{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XMRIR7XJHUFCSOIXARVEYG4GGS","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":"6d32c1580af5b38ccce2adc502e75b0f89d3afbd7a2d1dd3eb52b41a5d3008ff","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-04-22T05:44:44Z","title_canon_sha256":"7f6c27f1ef6bd94c2085edc2aecddae11a8c56b51a9c766e230d529f01210c5b"},"schema_version":"1.0","source":{"id":"1504.05659","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05659","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05659v1","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05659","created_at":"2026-05-18T02:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"XMRIR7XJHUFC","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XMRIR7XJHUFCSOIX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XMRIR7XJ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:33a8999e90db3da9611476132e5a6fc92f7abf55e8cc87ca354e8c78af81d608","target":"graph","created_at":"2026-05-18T02:18:13Z","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":"The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis functions. In this research, we propose a class of basis functions extracted from thin-plate splines. These functions are ordered in terms of their degrees of smoothness with a higher-order function corresponding to larger-scale features and a lower-order one corresponding to smaller-scale details, leading to a parsimonious representation for a nonstationar","authors_text":"Hsin-Cheng Huang, ShengLi Tzeng","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-04-22T05:44:44Z","title":"Multi-Resolution Spatial Random-Effects Models for Irregularly Spaced Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05659","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":"sha256:0cb7f99c71f4cd307b78e60a2b0b5c74daa7d1127ee1e9bfd0f302b53d309be1","target":"record","created_at":"2026-05-18T02:18:13Z","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":"6d32c1580af5b38ccce2adc502e75b0f89d3afbd7a2d1dd3eb52b41a5d3008ff","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2015-04-22T05:44:44Z","title_canon_sha256":"7f6c27f1ef6bd94c2085edc2aecddae11a8c56b51a9c766e230d529f01210c5b"},"schema_version":"1.0","source":{"id":"1504.05659","kind":"arxiv","version":1}},"canonical_sha256":"bb2288fee93d0a293917046a4c1b86349574e4ea15a981477d18859912a196e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb2288fee93d0a293917046a4c1b86349574e4ea15a981477d18859912a196e9","first_computed_at":"2026-05-18T02:18:13.040019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:13.040019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pr1nNRIPdTr5ETL1B++2Tke5LBs4iqWkNaQr6FXsuZtNb3yyzqK0UbvOBaLGx1aQzkbYtcZ+tPpoYI5y6A5mCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:13.040683Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05659","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cb7f99c71f4cd307b78e60a2b0b5c74daa7d1127ee1e9bfd0f302b53d309be1","sha256:33a8999e90db3da9611476132e5a6fc92f7abf55e8cc87ca354e8c78af81d608"],"state_sha256":"b9b2f437f8cd4f2ef0c608820fd1662c70d70655e6a915ca6cbd0ba32e2a44d7"}