiNvYSGUis2i9Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:45:26.683682Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.01263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c5f5cd7a933e06faa3110470bbed49fcff3e055f7b0610691870d25f9d2f953","sha256:1f63bf1d66b5c7521a515d9c25f5a4ce35ba722078febf56a6b0b64bca0dedf0"],"state_sha256":"2a5328a28d5ce4fc15c7db8fa41093b1250898b52fae4f6d1c55f3ee2fbf79a2"}