{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:S7WV2LZOKBUZQDEACMZKG45EOT","short_pith_number":"pith:S7WV2LZO","canonical_record":{"source":{"id":"2301.01372","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-01-03T22:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"668df219377bcebe23a8c0bfd60da034257b4169b7872074b4e6ee544144798d","abstract_canon_sha256":"e41a2a5f87b95b4a326c62e952b58796b7b84d574844b479f62eeb58a0ef48db"},"schema_version":"1.0"},"canonical_sha256":"97ed5d2f2e5069980c801332a373a474cfeaeb7735987270a6bca193ba63722f","source":{"kind":"arxiv","id":"2301.01372","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.01372","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"arxiv_version","alias_value":"2301.01372v2","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.01372","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_12","alias_value":"S7WV2LZOKBUZ","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"S7WV2LZOKBUZQDEA","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"S7WV2LZO","created_at":"2026-07-05T05:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:S7WV2LZOKBUZQDEACMZKG45EOT","target":"record","payload":{"canonical_record":{"source":{"id":"2301.01372","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-01-03T22:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"668df219377bcebe23a8c0bfd60da034257b4169b7872074b4e6ee544144798d","abstract_canon_sha256":"e41a2a5f87b95b4a326c62e952b58796b7b84d574844b479f62eeb58a0ef48db"},"schema_version":"1.0"},"canonical_sha256":"97ed5d2f2e5069980c801332a373a474cfeaeb7735987270a6bca193ba63722f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:32:33.905217Z","signature_b64":"lDHQSg3PwcPiscZD0XGHvTOPiiZMdEi/b7fza73XHIFR/tFCWGLhJ0aic6k1GK3VnM+Woo9gNfIlBWBJNDyeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97ed5d2f2e5069980c801332a373a474cfeaeb7735987270a6bca193ba63722f","last_reissued_at":"2026-07-05T05:32:33.904715Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:32:33.904715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.01372","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:32:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3j6/xPkTW+T97uB6uZHvyzgAKDUyQmxJC7YdQ6pnpRdXQVXEk3bd4+f2kE+IhOIoOCozAtQShMyK1ERhwbRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:32:41.618268Z"},"content_sha256":"d0747ed34f2ff19fa5ae2cabc6334e2cfa7ba9e285dd1922baee0b57f37ea62f","schema_version":"1.0","event_id":"sha256:d0747ed34f2ff19fa5ae2cabc6334e2cfa7ba9e285dd1922baee0b57f37ea62f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:S7WV2LZOKBUZQDEACMZKG45EOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatially Varying Anisotropy for Gaussian Random Fields in Three-Dimensional Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Geir-Arne Fuglstad, Martin Outzen Berild","submitted_at":"2023-01-03T22:02:56Z","abstract_excerpt":"Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces such as the ocean. In the ocean, the variability of the response may vary with depth, and ocean currents may lead to spatially varying anisotropy. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations (SPDEs) where computations are done using Gaussian Markov random field approximations.\n  The approach is proven in a simulation study where the amount of data required to estimate these models is explored. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.01372","kind":"arxiv","version":2},"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/2301.01372/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:32:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GCyJM9a2c69fA2bMBQdmshn4ws3DzmBA5jFvek5nJdvPNiuYvQafrMbvd0ILI2RD7EQbTKe7lIj4gCkprGFuCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T00:32:41.618810Z"},"content_sha256":"b6bccf6951955d76aa6a84ddc9ee7072481b6bf5b70f0fd8be323e69d8caab5b","schema_version":"1.0","event_id":"sha256:b6bccf6951955d76aa6a84ddc9ee7072481b6bf5b70f0fd8be323e69d8caab5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S7WV2LZOKBUZQDEACMZKG45EOT/bundle.json","state_url":"https://pith.science/pith/S7WV2LZOKBUZQDEACMZKG45EOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S7WV2LZOKBUZQDEACMZKG45EOT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-21T00:32:41Z","links":{"resolver":"https://pith.science/pith/S7WV2LZOKBUZQDEACMZKG45EOT","bundle":"https://pith.science/pith/S7WV2LZOKBUZQDEACMZKG45EOT/bundle.json","state":"https://pith.science/pith/S7WV2LZOKBUZQDEACMZKG45EOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S7WV2LZOKBUZQDEACMZKG45EOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:S7WV2LZOKBUZQDEACMZKG45EOT","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":"e41a2a5f87b95b4a326c62e952b58796b7b84d574844b479f62eeb58a0ef48db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-01-03T22:02:56Z","title_canon_sha256":"668df219377bcebe23a8c0bfd60da034257b4169b7872074b4e6ee544144798d"},"schema_version":"1.0","source":{"id":"2301.01372","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.01372","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"arxiv_version","alias_value":"2301.01372v2","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.01372","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_12","alias_value":"S7WV2LZOKBUZ","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"S7WV2LZOKBUZQDEA","created_at":"2026-07-05T05:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"S7WV2LZO","created_at":"2026-07-05T05:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:b6bccf6951955d76aa6a84ddc9ee7072481b6bf5b70f0fd8be323e69d8caab5b","target":"graph","created_at":"2026-07-05T05:32:33Z","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/2301.01372/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Isotropic covariance structures can be unreasonable for phenomena in three-dimensional spaces such as the ocean. In the ocean, the variability of the response may vary with depth, and ocean currents may lead to spatially varying anisotropy. We construct a class of non-stationary anisotropic Gaussian random fields (GRFs) in three dimensions through stochastic partial differential equations (SPDEs) where computations are done using Gaussian Markov random field approximations.\n  The approach is proven in a simulation study where the amount of data required to estimate these models is explored. Th","authors_text":"Geir-Arne Fuglstad, Martin Outzen Berild","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-01-03T22:02:56Z","title":"Spatially Varying Anisotropy for Gaussian Random Fields in Three-Dimensional Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.01372","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:d0747ed34f2ff19fa5ae2cabc6334e2cfa7ba9e285dd1922baee0b57f37ea62f","target":"record","created_at":"2026-07-05T05:32:33Z","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":"e41a2a5f87b95b4a326c62e952b58796b7b84d574844b479f62eeb58a0ef48db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2023-01-03T22:02:56Z","title_canon_sha256":"668df219377bcebe23a8c0bfd60da034257b4169b7872074b4e6ee544144798d"},"schema_version":"1.0","source":{"id":"2301.01372","kind":"arxiv","version":2}},"canonical_sha256":"97ed5d2f2e5069980c801332a373a474cfeaeb7735987270a6bca193ba63722f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97ed5d2f2e5069980c801332a373a474cfeaeb7735987270a6bca193ba63722f","first_computed_at":"2026-07-05T05:32:33.904715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:32:33.904715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lDHQSg3PwcPiscZD0XGHvTOPiiZMdEi/b7fza73XHIFR/tFCWGLhJ0aic6k1GK3VnM+Woo9gNfIlBWBJNDyeBw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:32:33.905217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.01372","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0747ed34f2ff19fa5ae2cabc6334e2cfa7ba9e285dd1922baee0b57f37ea62f","sha256:b6bccf6951955d76aa6a84ddc9ee7072481b6bf5b70f0fd8be323e69d8caab5b"],"state_sha256":"12a2b97adf742e9f498c305fb7dd7f6dc9ae6b4b35fe06aec506567a12f6eb06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5Mc27LYKzUtQPvJAXbdD2M4kfVRu29zqlSoIOImZao6s4snqvSSYVj2m1Qk55UE9vXYGjGBFsLhaOKyZWhYAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T00:32:41.624837Z","bundle_sha256":"838df37d52b627f03123c139f1d55c3ec7e30e0df3d8e309210417fc2657c863"}}