{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NRLSS5DEDTWAO5SKKV5EPP7XMT","short_pith_number":"pith:NRLSS5DE","canonical_record":{"source":{"id":"1804.03016","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-04-09T14:21:08Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"29e43f28fb18d784a89954b5437b20c55b910569a4e396a1454527b5c61daf9d","abstract_canon_sha256":"090168f61f0461ec75ca15f194c46fc1302baa055e1f2182d73eaccf9f5ebc01"},"schema_version":"1.0"},"canonical_sha256":"6c572974641cec07764a557a47bff764e1bdf602cdd3d620d2289256da275efb","source":{"kind":"arxiv","id":"1804.03016","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03016","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03016v3","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03016","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"NRLSS5DEDTWA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NRLSS5DEDTWAO5SK","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NRLSS5DE","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NRLSS5DEDTWAO5SKKV5EPP7XMT","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03016","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-04-09T14:21:08Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"29e43f28fb18d784a89954b5437b20c55b910569a4e396a1454527b5c61daf9d","abstract_canon_sha256":"090168f61f0461ec75ca15f194c46fc1302baa055e1f2182d73eaccf9f5ebc01"},"schema_version":"1.0"},"canonical_sha256":"6c572974641cec07764a557a47bff764e1bdf602cdd3d620d2289256da275efb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:41.644551Z","signature_b64":"ZBGcmlTKAHSuU3+ZaDwKdXViqU/uPt/KevND527EEL81oaTzJNRF24VVWRGqyQJkfN2RQhopEZa2c2yd9pjrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c572974641cec07764a557a47bff764e1bdf602cdd3d620d2289256da275efb","last_reissued_at":"2026-05-18T00:15:41.643979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:41.643979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03016","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":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgabonTHwLn/wTETCCh7jEi3CAtWzkhS2W1bInTScGNq9oGrwknFqLEGMSkIZhhD3pkrSEpGGi3H5B3kW1LnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:34:28.444097Z"},"content_sha256":"142b9b691edfd891885c323566c18dbdd7cfc4fe9651b65b0e464fb5ed831f8f","schema_version":"1.0","event_id":"sha256:142b9b691edfd891885c323566c18dbdd7cfc4fe9651b65b0e464fb5ed831f8f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NRLSS5DEDTWAO5SKKV5EPP7XMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Bayes-Sard Cubature Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"stat.ME","authors_text":"Chris J. Oates, Simo S\\\"arkk\\\"a, Toni Karvonen","submitted_at":"2018-04-09T14:21:08Z","abstract_excerpt":"This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03016","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":""},"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":"2026-05-18T00:15:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0AzGMgaWIilGR6z06qtdhuqHFX0t9+Uck8yI7SC5nq+uSTZWxM6wvKSk5+eAckvFQ/9/e8hXcCjoAS0Fqr2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:34:28.444467Z"},"content_sha256":"8720cb6a1667eb334609c1092dacf1c27a5b1031ce68a6d7bf930d4bef52f112","schema_version":"1.0","event_id":"sha256:8720cb6a1667eb334609c1092dacf1c27a5b1031ce68a6d7bf930d4bef52f112"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/bundle.json","state_url":"https://pith.science/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/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":"2026-05-28T14:34:28Z","links":{"resolver":"https://pith.science/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT","bundle":"https://pith.science/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/bundle.json","state":"https://pith.science/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRLSS5DEDTWAO5SKKV5EPP7XMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NRLSS5DEDTWAO5SKKV5EPP7XMT","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":"090168f61f0461ec75ca15f194c46fc1302baa055e1f2182d73eaccf9f5ebc01","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-04-09T14:21:08Z","title_canon_sha256":"29e43f28fb18d784a89954b5437b20c55b910569a4e396a1454527b5c61daf9d"},"schema_version":"1.0","source":{"id":"1804.03016","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03016","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03016v3","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03016","created_at":"2026-05-18T00:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"NRLSS5DEDTWA","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NRLSS5DEDTWAO5SK","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NRLSS5DE","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:8720cb6a1667eb334609c1092dacf1c27a5b1031ce68a6d7bf930d4bef52f112","target":"graph","created_at":"2026-05-18T00:15:41Z","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":"This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are ","authors_text":"Chris J. Oates, Simo S\\\"arkk\\\"a, Toni Karvonen","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-04-09T14:21:08Z","title":"A Bayes-Sard Cubature Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03016","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":"sha256:142b9b691edfd891885c323566c18dbdd7cfc4fe9651b65b0e464fb5ed831f8f","target":"record","created_at":"2026-05-18T00:15:41Z","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":"090168f61f0461ec75ca15f194c46fc1302baa055e1f2182d73eaccf9f5ebc01","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2018-04-09T14:21:08Z","title_canon_sha256":"29e43f28fb18d784a89954b5437b20c55b910569a4e396a1454527b5c61daf9d"},"schema_version":"1.0","source":{"id":"1804.03016","kind":"arxiv","version":3}},"canonical_sha256":"6c572974641cec07764a557a47bff764e1bdf602cdd3d620d2289256da275efb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c572974641cec07764a557a47bff764e1bdf602cdd3d620d2289256da275efb","first_computed_at":"2026-05-18T00:15:41.643979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:41.643979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZBGcmlTKAHSuU3+ZaDwKdXViqU/uPt/KevND527EEL81oaTzJNRF24VVWRGqyQJkfN2RQhopEZa2c2yd9pjrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:41.644551Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03016","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:142b9b691edfd891885c323566c18dbdd7cfc4fe9651b65b0e464fb5ed831f8f","sha256:8720cb6a1667eb334609c1092dacf1c27a5b1031ce68a6d7bf930d4bef52f112"],"state_sha256":"0e64b3b38cc1d7fa67ac1b0820c1b1fedbd12d4461ec55e9ccfd6b2ee793fef5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Db4KIt49BzaNeLVCsNozbAxH42nLgAO0Oou26VkzTkXfnEc4nwCQZvehQc17uQm6oI4CupNA4xIPft2a5CZSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:34:28.446467Z","bundle_sha256":"6d73e409279565ca9144723a742e45f5b6d0156e855602b4a794acc61deac5f1"}}