{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3JGJFK4ZDRAKCMLGAXRH6434LG","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":"78e9ac1a5ab86002254e50bfa859072b495a667fb76b29d2c613f19d5d671fe1","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-07T22:01:37Z","title_canon_sha256":"a013388338cd459d8b921b1f256d7a05e8fd741e3995a46394784f933b1d49ef"},"schema_version":"1.0","source":{"id":"2607.06832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06832","created_at":"2026-07-09T00:19:30Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06832v1","created_at":"2026-07-09T00:19:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06832","created_at":"2026-07-09T00:19:30Z"},{"alias_kind":"pith_short_12","alias_value":"3JGJFK4ZDRAK","created_at":"2026-07-09T00:19:30Z"},{"alias_kind":"pith_short_16","alias_value":"3JGJFK4ZDRAKCMLG","created_at":"2026-07-09T00:19:30Z"},{"alias_kind":"pith_short_8","alias_value":"3JGJFK4Z","created_at":"2026-07-09T00:19:30Z"}],"graph_snapshots":[{"event_id":"sha256:330e4ab6fb52eb4f59a711dc15fb5c2f9adc65e00755caf90ff02d8c9ec72b54","target":"graph","created_at":"2026-07-09T00:19:30Z","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/2607.06832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Simulation experiments, multi-fidelity computer models and monitoring networks often produce several related outputs observed at different input locations, a sampling pattern known as heterotopic. Whether a joint multivariate kriging metamodel then predicts better than separate univariate metamodels has remained unresolved: careful simulation comparisons on common designs report little or no benefit from multivariate kriging, yet the multi-fidelity and geostatistical literatures are built on the premise that auxiliary outputs help. We show that, for separable multi-output Gaussian processes, t","authors_text":"Jun Fan, Kuo Wang, Zexun Chen","cross_cats":["stat.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-07T22:01:37Z","title":"When is multivariate kriging worthwhile? A design-geometry analysis of heterotopic multi-output Gaussian processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06832","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":"sha256:58ba5b77a51800433e9010604ec2be890efdaa51c04f96e8822a05aaef9a81fe","target":"record","created_at":"2026-07-09T00:19:30Z","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":"78e9ac1a5ab86002254e50bfa859072b495a667fb76b29d2c613f19d5d671fe1","cross_cats_sorted":["stat.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-07T22:01:37Z","title_canon_sha256":"a013388338cd459d8b921b1f256d7a05e8fd741e3995a46394784f933b1d49ef"},"schema_version":"1.0","source":{"id":"2607.06832","kind":"arxiv","version":1}},"canonical_sha256":"da4c92ab991c40a1316605e27f737c598e08ce6d3e4ac8c89a2b4d89e9993d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da4c92ab991c40a1316605e27f737c598e08ce6d3e4ac8c89a2b4d89e9993d68","first_computed_at":"2026-07-09T00:19:30.069380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T00:19:30.069380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jZXDKRxUDiO4eFpx1Es+neiLqf5r6HFpNmKWX09iKJeLw0YWzx1J/RWIgkPYaZWm5qC+Z4p+AwUPhDmDw4UwDA==","signature_status":"signed_v1","signed_at":"2026-07-09T00:19:30.070240Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58ba5b77a51800433e9010604ec2be890efdaa51c04f96e8822a05aaef9a81fe","sha256:330e4ab6fb52eb4f59a711dc15fb5c2f9adc65e00755caf90ff02d8c9ec72b54"],"state_sha256":"dfb26c7c927fac34d906709b8eecab61e165acc98ece371c7a04857b1c4a1559"}