{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KVSY6ML7SZWVFBRTZPB2LKKUTU","short_pith_number":"pith:KVSY6ML7","canonical_record":{"source":{"id":"1804.03801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T03:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"9e0afa43236798bfe319f7c4437313afef6927c3cf0c3c35e4dcae66d34fb949","abstract_canon_sha256":"fde1aa2142049eb1b34448565a3ddc135175414c991e22e84de15024566fa546"},"schema_version":"1.0"},"canonical_sha256":"55658f317f966d528633cbc3a5a9549d11ac00086cc290de9412433384e5700f","source":{"kind":"arxiv","id":"1804.03801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03801","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03801v1","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03801","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"KVSY6ML7SZWV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KVSY6ML7SZWVFBRT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KVSY6ML7","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KVSY6ML7SZWVFBRTZPB2LKKUTU","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T03:53:57Z","cross_cats_sorted":[],"title_canon_sha256":"9e0afa43236798bfe319f7c4437313afef6927c3cf0c3c35e4dcae66d34fb949","abstract_canon_sha256":"fde1aa2142049eb1b34448565a3ddc135175414c991e22e84de15024566fa546"},"schema_version":"1.0"},"canonical_sha256":"55658f317f966d528633cbc3a5a9549d11ac00086cc290de9412433384e5700f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:43.029678Z","signature_b64":"aHnzLkcuA4R4RnZrMw+o/udc1Br/gq7PF35XojyRDT8FHALI35oig6rQkxSUKLK4n806l5PYuZGSnVlEQxVeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55658f317f966d528633cbc3a5a9549d11ac00086cc290de9412433384e5700f","last_reissued_at":"2026-05-18T00:18:43.029191Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:43.029191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03801","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":"2026-05-18T00:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z4f1vR9VfuQuVyguPB6g3tMsSgT8UafrIFfWgbzEaeAfRFQY4nvy8ss+RX+gDuB4aF4AYjqRjDqqDr1+BZOvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:09:12.166225Z"},"content_sha256":"d3bad980ea2bd1664c9cc8bd43c6fbebe022c9fb3a550fea1edefc0228ab1644","schema_version":"1.0","event_id":"sha256:d3bad980ea2bd1664c9cc8bd43c6fbebe022c9fb3a550fea1edefc0228ab1644"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KVSY6ML7SZWVFBRTZPB2LKKUTU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Integrals Involved the Gaussian Function with a Small Standard Deviation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Yuesheng Xu, Yunyun Ma","submitted_at":"2018-04-11T03:53:57Z","abstract_excerpt":"We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to the integral normally lead to poor accuracy due to the rapid change in high order derivatives of its integrand when the standard deviation is small. The proposed quadrature schemes are based on graded meshes designed according to the standard deviation so that the quadrature errors on the resulting subintervals are approximately equal. The integral in each su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03801","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":"2026-05-18T00:18:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2lwjqr0EzOxsNhBVgNai6dx0F3cvwmdi/+S34HvyAjK3xbt58GTk8Ohq86zLuo2n12aDFLGmDE+TkhOfpROBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:09:12.166586Z"},"content_sha256":"54cfc871ab173014ad0feb5b6680581bb080cc14be36710a442cba739627b371","schema_version":"1.0","event_id":"sha256:54cfc871ab173014ad0feb5b6680581bb080cc14be36710a442cba739627b371"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/bundle.json","state_url":"https://pith.science/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/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":"2026-06-02T23:09:12Z","links":{"resolver":"https://pith.science/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU","bundle":"https://pith.science/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/bundle.json","state":"https://pith.science/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KVSY6ML7SZWVFBRTZPB2LKKUTU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KVSY6ML7SZWVFBRTZPB2LKKUTU","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":"fde1aa2142049eb1b34448565a3ddc135175414c991e22e84de15024566fa546","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T03:53:57Z","title_canon_sha256":"9e0afa43236798bfe319f7c4437313afef6927c3cf0c3c35e4dcae66d34fb949"},"schema_version":"1.0","source":{"id":"1804.03801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03801","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03801v1","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03801","created_at":"2026-05-18T00:18:43Z"},{"alias_kind":"pith_short_12","alias_value":"KVSY6ML7SZWV","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KVSY6ML7SZWVFBRT","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KVSY6ML7","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:54cfc871ab173014ad0feb5b6680581bb080cc14be36710a442cba739627b371","target":"graph","created_at":"2026-05-18T00:18:43Z","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 develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to the integral normally lead to poor accuracy due to the rapid change in high order derivatives of its integrand when the standard deviation is small. The proposed quadrature schemes are based on graded meshes designed according to the standard deviation so that the quadrature errors on the resulting subintervals are approximately equal. The integral in each su","authors_text":"Yuesheng Xu, Yunyun Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T03:53:57Z","title":"Computing Integrals Involved the Gaussian Function with a Small Standard Deviation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03801","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:d3bad980ea2bd1664c9cc8bd43c6fbebe022c9fb3a550fea1edefc0228ab1644","target":"record","created_at":"2026-05-18T00:18:43Z","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":"fde1aa2142049eb1b34448565a3ddc135175414c991e22e84de15024566fa546","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-04-11T03:53:57Z","title_canon_sha256":"9e0afa43236798bfe319f7c4437313afef6927c3cf0c3c35e4dcae66d34fb949"},"schema_version":"1.0","source":{"id":"1804.03801","kind":"arxiv","version":1}},"canonical_sha256":"55658f317f966d528633cbc3a5a9549d11ac00086cc290de9412433384e5700f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55658f317f966d528633cbc3a5a9549d11ac00086cc290de9412433384e5700f","first_computed_at":"2026-05-18T00:18:43.029191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:43.029191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aHnzLkcuA4R4RnZrMw+o/udc1Br/gq7PF35XojyRDT8FHALI35oig6rQkxSUKLK4n806l5PYuZGSnVlEQxVeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:43.029678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3bad980ea2bd1664c9cc8bd43c6fbebe022c9fb3a550fea1edefc0228ab1644","sha256:54cfc871ab173014ad0feb5b6680581bb080cc14be36710a442cba739627b371"],"state_sha256":"fbd9cd681f5ad53d2fc1327c655b2ae91449f2f53ea10c4755609b2a41852c79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RmV5SFB4ZxHzdNqqSEM7Xzx3FhUDSoUKNzqpOVCbkZg7O5LJH6M5ks47TmeL0Bq3b2Ym+Mm/iHkQuQfdfmKJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:09:12.168525Z","bundle_sha256":"b4a525d00da13db454c0fcc2a549fdad12f381fe19b5ff17777e7c3e0264760b"}}