{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VCVVU7UN74YSFKIOYXS443UMJI","short_pith_number":"pith:VCVVU7UN","canonical_record":{"source":{"id":"1809.09438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-25T12:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f21f802bec0060542583cd0acc1832dfe6668ca27089975cd0e76db07f1aaa7","abstract_canon_sha256":"b45a5ac1d3a32400b293c60bda3e45d79c83562658358977efee89d5cb0e2a13"},"schema_version":"1.0"},"canonical_sha256":"a8ab5a7e8dff3122a90ec5e5ce6e8c4a12711271a4eb5ab97eb3db2cdb14ba68","source":{"kind":"arxiv","id":"1809.09438","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09438","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09438v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09438","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"VCVVU7UN74YS","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VCVVU7UN74YSFKIO","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VCVVU7UN","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VCVVU7UN74YSFKIOYXS443UMJI","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09438","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-25T12:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f21f802bec0060542583cd0acc1832dfe6668ca27089975cd0e76db07f1aaa7","abstract_canon_sha256":"b45a5ac1d3a32400b293c60bda3e45d79c83562658358977efee89d5cb0e2a13"},"schema_version":"1.0"},"canonical_sha256":"a8ab5a7e8dff3122a90ec5e5ce6e8c4a12711271a4eb5ab97eb3db2cdb14ba68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:53.333892Z","signature_b64":"rUJWfWuDrwV6HexdTisYIcN/LfDanmOE23iiLxTXy5bBMgBglbs7kAZOKog39OE2tzS5qi7Ew/7WFDbXGKcKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ab5a7e8dff3122a90ec5e5ce6e8c4a12711271a4eb5ab97eb3db2cdb14ba68","last_reissued_at":"2026-05-18T00:04:53.333354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:53.333354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09438","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KCBxidlsQIGlkafZrJ08yIz2GwMv6LRFl41FjXNNdy5xTvfPUCmLAttCblNk+9jl8jelAppRu9ii7oOKFvd8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:18.815667Z"},"content_sha256":"098d96a766102a28ed9ac4a1d9ec0a7f61310ad49d2fa367bf4377a1b3f528d3","schema_version":"1.0","event_id":"sha256:098d96a766102a28ed9ac4a1d9ec0a7f61310ad49d2fa367bf4377a1b3f528d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VCVVU7UN74YSFKIOYXS443UMJI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast cubature of high dimensional biharmonic potential based on Approximate Approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Flavia Lanzara, Gunther Schmidt, Vladimir Maz'ya","submitted_at":"2018-09-25T12:47:39Z","abstract_excerpt":"We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast and effective also in very high dimensions. Numerical tests show that the formulas are accurate and provide the predicted approximation rate (O(h^8)) up to the dimension 10^7."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09438","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":"2026-05-18T00:04:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2BwzKirAQX9kJcrIIz3M7uvzF3jck4Mm1ljRvSvc3Ez2LU6k/d9Phmo15bm1HErLXTLyZKVpmbhEDKQET6MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:38:18.816005Z"},"content_sha256":"05d08e0dd5f751011fb52582e0da3fec11823e84f8e57630a96de2be3bb4a06f","schema_version":"1.0","event_id":"sha256:05d08e0dd5f751011fb52582e0da3fec11823e84f8e57630a96de2be3bb4a06f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCVVU7UN74YSFKIOYXS443UMJI/bundle.json","state_url":"https://pith.science/pith/VCVVU7UN74YSFKIOYXS443UMJI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCVVU7UN74YSFKIOYXS443UMJI/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":"2026-06-22T12:38:18Z","links":{"resolver":"https://pith.science/pith/VCVVU7UN74YSFKIOYXS443UMJI","bundle":"https://pith.science/pith/VCVVU7UN74YSFKIOYXS443UMJI/bundle.json","state":"https://pith.science/pith/VCVVU7UN74YSFKIOYXS443UMJI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCVVU7UN74YSFKIOYXS443UMJI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VCVVU7UN74YSFKIOYXS443UMJI","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":"b45a5ac1d3a32400b293c60bda3e45d79c83562658358977efee89d5cb0e2a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-25T12:47:39Z","title_canon_sha256":"1f21f802bec0060542583cd0acc1832dfe6668ca27089975cd0e76db07f1aaa7"},"schema_version":"1.0","source":{"id":"1809.09438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09438","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09438v1","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09438","created_at":"2026-05-18T00:04:53Z"},{"alias_kind":"pith_short_12","alias_value":"VCVVU7UN74YS","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VCVVU7UN74YSFKIO","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VCVVU7UN","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:05d08e0dd5f751011fb52582e0da3fec11823e84f8e57630a96de2be3bb4a06f","target":"graph","created_at":"2026-05-18T00:04:53Z","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":"We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast and effective also in very high dimensions. Numerical tests show that the formulas are accurate and provide the predicted approximation rate (O(h^8)) up to the dimension 10^7.","authors_text":"Flavia Lanzara, Gunther Schmidt, Vladimir Maz'ya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-25T12:47:39Z","title":"Fast cubature of high dimensional biharmonic potential based on Approximate Approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09438","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":"sha256:098d96a766102a28ed9ac4a1d9ec0a7f61310ad49d2fa367bf4377a1b3f528d3","target":"record","created_at":"2026-05-18T00:04:53Z","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":"b45a5ac1d3a32400b293c60bda3e45d79c83562658358977efee89d5cb0e2a13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-25T12:47:39Z","title_canon_sha256":"1f21f802bec0060542583cd0acc1832dfe6668ca27089975cd0e76db07f1aaa7"},"schema_version":"1.0","source":{"id":"1809.09438","kind":"arxiv","version":1}},"canonical_sha256":"a8ab5a7e8dff3122a90ec5e5ce6e8c4a12711271a4eb5ab97eb3db2cdb14ba68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8ab5a7e8dff3122a90ec5e5ce6e8c4a12711271a4eb5ab97eb3db2cdb14ba68","first_computed_at":"2026-05-18T00:04:53.333354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:53.333354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rUJWfWuDrwV6HexdTisYIcN/LfDanmOE23iiLxTXy5bBMgBglbs7kAZOKog39OE2tzS5qi7Ew/7WFDbXGKcKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:53.333892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:098d96a766102a28ed9ac4a1d9ec0a7f61310ad49d2fa367bf4377a1b3f528d3","sha256:05d08e0dd5f751011fb52582e0da3fec11823e84f8e57630a96de2be3bb4a06f"],"state_sha256":"9b8cc712c1a08dc118cced5539fb0cca1e7acd5465381b1d61e2194bc88373af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eO/WBzUfSu+7mX0SgZ54r1vVNBaxyriv1z6w2vQuZZxR2L9Vsc/EcI3VfGacBolkyRuRPnig0N+tzDptbzOVAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:38:18.817912Z","bundle_sha256":"7c16646f612948157624e5a4a0884f28a7e6977515397cd59fbc1906574c591c"}}