{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3UTX22KYOANP55N22MZGIMOGAA","short_pith_number":"pith:3UTX22KY","canonical_record":{"source":{"id":"1403.2649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-11T17:02:59Z","cross_cats_sorted":["cs.NA","stat.CO"],"title_canon_sha256":"b2d19236b27645e280ec87b2705545b89d75db33be8616c850bfac11c36fdeb5","abstract_canon_sha256":"45d50153e147867299f9f8b8ba2cd0c5a165d757178579d457da2ef2711212f9"},"schema_version":"1.0"},"canonical_sha256":"dd277d6958701afef5bad3326431c6003db097f9a8546d4bcf39ca0e9418e727","source":{"kind":"arxiv","id":"1403.2649","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2649","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2649v1","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2649","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"pith_short_12","alias_value":"3UTX22KYOANP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3UTX22KYOANP55N2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3UTX22KY","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3UTX22KYOANP55N22MZGIMOGAA","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-11T17:02:59Z","cross_cats_sorted":["cs.NA","stat.CO"],"title_canon_sha256":"b2d19236b27645e280ec87b2705545b89d75db33be8616c850bfac11c36fdeb5","abstract_canon_sha256":"45d50153e147867299f9f8b8ba2cd0c5a165d757178579d457da2ef2711212f9"},"schema_version":"1.0"},"canonical_sha256":"dd277d6958701afef5bad3326431c6003db097f9a8546d4bcf39ca0e9418e727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:42.883860Z","signature_b64":"yTG15pofIy++oAOq+xSMZj5se2v7m7pQiFLguCA4Hmqk9vwv6s1WvUeAabWFFjgjzmQ0p1H2uDUit4m6AyPZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd277d6958701afef5bad3326431c6003db097f9a8546d4bcf39ca0e9418e727","last_reissued_at":"2026-05-18T02:56:42.883478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:42.883478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2649","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":"2026-05-18T02:56:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fWDtqBUknaxXIvGOakGjTeQv8e++uVkt52BsxnhL1bRENIGqwGYyIaoO2DZng6aOxlOnmFbOM/48aamoQZwyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:02:17.310483Z"},"content_sha256":"f5da8fe6b4480d3f37b441ee5c3ed718bf55f6f3f8d2f93331f0f1a89ca3d1a3","schema_version":"1.0","event_id":"sha256:f5da8fe6b4480d3f37b441ee5c3ed718bf55f6f3f8d2f93331f0f1a89ca3d1a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3UTX22KYOANP55N22MZGIMOGAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Low discrepancy constructions in the triangle","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":"2014-03-11T17:02:59Z","abstract_excerpt":"Most quasi-Monte Carlo research focuses on sampling from the unit cube. Many problems, especially in computer graphics, are defined via quadrature over the unit triangle. Quasi-Monte Carlo methods for the triangle have been developed by Pillands and Cools (2005) and by Brandolini et al. (2013). This paper presents two QMC constructions in the triangle with a vanishing discrepancy. The first is a version of the van der Corput sequence customized to the unit triangle. It is an extensible digital construction that attains a discrepancy below 12/sqrt(N). The second construction rotates an integer "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2649","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":"2026-05-18T02:56:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IGAEOzHadvx3fFvTOOnAtyf99O42b5+ZlLyBa/137DOQzFHvKcUjOWbfA97Bo+fsCOpxKydR71ob3uhbHuNYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T02:02:17.310834Z"},"content_sha256":"928a28058202e37438f9f0a4e4eaa7ab5748fca40deac1b9fdf5de9671217783","schema_version":"1.0","event_id":"sha256:928a28058202e37438f9f0a4e4eaa7ab5748fca40deac1b9fdf5de9671217783"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UTX22KYOANP55N22MZGIMOGAA/bundle.json","state_url":"https://pith.science/pith/3UTX22KYOANP55N22MZGIMOGAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UTX22KYOANP55N22MZGIMOGAA/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":"2026-06-22T02:02:17Z","links":{"resolver":"https://pith.science/pith/3UTX22KYOANP55N22MZGIMOGAA","bundle":"https://pith.science/pith/3UTX22KYOANP55N22MZGIMOGAA/bundle.json","state":"https://pith.science/pith/3UTX22KYOANP55N22MZGIMOGAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UTX22KYOANP55N22MZGIMOGAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3UTX22KYOANP55N22MZGIMOGAA","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":"45d50153e147867299f9f8b8ba2cd0c5a165d757178579d457da2ef2711212f9","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-11T17:02:59Z","title_canon_sha256":"b2d19236b27645e280ec87b2705545b89d75db33be8616c850bfac11c36fdeb5"},"schema_version":"1.0","source":{"id":"1403.2649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2649","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2649v1","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2649","created_at":"2026-05-18T02:56:42Z"},{"alias_kind":"pith_short_12","alias_value":"3UTX22KYOANP","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3UTX22KYOANP55N2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3UTX22KY","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:928a28058202e37438f9f0a4e4eaa7ab5748fca40deac1b9fdf5de9671217783","target":"graph","created_at":"2026-05-18T02:56:42Z","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":"Most quasi-Monte Carlo research focuses on sampling from the unit cube. Many problems, especially in computer graphics, are defined via quadrature over the unit triangle. Quasi-Monte Carlo methods for the triangle have been developed by Pillands and Cools (2005) and by Brandolini et al. (2013). This paper presents two QMC constructions in the triangle with a vanishing discrepancy. The first is a version of the van der Corput sequence customized to the unit triangle. It is an extensible digital construction that attains a discrepancy below 12/sqrt(N). The second construction rotates an integer ","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":"2014-03-11T17:02:59Z","title":"Low discrepancy constructions in the triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2649","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:f5da8fe6b4480d3f37b441ee5c3ed718bf55f6f3f8d2f93331f0f1a89ca3d1a3","target":"record","created_at":"2026-05-18T02:56:42Z","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":"45d50153e147867299f9f8b8ba2cd0c5a165d757178579d457da2ef2711212f9","cross_cats_sorted":["cs.NA","stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-03-11T17:02:59Z","title_canon_sha256":"b2d19236b27645e280ec87b2705545b89d75db33be8616c850bfac11c36fdeb5"},"schema_version":"1.0","source":{"id":"1403.2649","kind":"arxiv","version":1}},"canonical_sha256":"dd277d6958701afef5bad3326431c6003db097f9a8546d4bcf39ca0e9418e727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd277d6958701afef5bad3326431c6003db097f9a8546d4bcf39ca0e9418e727","first_computed_at":"2026-05-18T02:56:42.883478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:42.883478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yTG15pofIy++oAOq+xSMZj5se2v7m7pQiFLguCA4Hmqk9vwv6s1WvUeAabWFFjgjzmQ0p1H2uDUit4m6AyPZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:42.883860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5da8fe6b4480d3f37b441ee5c3ed718bf55f6f3f8d2f93331f0f1a89ca3d1a3","sha256:928a28058202e37438f9f0a4e4eaa7ab5748fca40deac1b9fdf5de9671217783"],"state_sha256":"055d32f1e02fd0ab5190274f3342c29319bb3cc9d06c8d13bd1265bc5b3facb2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6ucNwU6NYIb7VgmkN/M5UKDr7h5EPVIYqloRl1CzbM9GrVJDAOa4IBxJe7zEi73riBuXGkX4CdaN8JrxO6RDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T02:02:17.312828Z","bundle_sha256":"37dec849e4541142daa0e3aa3d7deda6599f1916e7f8253290cf54b805279f86"}}