{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OXAEC5LF4PIJTD55QUYB2OOETZ","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":"bed6f0bf9533cce721550b2cd39e4cb88195306193055c901b6cfe8ef2c754bd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-30T11:54:59Z","title_canon_sha256":"26566b42aa13d8e15f5f022bbc89bf45427517220d77c961574ad962c2ff4607"},"schema_version":"1.0","source":{"id":"1701.08562","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08562","created_at":"2026-06-04T18:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08562v1","created_at":"2026-06-04T18:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08562","created_at":"2026-06-04T18:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"OXAEC5LF4PIJ","created_at":"2026-06-04T18:10:26Z"},{"alias_kind":"pith_short_16","alias_value":"OXAEC5LF4PIJTD55","created_at":"2026-06-04T18:10:26Z"},{"alias_kind":"pith_short_8","alias_value":"OXAEC5LF","created_at":"2026-06-04T18:10:26Z"}],"graph_snapshots":[{"event_id":"sha256:1808d91e4c33e27f28e3f5d9df0cc59a01dcdee94dd9fb56b58d28f4b22e3945","target":"graph","created_at":"2026-06-04T18:10:26Z","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/1701.08562/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study quasi-Monte Carlo integration for twice differentiable functions defined over a triangle. We provide an explicit construction of infinite sequences of points including one by Basu and Owen (2015) as a special case, which achieves the integration error of order $N^{-1}(\\log N)^3$ for any $N\\geq 2$. Since a lower bound of order $N^{-1}$ on the integration error holds for any linear quadrature rule, the upper bound we obtain is best possible apart from the $\\log N$ factor. The major ingredient in our proof of the upper bound is the dyadic Walsh analysis of twice differentiable functions ","authors_text":"Kosuke Suzuki, Takashi Goda, Takehito Yoshiki","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-30T11:54:59Z","title":"Quasi-Monte Carlo integration for twice differentiable functions over a triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08562","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":"sha256:97e52c55c0fddf31e5624bea0572d8f279bd92fe66b174584ed0507ce16897bc","target":"record","created_at":"2026-06-04T18:10:26Z","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":"bed6f0bf9533cce721550b2cd39e4cb88195306193055c901b6cfe8ef2c754bd","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-01-30T11:54:59Z","title_canon_sha256":"26566b42aa13d8e15f5f022bbc89bf45427517220d77c961574ad962c2ff4607"},"schema_version":"1.0","source":{"id":"1701.08562","kind":"arxiv","version":1}},"canonical_sha256":"75c0417565e3d0998fbd85301d39c49e4a600250f3a29ce870f631c66905479b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75c0417565e3d0998fbd85301d39c49e4a600250f3a29ce870f631c66905479b","first_computed_at":"2026-06-04T18:10:26.882089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:10:26.882089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"veQ2EJ9YkJjTdt0pRwf8JmmJ889OJo9tSaSlMWs5cC0q2W44pBSdZzD/H/BgwQN33DV5js+6OBTjqzlxuW1iBg==","signature_status":"signed_v1","signed_at":"2026-06-04T18:10:26.882604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08562","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97e52c55c0fddf31e5624bea0572d8f279bd92fe66b174584ed0507ce16897bc","sha256:1808d91e4c33e27f28e3f5d9df0cc59a01dcdee94dd9fb56b58d28f4b22e3945"],"state_sha256":"6f91f1c47db69e16ff4a526bd328511353a0ae96e23460bb088f59d23ba1ea55"}