{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XSMQPJ7H4CSX6XYW2W3KDUJHEM","short_pith_number":"pith:XSMQPJ7H","canonical_record":{"source":{"id":"2004.12654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-27T09:05:37Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"81043de56d8b7fdd9b54e4d3c1d23dce4c7d553e1bd9b4c8bde3e8ad53a998d2","abstract_canon_sha256":"0102dec7ab0069755a5c732a877bf33f8e98d79cf23f396f7403f54bdc2d9238"},"schema_version":"1.0"},"canonical_sha256":"bc9907a7e7e0a57f5f16d5b6a1d12723328313c7a0bd6ea6688c965bd0320429","source":{"kind":"arxiv","id":"2004.12654","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.12654","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"2004.12654v2","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.12654","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"XSMQPJ7H4CSX","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"XSMQPJ7H4CSX6XYW","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"XSMQPJ7H","created_at":"2026-07-05T02:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XSMQPJ7H4CSX6XYW2W3KDUJHEM","target":"record","payload":{"canonical_record":{"source":{"id":"2004.12654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-27T09:05:37Z","cross_cats_sorted":["cs.NA","math.FA"],"title_canon_sha256":"81043de56d8b7fdd9b54e4d3c1d23dce4c7d553e1bd9b4c8bde3e8ad53a998d2","abstract_canon_sha256":"0102dec7ab0069755a5c732a877bf33f8e98d79cf23f396f7403f54bdc2d9238"},"schema_version":"1.0"},"canonical_sha256":"bc9907a7e7e0a57f5f16d5b6a1d12723328313c7a0bd6ea6688c965bd0320429","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:28:16.572767Z","signature_b64":"GIa1S1pzFcgXl/7Q5HTlQRQDdI+ee+jC2xSIIoyvAeCHuGvgpd//GEWIBK4Oap6RsA93MZr4Qb/ygO3kEEnoAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc9907a7e7e0a57f5f16d5b6a1d12723328313c7a0bd6ea6688c965bd0320429","last_reissued_at":"2026-07-05T02:28:16.572237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:28:16.572237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.12654","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":"2026-07-05T02:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IKi67QqENvh10mA+pUqyXow4ykApWxpzs74jAhut3J98GloE4FGksZAzF76J2l4Z0It7YUYtGnnR8rYFHo0XCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:26:39.936011Z"},"content_sha256":"66edf9943043de412d29002e75a2904e953d9ba07e74752901f4edb5f1465337","schema_version":"1.0","event_id":"sha256:66edf9943043de412d29002e75a2904e953d9ba07e74752901f4edb5f1465337"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XSMQPJ7H4CSX6XYW2W3KDUJHEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integration in reproducing kernel Hilbert spaces of Gaussian kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.FA"],"primary_cat":"math.NA","authors_text":"Chris J. Oates, Mark Girolami, Toni Karvonen","submitted_at":"2020-04-27T09:05:37Z","abstract_excerpt":"The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm for efficient numerical integration of functions reproduced by Gaussian kernels has not been fully solved. In this article we construct two classes of algorithms that use $N$ evaluations to integrate $d$-variate functions reproduced by Gaussian kernels and prove the exponential or super-algebraic decay of their worst-case errors. In contrast to earli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.12654","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/2004.12654/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":"2026-07-05T02:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3VfdJ3WT9KXuEnq1HIiDsahKXcgXjQZcf7S97xTT1HFEXA+KXPsN1xOloeaAXhOhzYbXeQ/z5FJtcv0cPYv/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:26:39.937084Z"},"content_sha256":"806098c648782a51ce99c4e56ee7117be86ea8dac9317db6cfcfb35616421ae7","schema_version":"1.0","event_id":"sha256:806098c648782a51ce99c4e56ee7117be86ea8dac9317db6cfcfb35616421ae7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/bundle.json","state_url":"https://pith.science/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/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":"2026-08-07T09:26:39Z","links":{"resolver":"https://pith.science/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM","bundle":"https://pith.science/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/bundle.json","state":"https://pith.science/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSMQPJ7H4CSX6XYW2W3KDUJHEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XSMQPJ7H4CSX6XYW2W3KDUJHEM","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":"0102dec7ab0069755a5c732a877bf33f8e98d79cf23f396f7403f54bdc2d9238","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-27T09:05:37Z","title_canon_sha256":"81043de56d8b7fdd9b54e4d3c1d23dce4c7d553e1bd9b4c8bde3e8ad53a998d2"},"schema_version":"1.0","source":{"id":"2004.12654","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.12654","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"2004.12654v2","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.12654","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"XSMQPJ7H4CSX","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"XSMQPJ7H4CSX6XYW","created_at":"2026-07-05T02:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"XSMQPJ7H","created_at":"2026-07-05T02:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:806098c648782a51ce99c4e56ee7117be86ea8dac9317db6cfcfb35616421ae7","target":"graph","created_at":"2026-07-05T02:28:16Z","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/2004.12654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm for efficient numerical integration of functions reproduced by Gaussian kernels has not been fully solved. In this article we construct two classes of algorithms that use $N$ evaluations to integrate $d$-variate functions reproduced by Gaussian kernels and prove the exponential or super-algebraic decay of their worst-case errors. In contrast to earli","authors_text":"Chris J. Oates, Mark Girolami, Toni Karvonen","cross_cats":["cs.NA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-27T09:05:37Z","title":"Integration in reproducing kernel Hilbert spaces of Gaussian kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.12654","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":"sha256:66edf9943043de412d29002e75a2904e953d9ba07e74752901f4edb5f1465337","target":"record","created_at":"2026-07-05T02:28:16Z","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":"0102dec7ab0069755a5c732a877bf33f8e98d79cf23f396f7403f54bdc2d9238","cross_cats_sorted":["cs.NA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-04-27T09:05:37Z","title_canon_sha256":"81043de56d8b7fdd9b54e4d3c1d23dce4c7d553e1bd9b4c8bde3e8ad53a998d2"},"schema_version":"1.0","source":{"id":"2004.12654","kind":"arxiv","version":2}},"canonical_sha256":"bc9907a7e7e0a57f5f16d5b6a1d12723328313c7a0bd6ea6688c965bd0320429","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc9907a7e7e0a57f5f16d5b6a1d12723328313c7a0bd6ea6688c965bd0320429","first_computed_at":"2026-07-05T02:28:16.572237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:28:16.572237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GIa1S1pzFcgXl/7Q5HTlQRQDdI+ee+jC2xSIIoyvAeCHuGvgpd//GEWIBK4Oap6RsA93MZr4Qb/ygO3kEEnoAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:28:16.572767Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.12654","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66edf9943043de412d29002e75a2904e953d9ba07e74752901f4edb5f1465337","sha256:806098c648782a51ce99c4e56ee7117be86ea8dac9317db6cfcfb35616421ae7"],"state_sha256":"7b510be1f79bf969ac8e3c227c3d5d3f7b556bd5ec84f096d754afa9a5d3b490"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ascv5C2uARUHXesHjRoMM939X8kfsUk2ys3TxCmh4zdB5dEFw/xyGTn9oDVnj5PZqrwDFYWNcjNxqayH40BFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T09:26:39.953985Z","bundle_sha256":"69e2684a7435105a32632bee3b4f2a5b5686311e86b5e698ec903b3d3403258e"}}