{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JLQMCFRUFSLYX726KKRFRJXREM","short_pith_number":"pith:JLQMCFRU","canonical_record":{"source":{"id":"1501.03296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T09:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"ef5a12c872a05c7f20ff195a4d118d73ccb7f19694e3697d0239bc77e7ac686d","abstract_canon_sha256":"b15640948dc2bd7b6ee2d966227f148de0d50819ebe523a9ef504fe9ec115996"},"schema_version":"1.0"},"canonical_sha256":"4ae0c116342c978bff5e52a258a6f12328287f695bfc0ba0b789bf1007fe463e","source":{"kind":"arxiv","id":"1501.03296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03296","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03296v1","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03296","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"JLQMCFRUFSLY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JLQMCFRUFSLYX726","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JLQMCFRU","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JLQMCFRUFSLYX726KKRFRJXREM","target":"record","payload":{"canonical_record":{"source":{"id":"1501.03296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T09:55:43Z","cross_cats_sorted":[],"title_canon_sha256":"ef5a12c872a05c7f20ff195a4d118d73ccb7f19694e3697d0239bc77e7ac686d","abstract_canon_sha256":"b15640948dc2bd7b6ee2d966227f148de0d50819ebe523a9ef504fe9ec115996"},"schema_version":"1.0"},"canonical_sha256":"4ae0c116342c978bff5e52a258a6f12328287f695bfc0ba0b789bf1007fe463e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:24.323850Z","signature_b64":"1uPByH5yPCNn7I0AZzZZwFy8XkUjNPErx/o7Zy9Vge/XAY82611Geoje3NtThls03pgFAhauvNRiwcvMf9pGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ae0c116342c978bff5e52a258a6f12328287f695bfc0ba0b789bf1007fe463e","last_reissued_at":"2026-05-18T02:29:24.323426Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:24.323426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.03296","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00gaYFoZ7zdrKsBjJSDLg3/FhFK5yxnQ5WsySxwfzVZMsZaU2aILDE6qdec61JxYTBHYI+fd/p7CZ3FXUwf7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:17:16.023491Z"},"content_sha256":"46531997ef1d8d63be2845858427ec391672e1c433e70f77211d75f5423f4389","schema_version":"1.0","event_id":"sha256:46531997ef1d8d63be2845858427ec391672e1c433e70f77211d75f5423f4389"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JLQMCFRUFSLYX726KKRFRJXREM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Emmanuil H. Georgoulis, Fuat Usta, Jeremy Levesley, Zhaonan Dong","submitted_at":"2015-01-14T09:55:43Z","abstract_excerpt":"A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional integrals. The algorithm is based on the recent Multilevel Sparse Kernel-based Interpolation (MLSKI) method (Georgoulis, Levesley \\& Subhan, \\emph{SIAM J. Sci. Comput.}, 35(2), pp.~A815--A831, 2013), with particular focus on the fast implementation of Gaussian-based MLSKI for interpolation and integration problems of high-dimen-sional functions $f:[0,1]^d\\to\\mathbb{R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03296","kind":"arxiv","version":1},"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":"2026-05-18T02:29:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vCJgYIGy9vi+SXiqEOvoQAYkDRFJp0VDnf00vI2CnuRqZOjO1glA3n9YzDyezDYyJSGcf4kZ0Gf2F/A7T28UCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:17:16.023830Z"},"content_sha256":"fc46f4edfd405932aefa78b84b8299d74176cf7c26983aa63241b14d56f92b11","schema_version":"1.0","event_id":"sha256:fc46f4edfd405932aefa78b84b8299d74176cf7c26983aa63241b14d56f92b11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JLQMCFRUFSLYX726KKRFRJXREM/bundle.json","state_url":"https://pith.science/pith/JLQMCFRUFSLYX726KKRFRJXREM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JLQMCFRUFSLYX726KKRFRJXREM/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":"2026-06-23T04:17:16Z","links":{"resolver":"https://pith.science/pith/JLQMCFRUFSLYX726KKRFRJXREM","bundle":"https://pith.science/pith/JLQMCFRUFSLYX726KKRFRJXREM/bundle.json","state":"https://pith.science/pith/JLQMCFRUFSLYX726KKRFRJXREM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JLQMCFRUFSLYX726KKRFRJXREM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JLQMCFRUFSLYX726KKRFRJXREM","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":"b15640948dc2bd7b6ee2d966227f148de0d50819ebe523a9ef504fe9ec115996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T09:55:43Z","title_canon_sha256":"ef5a12c872a05c7f20ff195a4d118d73ccb7f19694e3697d0239bc77e7ac686d"},"schema_version":"1.0","source":{"id":"1501.03296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.03296","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"arxiv_version","alias_value":"1501.03296v1","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03296","created_at":"2026-05-18T02:29:24Z"},{"alias_kind":"pith_short_12","alias_value":"JLQMCFRUFSLY","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JLQMCFRUFSLYX726","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JLQMCFRU","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:fc46f4edfd405932aefa78b84b8299d74176cf7c26983aa63241b14d56f92b11","target":"graph","created_at":"2026-05-18T02:29:24Z","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":"A fast multilevel algorithm based on directionally scaled tensor-product Gaussian kernels on structured sparse grids is proposed for interpolation of high-dimensional functions and for the numerical integration of high-dimensional integrals. The algorithm is based on the recent Multilevel Sparse Kernel-based Interpolation (MLSKI) method (Georgoulis, Levesley \\& Subhan, \\emph{SIAM J. Sci. Comput.}, 35(2), pp.~A815--A831, 2013), with particular focus on the fast implementation of Gaussian-based MLSKI for interpolation and integration problems of high-dimen-sional functions $f:[0,1]^d\\to\\mathbb{R","authors_text":"Emmanuil H. Georgoulis, Fuat Usta, Jeremy Levesley, Zhaonan Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T09:55:43Z","title":"Fast multilevel sparse Gaussian kernels for high-dimensional approximation and integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03296","kind":"arxiv","version":1},"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":"sha256:46531997ef1d8d63be2845858427ec391672e1c433e70f77211d75f5423f4389","target":"record","created_at":"2026-05-18T02:29:24Z","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":"b15640948dc2bd7b6ee2d966227f148de0d50819ebe523a9ef504fe9ec115996","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-14T09:55:43Z","title_canon_sha256":"ef5a12c872a05c7f20ff195a4d118d73ccb7f19694e3697d0239bc77e7ac686d"},"schema_version":"1.0","source":{"id":"1501.03296","kind":"arxiv","version":1}},"canonical_sha256":"4ae0c116342c978bff5e52a258a6f12328287f695bfc0ba0b789bf1007fe463e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ae0c116342c978bff5e52a258a6f12328287f695bfc0ba0b789bf1007fe463e","first_computed_at":"2026-05-18T02:29:24.323426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:24.323426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1uPByH5yPCNn7I0AZzZZwFy8XkUjNPErx/o7Zy9Vge/XAY82611Geoje3NtThls03pgFAhauvNRiwcvMf9pGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:24.323850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.03296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46531997ef1d8d63be2845858427ec391672e1c433e70f77211d75f5423f4389","sha256:fc46f4edfd405932aefa78b84b8299d74176cf7c26983aa63241b14d56f92b11"],"state_sha256":"2ebde1ad707fc47683667228be810bdb9b976aa56138ab54ba7f44c584206ca5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2pKFXfwtrfyBsJnD6UW2Guap4DSBQz2+RSYDItOBEWqszV8QaINnyJX9EErAqpU/v6Nddkm5631w3XJU+vaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:17:16.025778Z","bundle_sha256":"7d36882c94e0ff43ed9a9cecf87758de2046611bce4cf427b35611f7cf3c47c4"}}