{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FRFJYNWO72UD35TCLI6FKYV7PQ","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":"cde47a16332a1e1c0240b875020c84c23b5981b62d42a082c19ed8f522a61ae8","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T11:52:42Z","title_canon_sha256":"1a76ae8395002f75f515864d73266c8c8035c183069f13dec67b421e073e46bf"},"schema_version":"1.0","source":{"id":"1501.03323","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03323","created_at":"2026-06-04T17:08:59Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03323v2","created_at":"2026-06-04T17:08:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03323","created_at":"2026-06-04T17:08:59Z"},{"alias_kind":"pith_short_12","alias_value":"FRFJYNWO72UD","created_at":"2026-06-04T17:08:59Z"},{"alias_kind":"pith_short_16","alias_value":"FRFJYNWO72UD35TC","created_at":"2026-06-04T17:08:59Z"},{"alias_kind":"pith_short_8","alias_value":"FRFJYNWO","created_at":"2026-06-04T17:08:59Z"}],"graph_snapshots":[{"event_id":"sha256:5d933f4d6ffed9485d7bbb84a49f831f83f03f7d4f1f2ff11c5be7c95cc02e2c","target":"graph","created_at":"2026-06-04T17:08:59Z","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/1501.03323/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper addresses model dimensionality reduction for Bayesian inference based on prior Gaussian fields with uncertainty in the covariance function hyper-parameters. The dimensionality reduction is traditionally achieved using the Karhunen-\\Loeve expansion of a prior Gaussian process assuming covariance function with fixed hyper-parameters, despite the fact that these are uncertain in nature. The posterior distribution of the Karhunen-Lo\\`{e}ve coordinates is then inferred using available observations. The resulting inferred field is therefore dependent on the assumed hyper-parameters. Here,","authors_text":"Ibrahim Hoteit, Ihab Sraj, Olivier P. Le Ma\\^itre, Omar M. Knio","cross_cats":["cs.NA","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T11:52:42Z","title":"Coordinate Transformation and Polynomial Chaos for the Bayesian Inference of a Gaussian Process with Parametrized Prior Covariance Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03323","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:b29538e11bda52986c9dc8d045d73644ad90dd59feac3d6a6c3fcb5e6e36db58","target":"record","created_at":"2026-06-04T17:08:59Z","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":"cde47a16332a1e1c0240b875020c84c23b5981b62d42a082c19ed8f522a61ae8","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T11:52:42Z","title_canon_sha256":"1a76ae8395002f75f515864d73266c8c8035c183069f13dec67b421e073e46bf"},"schema_version":"1.0","source":{"id":"1501.03323","kind":"arxiv","version":2}},"canonical_sha256":"2c4a9c36cefea83df6625a3c5562bf7c3b87ed3180236bbbeb71a5d157ffcfec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c4a9c36cefea83df6625a3c5562bf7c3b87ed3180236bbbeb71a5d157ffcfec","first_computed_at":"2026-06-04T17:08:59.154677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T17:08:59.154677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mo790PQNct+NJcLrjVX6VmoBSta8F3WldpjD7jBBRuODnxzrFT8E+stRbGMx2oXAIiL2Mv+xxUWXCwlffYzKCg==","signature_status":"signed_v1","signed_at":"2026-06-04T17:08:59.155180Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03323","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b29538e11bda52986c9dc8d045d73644ad90dd59feac3d6a6c3fcb5e6e36db58","sha256:5d933f4d6ffed9485d7bbb84a49f831f83f03f7d4f1f2ff11c5be7c95cc02e2c"],"state_sha256":"03f63c053e114af282237b1b5754e38fcbc4be04d8e97eaab0d7d03dd35f5c93"}