{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZNHCQ25OSQWHUET475HRWZ27UW","short_pith_number":"pith:ZNHCQ25O","canonical_record":{"source":{"id":"1609.07444","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-23T17:39:36Z","cross_cats_sorted":["cs.NA","stat.CO"],"title_canon_sha256":"a0674055ee5316f7376e0c8620d60921115ddfa515cc931e7da493e28f54739a","abstract_canon_sha256":"e531cbf4c923498c0691cb49fb49deb722139196843ef39f36c0c6ae03b0086d"},"schema_version":"1.0"},"canonical_sha256":"cb4e286bae942c7a127cff4f1b675fa5afbf1a922e8dc36d5a0b30f59f34887b","source":{"kind":"arxiv","id":"1609.07444","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07444","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07444v3","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07444","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZNHCQ25OSQWH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZNHCQ25OSQWHUET4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZNHCQ25O","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZNHCQ25OSQWHUET475HRWZ27UW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07444","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-23T17:39:36Z","cross_cats_sorted":["cs.NA","stat.CO"],"title_canon_sha256":"a0674055ee5316f7376e0c8620d60921115ddfa515cc931e7da493e28f54739a","abstract_canon_sha256":"e531cbf4c923498c0691cb49fb49deb722139196843ef39f36c0c6ae03b0086d"},"schema_version":"1.0"},"canonical_sha256":"cb4e286bae942c7a127cff4f1b675fa5afbf1a922e8dc36d5a0b30f59f34887b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:31.728727Z","signature_b64":"O6Gd3wnfqKE9a/T2vqlThea6dNEdEwjhMmEBtOPcgMyo2zLttmDOFhYS/wVNN9uNmJgV7oXncT0SWYMoAJv5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb4e286bae942c7a127cff4f1b675fa5afbf1a922e8dc36d5a0b30f59f34887b","last_reissued_at":"2026-05-18T00:46:31.728145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:31.728145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07444","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6cqa6PPZBWu4c2tMDCBrf1GKuq25AGBE60wOOI6e2du/U3e4DOloOKBq9vFM7o4xCI4kbI34VUGGup1q2x8mDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:55:24.979728Z"},"content_sha256":"8b976d7e1f78b4679d48d1ac2321be46126acfb0291e8a110b80f06d6e9e14d9","schema_version":"1.0","event_id":"sha256:8b976d7e1f78b4679d48d1ac2321be46126acfb0291e8a110b80f06d6e9e14d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZNHCQ25OSQWHUET475HRWZ27UW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-Monte Carlo for an Integrand with a Singularity along a Diagonal in the Square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","stat.CO"],"primary_cat":"math.NA","authors_text":"Art B. Owen, Kinjal Basu","submitted_at":"2016-09-23T17:39:36Z","abstract_excerpt":"Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube $[0,1]^d$ or at isolated possibly unknown points within $[0,1]^d$. Here we consider functions on the square $[0,1]^2$ that may become singular as the point approaches the diagonal line $x_1=x_2$, and we study three quadrature methods. The first method splits the square into two triangles separated by a region around the line of singularity, and applies recently developed triangle QMC rul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07444","kind":"arxiv","version":3},"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":"2026-05-18T00:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ap2aR1WF1yC0+sXnhbkHsIktxNU/NA9rZLlAKc0Ko37HkANIATuGbxXmj9I0cUDz7OOWTUr3B9jWlENo/RPnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:55:24.980068Z"},"content_sha256":"dd0e8a5f48a1d296938b791e8899f20e3dcc12e287080897f85154157f8c17ff","schema_version":"1.0","event_id":"sha256:dd0e8a5f48a1d296938b791e8899f20e3dcc12e287080897f85154157f8c17ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNHCQ25OSQWHUET475HRWZ27UW/bundle.json","state_url":"https://pith.science/pith/ZNHCQ25OSQWHUET475HRWZ27UW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNHCQ25OSQWHUET475HRWZ27UW/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":"2026-06-04T03:55:24Z","links":{"resolver":"https://pith.science/pith/ZNHCQ25OSQWHUET475HRWZ27UW","bundle":"https://pith.science/pith/ZNHCQ25OSQWHUET475HRWZ27UW/bundle.json","state":"https://pith.science/pith/ZNHCQ25OSQWHUET475HRWZ27UW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNHCQ25OSQWHUET475HRWZ27UW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZNHCQ25OSQWHUET475HRWZ27UW","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":"e531cbf4c923498c0691cb49fb49deb722139196843ef39f36c0c6ae03b0086d","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-23T17:39:36Z","title_canon_sha256":"a0674055ee5316f7376e0c8620d60921115ddfa515cc931e7da493e28f54739a"},"schema_version":"1.0","source":{"id":"1609.07444","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07444","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07444v3","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07444","created_at":"2026-05-18T00:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZNHCQ25OSQWH","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZNHCQ25OSQWHUET4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZNHCQ25O","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:dd0e8a5f48a1d296938b791e8899f20e3dcc12e287080897f85154157f8c17ff","target":"graph","created_at":"2026-05-18T00:46:31Z","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":"Quasi-Monte Carlo methods are designed for integrands of bounded variation, and this excludes singular integrands. Several methods are known for integrands that become singular on the boundary of the unit cube $[0,1]^d$ or at isolated possibly unknown points within $[0,1]^d$. Here we consider functions on the square $[0,1]^2$ that may become singular as the point approaches the diagonal line $x_1=x_2$, and we study three quadrature methods. The first method splits the square into two triangles separated by a region around the line of singularity, and applies recently developed triangle QMC rul","authors_text":"Art B. Owen, Kinjal Basu","cross_cats":["cs.NA","stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-23T17:39:36Z","title":"Quasi-Monte Carlo for an Integrand with a Singularity along a Diagonal in the Square"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07444","kind":"arxiv","version":3},"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":"sha256:8b976d7e1f78b4679d48d1ac2321be46126acfb0291e8a110b80f06d6e9e14d9","target":"record","created_at":"2026-05-18T00:46:31Z","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":"e531cbf4c923498c0691cb49fb49deb722139196843ef39f36c0c6ae03b0086d","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-09-23T17:39:36Z","title_canon_sha256":"a0674055ee5316f7376e0c8620d60921115ddfa515cc931e7da493e28f54739a"},"schema_version":"1.0","source":{"id":"1609.07444","kind":"arxiv","version":3}},"canonical_sha256":"cb4e286bae942c7a127cff4f1b675fa5afbf1a922e8dc36d5a0b30f59f34887b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb4e286bae942c7a127cff4f1b675fa5afbf1a922e8dc36d5a0b30f59f34887b","first_computed_at":"2026-05-18T00:46:31.728145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:31.728145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O6Gd3wnfqKE9a/T2vqlThea6dNEdEwjhMmEBtOPcgMyo2zLttmDOFhYS/wVNN9uNmJgV7oXncT0SWYMoAJv5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:31.728727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07444","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b976d7e1f78b4679d48d1ac2321be46126acfb0291e8a110b80f06d6e9e14d9","sha256:dd0e8a5f48a1d296938b791e8899f20e3dcc12e287080897f85154157f8c17ff"],"state_sha256":"8b277513344a4a32ea13632938e6ee02d9c933ae316f4fbf3bd7909d39e38349"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrXjioXftGpxsG5lseqO8J0IBQyZr4JroojJRp1HujHi5Un99dPCK+/RsR/dht9b3ea8iF7dpRgmKx1jCE5RDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:55:24.982088Z","bundle_sha256":"a96950d7f1c552ee45bd55b760533c02aa148e9acc0c1a31aa6a62f83db06406"}}