{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NDMVIBJQZXCRGLKKFC5YLZ2XNU","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":"17399f1573f02c9f374a77a60383221ceba28757277137f446d819be84639a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-13T21:32:45Z","title_canon_sha256":"2010e8b1ca1aad83a0fa6b8e50a9473e958aee9efd4deee9f25ca7dd71129f1e"},"schema_version":"1.0","source":{"id":"1109.2936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2936","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2936v2","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2936","created_at":"2026-05-18T03:28:54Z"},{"alias_kind":"pith_short_12","alias_value":"NDMVIBJQZXCR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NDMVIBJQZXCRGLKK","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NDMVIBJQ","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:4e0cbcd49111fb65e2b5e31a50f97d7b09c1092cb6c9d949a2c8146611df56e0","target":"graph","created_at":"2026-05-18T03:28:54Z","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":"Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses a numerical integration rule to approximate the Fourier-type coefficients of a truncated expansion in orthogonal polynomials. For problems in more than two or three dimensions, a sparse grid numerical integration rule offers accuracy with a smaller node set compared to tensor product approximation. However, when using a sparse rule to approximately integrat","authors_text":"Eric T. Phipps, Michael S. Eldred, Paul G. Constantine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-13T21:32:45Z","title":"Sparse Pseudospectral Approximation Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2936","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:b3a4818f39ebc9ddb7bb48fef2a52680ef3591f5e7902a7ed690eee1423ff120","target":"record","created_at":"2026-05-18T03:28:54Z","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":"17399f1573f02c9f374a77a60383221ceba28757277137f446d819be84639a53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-09-13T21:32:45Z","title_canon_sha256":"2010e8b1ca1aad83a0fa6b8e50a9473e958aee9efd4deee9f25ca7dd71129f1e"},"schema_version":"1.0","source":{"id":"1109.2936","kind":"arxiv","version":2}},"canonical_sha256":"68d9540530cdc5132d4a28bb85e7576d1aaf7bd9ac4598d766ee0de78bd73925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68d9540530cdc5132d4a28bb85e7576d1aaf7bd9ac4598d766ee0de78bd73925","first_computed_at":"2026-05-18T03:28:54.207658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:54.207658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V6Hy3Mf9BdqNTdPJatkmyfEohNL1fm9PaLn3MMKLh22khoI7wZG7d8CMpKA1VUYlywxX8QztiOJd1Fw74rgTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:54.208421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3a4818f39ebc9ddb7bb48fef2a52680ef3591f5e7902a7ed690eee1423ff120","sha256:4e0cbcd49111fb65e2b5e31a50f97d7b09c1092cb6c9d949a2c8146611df56e0"],"state_sha256":"a56f4ed9ae9f86510f1e3014eccad68ae1c9b6f2ab76c4a7914953e12f9b3fc6"}