{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HYEU6B73ZNQF6CFISNFUL4XFL4","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":"0a6f04a6f823bb45d81359c441eb45ec51891c21a121c7a6a1cbb06201bc6e52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-09-08T18:03:12Z","title_canon_sha256":"0edcac7726a589b1f2c493c8c2ca87ecc56e006dbee187e9df4da4c290df68f4"},"schema_version":"1.0","source":{"id":"1709.04419","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04419","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04419v2","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04419","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"HYEU6B73ZNQF","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HYEU6B73ZNQF6CFI","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HYEU6B73","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:588e7f4d2d16407c3d00d3fed15387a393adb2bd5ae54cb2fc1533a0c7588f05","target":"graph","created_at":"2026-05-18T00:05:56Z","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":"We use available measurements to estimate the unknown parameters (variance, smoothness parameter, and covariance length) of a covariance function by maximizing the joint Gaussian log-likelihood function. To overcome cubic complexity in the linear algebra, we approximate the discretized covariance function in the hierarchical (H-) matrix format. The H-matrix format has a log-linear computational cost and storage $O(kn \\log n)$, where the rank $k$ is a small integer and $n$ is the number of locations. The H-matrix technique allows us to work with general covariance matrices in an efficient way, ","authors_text":"Alexander Litvinenko, David Keyes, Marc G. Genton, Ying Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-09-08T18:03:12Z","title":"Likelihood Approximation With Hierarchical Matrices For Large Spatial Datasets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04419","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:e904a84f79c737cf9e5d147f36266be264cf1ff3e8ad32f06998c831a5e73ebf","target":"record","created_at":"2026-05-18T00:05:56Z","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":"0a6f04a6f823bb45d81359c441eb45ec51891c21a121c7a6a1cbb06201bc6e52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2017-09-08T18:03:12Z","title_canon_sha256":"0edcac7726a589b1f2c493c8c2ca87ecc56e006dbee187e9df4da4c290df68f4"},"schema_version":"1.0","source":{"id":"1709.04419","kind":"arxiv","version":2}},"canonical_sha256":"3e094f07fbcb605f08a8934b45f2e55f281e85be72b4ad89868514a26989023a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e094f07fbcb605f08a8934b45f2e55f281e85be72b4ad89868514a26989023a","first_computed_at":"2026-05-18T00:05:56.614022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:56.614022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyOMNM9rrTfJyTEx2cf4TsbmAy94TtaqUf+FDFWd7mTI880TrAfz7pHwSSx2G67srjwTT+hX20JE1E4DSSmSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:56.614548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04419","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e904a84f79c737cf9e5d147f36266be264cf1ff3e8ad32f06998c831a5e73ebf","sha256:588e7f4d2d16407c3d00d3fed15387a393adb2bd5ae54cb2fc1533a0c7588f05"],"state_sha256":"f3f68383a94e660bc7061afa7a8248b19b68322b9eed8094fb30071ba2114c38"}