{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JQ3QTRLQUFVTH7V3K2XKBU5M2U","short_pith_number":"pith:JQ3QTRLQ","canonical_record":{"source":{"id":"2312.07502","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"df458ea60ba146504f8cb81ff32c6dbcbc040d22a282fb87032b6e8f7dae081a","abstract_canon_sha256":"5ca5fbe011e593714c51f42393c7a6427e918ba97f208bd330adfff580c514bf"},"schema_version":"1.0"},"canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","source":{"kind":"arxiv","id":"2312.07502","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.07502","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"arxiv_version","alias_value":"2312.07502v3","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.07502","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_12","alias_value":"JQ3QTRLQUFVT","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_16","alias_value":"JQ3QTRLQUFVTH7V3","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_8","alias_value":"JQ3QTRLQ","created_at":"2026-07-05T11:34:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JQ3QTRLQUFVTH7V3K2XKBU5M2U","target":"record","payload":{"canonical_record":{"source":{"id":"2312.07502","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"df458ea60ba146504f8cb81ff32c6dbcbc040d22a282fb87032b6e8f7dae081a","abstract_canon_sha256":"5ca5fbe011e593714c51f42393c7a6427e918ba97f208bd330adfff580c514bf"},"schema_version":"1.0"},"canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:34:40.782235Z","signature_b64":"bFcXJ3JgHQyPSE6Fl+PGCBMfgn7K5FOLCCQ1kyEUpLGSG81BU+tMdIy2FfRVEd7kUaDsCqXKcNgQ9EqJzLxxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","last_reissued_at":"2026-07-05T11:34:40.781763Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:34:40.781763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.07502","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:34:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btg3yRd7cXE0RwnuGBCRVd9gsCMZnR3DcDHSksRsbDJDIbgwtplHpGEjpxkmysD83nH6+hczoOuNEksfvXGTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:57:18.239965Z"},"content_sha256":"21d4320c2d3407ae4a6c1ae12b1c80f052a96fd4a997be48642440c27b28f89a","schema_version":"1.0","event_id":"sha256:21d4320c2d3407ae4a6c1ae12b1c80f052a96fd4a997be48642440c27b28f89a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JQ3QTRLQUFVTH7V3K2XKBU5M2U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Posterior Concentration for Gaussian Process Priors under Rescaled and Hierarchical Mat\\'ern and Confluent Hypergeometric Covariance Functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anindya Bhadra, Xiao Fang","submitted_at":"2023-12-12T18:35:31Z","abstract_excerpt":"In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to achieve optimal or near-optimal posterior contraction rates if the smoothness of the Gaussian process matches that of the target function. Among those priors, Gaussian processes with a parametric Mat\\'ern covariance function is particularly notable in that its degree of smoothness can be determined by a dedicated smoothness parameter. \\citet{ma2022beyond} recentl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07502","kind":"arxiv","version":3},"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/2312.07502/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":"2026-07-05T11:34:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TmTyEzJZpUw860KmOBi3AccrJW0/1hFknjsx5hYgdAu1zHmdgK0D3MeZP+ySZ/FQaQuZ2LTFsImBahCsmbqgDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T00:57:18.241819Z"},"content_sha256":"e8d57f8816806746ffef2e6932455397cbc50b6192b8e992ca987a0d55df7747","schema_version":"1.0","event_id":"sha256:e8d57f8816806746ffef2e6932455397cbc50b6192b8e992ca987a0d55df7747"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/bundle.json","state_url":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/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":"2026-08-16T00:57:18Z","links":{"resolver":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U","bundle":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/bundle.json","state":"https://pith.science/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JQ3QTRLQUFVTH7V3K2XKBU5M2U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JQ3QTRLQUFVTH7V3K2XKBU5M2U","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":"5ca5fbe011e593714c51f42393c7a6427e918ba97f208bd330adfff580c514bf","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","title_canon_sha256":"df458ea60ba146504f8cb81ff32c6dbcbc040d22a282fb87032b6e8f7dae081a"},"schema_version":"1.0","source":{"id":"2312.07502","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.07502","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"arxiv_version","alias_value":"2312.07502v3","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.07502","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_12","alias_value":"JQ3QTRLQUFVT","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_16","alias_value":"JQ3QTRLQUFVTH7V3","created_at":"2026-07-05T11:34:40Z"},{"alias_kind":"pith_short_8","alias_value":"JQ3QTRLQ","created_at":"2026-07-05T11:34:40Z"}],"graph_snapshots":[{"event_id":"sha256:e8d57f8816806746ffef2e6932455397cbc50b6192b8e992ca987a0d55df7747","target":"graph","created_at":"2026-07-05T11:34:40Z","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/2312.07502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In nonparameteric Bayesian approaches, Gaussian stochastic processes can serve as priors on real-valued function spaces. Existing literature on the posterior convergence rates under Gaussian process priors shows that it is possible to achieve optimal or near-optimal posterior contraction rates if the smoothness of the Gaussian process matches that of the target function. Among those priors, Gaussian processes with a parametric Mat\\'ern covariance function is particularly notable in that its degree of smoothness can be determined by a dedicated smoothness parameter. \\citet{ma2022beyond} recentl","authors_text":"Anindya Bhadra, Xiao Fang","cross_cats":["stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","title":"Posterior Concentration for Gaussian Process Priors under Rescaled and Hierarchical Mat\\'ern and Confluent Hypergeometric Covariance Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07502","kind":"arxiv","version":3},"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":"sha256:21d4320c2d3407ae4a6c1ae12b1c80f052a96fd4a997be48642440c27b28f89a","target":"record","created_at":"2026-07-05T11:34:40Z","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":"5ca5fbe011e593714c51f42393c7a6427e918ba97f208bd330adfff580c514bf","cross_cats_sorted":["stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2023-12-12T18:35:31Z","title_canon_sha256":"df458ea60ba146504f8cb81ff32c6dbcbc040d22a282fb87032b6e8f7dae081a"},"schema_version":"1.0","source":{"id":"2312.07502","kind":"arxiv","version":3}},"canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c3709c570a16b33febb56aea0d3acd53cfbaeba93aec3989a467457d2e8cd70","first_computed_at":"2026-07-05T11:34:40.781763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:34:40.781763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bFcXJ3JgHQyPSE6Fl+PGCBMfgn7K5FOLCCQ1kyEUpLGSG81BU+tMdIy2FfRVEd7kUaDsCqXKcNgQ9EqJzLxxCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:34:40.782235Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.07502","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21d4320c2d3407ae4a6c1ae12b1c80f052a96fd4a997be48642440c27b28f89a","sha256:e8d57f8816806746ffef2e6932455397cbc50b6192b8e992ca987a0d55df7747"],"state_sha256":"7e62afe31b94c22b7b84d55ac0fb17667ade4e7dadb14d24aa14f95eb5dd8fd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JmSLe44rN+hhqtjqdvYQJFq+lAVMmiHdlc9cWDhlEBYpIv9nMn23gRI0kuP2LylD4axqpLpWb8A/GaeN2Ue0CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T00:57:18.246785Z","bundle_sha256":"7fee675ffe9f45c341a5cf4cafe84065bb6ead46dd870b233ffb69025fe2a3c8"}}