{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:24KAWR7AE22PWWPUY4WYC5DVOW","short_pith_number":"pith:24KAWR7A","canonical_record":{"source":{"id":"2401.15813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-01-29T00:27:50Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"66da6ce456a3f91e9f325869499bef9dc0b5db595d64a4c4ba428b9a8a1de256","abstract_canon_sha256":"634018dad81289e461dcce38131e476a99692d8d2c116638a5b9537f7eb6218a"},"schema_version":"1.0"},"canonical_sha256":"d7140b47e026b4fb59f4c72d817475758ebb97fbe287a5a9211d9132abe98943","source":{"kind":"arxiv","id":"2401.15813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.15813","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"2401.15813v2","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.15813","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"24KAWR7AE22P","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_16","alias_value":"24KAWR7AE22PWWPU","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_8","alias_value":"24KAWR7A","created_at":"2026-07-05T07:41:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:24KAWR7AE22PWWPUY4WYC5DVOW","target":"record","payload":{"canonical_record":{"source":{"id":"2401.15813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-01-29T00:27:50Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"66da6ce456a3f91e9f325869499bef9dc0b5db595d64a4c4ba428b9a8a1de256","abstract_canon_sha256":"634018dad81289e461dcce38131e476a99692d8d2c116638a5b9537f7eb6218a"},"schema_version":"1.0"},"canonical_sha256":"d7140b47e026b4fb59f4c72d817475758ebb97fbe287a5a9211d9132abe98943","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:41:47.427011Z","signature_b64":"nhizKSpC4hPHJ01d7JoXdQnrEkXioOjokK3Z5jUoBO8gfLx9KL50Aa5qof3iU+u60yCs7eJobqTrr5Z0J2W+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7140b47e026b4fb59f4c72d817475758ebb97fbe287a5a9211d9132abe98943","last_reissued_at":"2026-07-05T07:41:47.426428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:41:47.426428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.15813","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":"2026-07-05T07:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8TgnWAWqWDH0tykYMU5WsDPcIFZoCNvTQRDoBFSqZLaqSKRJTpEHRLCNH8j2pUxYlCbRF2rwhrJhR5MKVVECDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:56:11.393894Z"},"content_sha256":"1ff63cc39ebda14a2dbc61bbc2f957759b2791b099383e7aac8df9b4782553a2","schema_version":"1.0","event_id":"sha256:1ff63cc39ebda14a2dbc61bbc2f957759b2791b099383e7aac8df9b4782553a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:24KAWR7AE22PWWPUY4WYC5DVOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic properties of Vecchia approximation for Gaussian processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Florian Sch\\\"afer, Joseph Guinness, Matthias Katzfuss, Myeongjong Kang","submitted_at":"2024-01-29T00:27:50Z","abstract_excerpt":"Vecchia approximation has been widely used to accurately scale Gaussian-process (GP) inference to large datasets, by expressing the joint density as a product of conditional densities with small conditioning sets. We study fixed-domain asymptotic properties of Vecchia-based GP inference for a large class of covariance functions (including Mat\\'ern covariances) with boundary conditioning. In this setting, we establish that consistency and asymptotic normality of maximum exact-likelihood estimators imply those of maximum Vecchia-likelihood estimators, and that exact GP prediction can be approxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15813","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/2401.15813/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":"2026-07-05T07:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGu9MdSwML1AbVUEMmqQO/35aa2bdcjjT9VHgS3R9gw7KEaAjYlPkd3pZ+T4jFox+pKw7k0wpM6qBefPxSGVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T05:56:11.394424Z"},"content_sha256":"70caacd3652a1f5d08777efaf2d8877355155c1cd70e0d6a44e12ca515cec415","schema_version":"1.0","event_id":"sha256:70caacd3652a1f5d08777efaf2d8877355155c1cd70e0d6a44e12ca515cec415"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24KAWR7AE22PWWPUY4WYC5DVOW/bundle.json","state_url":"https://pith.science/pith/24KAWR7AE22PWWPUY4WYC5DVOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24KAWR7AE22PWWPUY4WYC5DVOW/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":"2026-08-12T05:56:11Z","links":{"resolver":"https://pith.science/pith/24KAWR7AE22PWWPUY4WYC5DVOW","bundle":"https://pith.science/pith/24KAWR7AE22PWWPUY4WYC5DVOW/bundle.json","state":"https://pith.science/pith/24KAWR7AE22PWWPUY4WYC5DVOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24KAWR7AE22PWWPUY4WYC5DVOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:24KAWR7AE22PWWPUY4WYC5DVOW","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":"634018dad81289e461dcce38131e476a99692d8d2c116638a5b9537f7eb6218a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-01-29T00:27:50Z","title_canon_sha256":"66da6ce456a3f91e9f325869499bef9dc0b5db595d64a4c4ba428b9a8a1de256"},"schema_version":"1.0","source":{"id":"2401.15813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.15813","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"2401.15813v2","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.15813","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"24KAWR7AE22P","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_16","alias_value":"24KAWR7AE22PWWPU","created_at":"2026-07-05T07:41:47Z"},{"alias_kind":"pith_short_8","alias_value":"24KAWR7A","created_at":"2026-07-05T07:41:47Z"}],"graph_snapshots":[{"event_id":"sha256:70caacd3652a1f5d08777efaf2d8877355155c1cd70e0d6a44e12ca515cec415","target":"graph","created_at":"2026-07-05T07:41:47Z","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/2401.15813/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Vecchia approximation has been widely used to accurately scale Gaussian-process (GP) inference to large datasets, by expressing the joint density as a product of conditional densities with small conditioning sets. We study fixed-domain asymptotic properties of Vecchia-based GP inference for a large class of covariance functions (including Mat\\'ern covariances) with boundary conditioning. In this setting, we establish that consistency and asymptotic normality of maximum exact-likelihood estimators imply those of maximum Vecchia-likelihood estimators, and that exact GP prediction can be approxim","authors_text":"Florian Sch\\\"afer, Joseph Guinness, Matthias Katzfuss, Myeongjong Kang","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-01-29T00:27:50Z","title":"Asymptotic properties of Vecchia approximation for Gaussian processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15813","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":"sha256:1ff63cc39ebda14a2dbc61bbc2f957759b2791b099383e7aac8df9b4782553a2","target":"record","created_at":"2026-07-05T07:41:47Z","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":"634018dad81289e461dcce38131e476a99692d8d2c116638a5b9537f7eb6218a","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2024-01-29T00:27:50Z","title_canon_sha256":"66da6ce456a3f91e9f325869499bef9dc0b5db595d64a4c4ba428b9a8a1de256"},"schema_version":"1.0","source":{"id":"2401.15813","kind":"arxiv","version":2}},"canonical_sha256":"d7140b47e026b4fb59f4c72d817475758ebb97fbe287a5a9211d9132abe98943","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d7140b47e026b4fb59f4c72d817475758ebb97fbe287a5a9211d9132abe98943","first_computed_at":"2026-07-05T07:41:47.426428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:41:47.426428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhizKSpC4hPHJ01d7JoXdQnrEkXioOjokK3Z5jUoBO8gfLx9KL50Aa5qof3iU+u60yCs7eJobqTrr5Z0J2W+DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:41:47.427011Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.15813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ff63cc39ebda14a2dbc61bbc2f957759b2791b099383e7aac8df9b4782553a2","sha256:70caacd3652a1f5d08777efaf2d8877355155c1cd70e0d6a44e12ca515cec415"],"state_sha256":"3bb8415426aa73c49f253427b5eb1449285100e3d38992d13196c4a488773bb8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZFQIXJ8N0K2bdPcioLsRFK8gYvjHRAOTinHAcoDudsbHsuXldXyVVqYqod7UN+MuYR5XzBGVxcHRmkbezLtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T05:56:11.401100Z","bundle_sha256":"ce939376416fad3c32e8c83433d0017528a25ce08ad06ce2e7c1c7bce7e904b2"}}