{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3JGJFK4ZDRAKCMLGAXRH6434LG","short_pith_number":"pith:3JGJFK4Z","schema_version":"1.0","canonical_sha256":"da4c92ab991c40a1316605e27f737c598e08ce6d3e4ac8c89a2b4d89e9993d68","source":{"kind":"arxiv","id":"2607.06832","version":1},"attestation_state":"computed","paper":{"title":"When is multivariate kriging worthwhile? A design-geometry analysis of heterotopic multi-output Gaussian processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"stat.ME","authors_text":"Jun Fan, Kuo Wang, Zexun Chen","submitted_at":"2026-07-07T22:01:37Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.06832","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2026-07-07T22:01:37Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"a013388338cd459d8b921b1f256d7a05e8fd741e3995a46394784f933b1d49ef","abstract_canon_sha256":"78e9ac1a5ab86002254e50bfa859072b495a667fb76b29d2c613f19d5d671fe1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T00:19:30.070240Z","signature_b64":"jZXDKRxUDiO4eFpx1Es+neiLqf5r6HFpNmKWX09iKJeLw0YWzx1J/RWIgkPYaZWm5qC+Z4p+AwUPhDmDw4UwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da4c92ab991c40a1316605e27f737c598e08ce6d3e4ac8c89a2b4d89e9993d68","last_reissued_at":"2026-07-09T00:19:30.069380Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T00:19:30.069380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"When is multivariate kriging worthwhile? A design-geometry analysis of heterotopic multi-output Gaussian processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"stat.ME","authors_text":"Jun Fan, Kuo Wang, Zexun Chen","submitted_at":"2026-07-07T22:01:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06832","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06832/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.06832","created_at":"2026-07-09T00:19:30.069534+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.06832v1","created_at":"2026-07-09T00:19:30.069534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06832","created_at":"2026-07-09T00:19:30.069534+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JGJFK4ZDRAK","created_at":"2026-07-09T00:19:30.069534+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JGJFK4ZDRAKCMLG","created_at":"2026-07-09T00:19:30.069534+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JGJFK4Z","created_at":"2026-07-09T00:19:30.069534+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG","json":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG.json","graph_json":"https://pith.science/api/pith-number/3JGJFK4ZDRAKCMLGAXRH6434LG/graph.json","events_json":"https://pith.science/api/pith-number/3JGJFK4ZDRAKCMLGAXRH6434LG/events.json","paper":"https://pith.science/paper/3JGJFK4Z"},"agent_actions":{"view_html":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG","download_json":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG.json","view_paper":"https://pith.science/paper/3JGJFK4Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.06832&json=true","fetch_graph":"https://pith.science/api/pith-number/3JGJFK4ZDRAKCMLGAXRH6434LG/graph.json","fetch_events":"https://pith.science/api/pith-number/3JGJFK4ZDRAKCMLGAXRH6434LG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG/action/storage_attestation","attest_author":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG/action/author_attestation","sign_citation":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG/action/citation_signature","submit_replication":"https://pith.science/pith/3JGJFK4ZDRAKCMLGAXRH6434LG/action/replication_record"}},"created_at":"2026-07-09T00:19:30.069534+00:00","updated_at":"2026-07-09T00:19:30.069534+00:00"}