{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CWOWHZ66GZSDGX7YEPWTQYVA3O","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":"a17e8584fc328bda626edba8d266b770a1cd6b90655cfb9e1635352de95d7176","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-28T04:50:56Z","title_canon_sha256":"c73310d7db7dd4fe3be0808af47f4e702f73f9eb80cef632b7867668a67e1572"},"schema_version":"1.0","source":{"id":"1302.7083","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7083","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7083v3","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7083","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"CWOWHZ66GZSD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CWOWHZ66GZSDGX7Y","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CWOWHZ66","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:778293dcbccf4a85fea08dbb2f5d0b007876830839163e6ee6d39c05ee5e4727","target":"graph","created_at":"2026-05-18T03:03:32Z","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":"This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional stochastic space in the context of limited amount of information. The proposed approach involves a procedure for the selection of an approximation basis and the evaluation of the associated coefficients. The selection of the approximation basis relies on the a priori choice of the High-Dimensional Model Representation format combined with a modified Least Angl","authors_text":"Lionel Mathelin","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-28T04:50:56Z","title":"Quantification of uncertainty from high-dimensional scattered data via polynomial approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7083","kind":"arxiv","version":3},"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:b5e3731129d3b9e25ba0b6e0f85a07e6b98db854d6a464161b83a2fda62fbc50","target":"record","created_at":"2026-05-18T03:03:32Z","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":"a17e8584fc328bda626edba8d266b770a1cd6b90655cfb9e1635352de95d7176","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-28T04:50:56Z","title_canon_sha256":"c73310d7db7dd4fe3be0808af47f4e702f73f9eb80cef632b7867668a67e1572"},"schema_version":"1.0","source":{"id":"1302.7083","kind":"arxiv","version":3}},"canonical_sha256":"159d63e7de3664335ff823ed3862a0dba60a7fd9100265ff73c13c5c499e34b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"159d63e7de3664335ff823ed3862a0dba60a7fd9100265ff73c13c5c499e34b5","first_computed_at":"2026-05-18T03:03:32.317607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:32.317607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YnqkhkKenQDOG9SixgNHYmc0/9DLT+Hno+F2p3MmKpym7hmXcecVS3Y23A0XAg0lzmI7EKhvxBLq0Mb+UudkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:32.318058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7083","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5e3731129d3b9e25ba0b6e0f85a07e6b98db854d6a464161b83a2fda62fbc50","sha256:778293dcbccf4a85fea08dbb2f5d0b007876830839163e6ee6d39c05ee5e4727"],"state_sha256":"d3ec6a8bb2811a10a6c46b6054f20d080927f055797c40291cba91e356caa65c"}