{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LLRE5DKF77V3GG473QAUUMWGQL","short_pith_number":"pith:LLRE5DKF","canonical_record":{"source":{"id":"1903.02261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-06T09:30:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"475b6400e93ef9b82d13be213507897c962a26985420f10c18d366bfaed4af9d","abstract_canon_sha256":"a7acc8f21b98c8ed9fb4adbe8200212a62ab16e82c840c6c5817cae3991f0c09"},"schema_version":"1.0"},"canonical_sha256":"5ae24e8d45ffebb31b9fdc014a32c682cc6dd4f5e301caa0e7e83f9cc83c3df0","source":{"kind":"arxiv","id":"1903.02261","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02261","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02261v2","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02261","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"LLRE5DKF77V3","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_16","alias_value":"LLRE5DKF77V3GG47","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_8","alias_value":"LLRE5DKF","created_at":"2026-06-04T20:13:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LLRE5DKF77V3GG473QAUUMWGQL","target":"record","payload":{"canonical_record":{"source":{"id":"1903.02261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-06T09:30:51Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"475b6400e93ef9b82d13be213507897c962a26985420f10c18d366bfaed4af9d","abstract_canon_sha256":"a7acc8f21b98c8ed9fb4adbe8200212a62ab16e82c840c6c5817cae3991f0c09"},"schema_version":"1.0"},"canonical_sha256":"5ae24e8d45ffebb31b9fdc014a32c682cc6dd4f5e301caa0e7e83f9cc83c3df0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T20:13:58.658452Z","signature_b64":"ArLI1CdXWz9i9gQnQkjRVgOwK8Oj4C2cRTqUo5Ey9evCeNsJym0mX0csTAbfSpUwas51naupLQjAfgoIct9XBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ae24e8d45ffebb31b9fdc014a32c682cc6dd4f5e301caa0e7e83f9cc83c3df0","last_reissued_at":"2026-06-04T20:13:58.657927Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T20:13:58.657927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.02261","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T20:13:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DfSDg4Vzw5rvZdR66UV8oAE5SZtmmjsh2yywH8hm7x6PcUxE64B+zmTIPrHW9KTR9a6GU+1aN6mbxyJWArhuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:52.898242Z"},"content_sha256":"4b6ee79b8fb50cf6eaaf1e99532329019b99f25eb388c8dcfb301c0bc6257976","schema_version":"1.0","event_id":"sha256:4b6ee79b8fb50cf6eaaf1e99532329019b99f25eb388c8dcfb301c0bc6257976"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LLRE5DKF77V3GG473QAUUMWGQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on Pairwise Negative Dependence of Randomized Rank-1 Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Marcin Wnuk, Michael Gnewuch","submitted_at":"2019-03-06T09:30:51Z","abstract_excerpt":"In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence structure of sampling schemes. The main goal of the framework is to determine conditions under which the negative dependence structure of a sampling scheme yields estimators with reduced variance compared to Monte Carlo estimators. For instance, she was able to show that in dimension d = 2 scrambled (0,m, d)-nets lead to randomized quasi-Monte Carlo estimators with variance no larger than the variance of Monte Carlo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02261","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1903.02261/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-04T20:13:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZR/H2LcsmYpgd9iiUMwO6v+TBq0GDDe4P03MJKKkPKNamnVur2jOAF0TA0MJJO92NAI5I6JFvf/pId2bU4wBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:52.898955Z"},"content_sha256":"9211590edc0964972d285b27545a17a613560b99cfdaae3e405a5bf5fbe3eddc","schema_version":"1.0","event_id":"sha256:9211590edc0964972d285b27545a17a613560b99cfdaae3e405a5bf5fbe3eddc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLRE5DKF77V3GG473QAUUMWGQL/bundle.json","state_url":"https://pith.science/pith/LLRE5DKF77V3GG473QAUUMWGQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLRE5DKF77V3GG473QAUUMWGQL/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":"2026-06-09T02:19:52Z","links":{"resolver":"https://pith.science/pith/LLRE5DKF77V3GG473QAUUMWGQL","bundle":"https://pith.science/pith/LLRE5DKF77V3GG473QAUUMWGQL/bundle.json","state":"https://pith.science/pith/LLRE5DKF77V3GG473QAUUMWGQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLRE5DKF77V3GG473QAUUMWGQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LLRE5DKF77V3GG473QAUUMWGQL","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":"a7acc8f21b98c8ed9fb4adbe8200212a62ab16e82c840c6c5817cae3991f0c09","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-06T09:30:51Z","title_canon_sha256":"475b6400e93ef9b82d13be213507897c962a26985420f10c18d366bfaed4af9d"},"schema_version":"1.0","source":{"id":"1903.02261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.02261","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"arxiv_version","alias_value":"1903.02261v2","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02261","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_12","alias_value":"LLRE5DKF77V3","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_16","alias_value":"LLRE5DKF77V3GG47","created_at":"2026-06-04T20:13:58Z"},{"alias_kind":"pith_short_8","alias_value":"LLRE5DKF","created_at":"2026-06-04T20:13:58Z"}],"graph_snapshots":[{"event_id":"sha256:9211590edc0964972d285b27545a17a613560b99cfdaae3e405a5bf5fbe3eddc","target":"graph","created_at":"2026-06-04T20:13:58Z","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/1903.02261/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence structure of sampling schemes. The main goal of the framework is to determine conditions under which the negative dependence structure of a sampling scheme yields estimators with reduced variance compared to Monte Carlo estimators. For instance, she was able to show that in dimension d = 2 scrambled (0,m, d)-nets lead to randomized quasi-Monte Carlo estimators with variance no larger than the variance of Monte Carlo","authors_text":"Marcin Wnuk, Michael Gnewuch","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-06T09:30:51Z","title":"Note on Pairwise Negative Dependence of Randomized Rank-1 Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02261","kind":"arxiv","version":2},"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":"sha256:4b6ee79b8fb50cf6eaaf1e99532329019b99f25eb388c8dcfb301c0bc6257976","target":"record","created_at":"2026-06-04T20:13:58Z","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":"a7acc8f21b98c8ed9fb4adbe8200212a62ab16e82c840c6c5817cae3991f0c09","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-06T09:30:51Z","title_canon_sha256":"475b6400e93ef9b82d13be213507897c962a26985420f10c18d366bfaed4af9d"},"schema_version":"1.0","source":{"id":"1903.02261","kind":"arxiv","version":2}},"canonical_sha256":"5ae24e8d45ffebb31b9fdc014a32c682cc6dd4f5e301caa0e7e83f9cc83c3df0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ae24e8d45ffebb31b9fdc014a32c682cc6dd4f5e301caa0e7e83f9cc83c3df0","first_computed_at":"2026-06-04T20:13:58.657927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T20:13:58.657927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ArLI1CdXWz9i9gQnQkjRVgOwK8Oj4C2cRTqUo5Ey9evCeNsJym0mX0csTAbfSpUwas51naupLQjAfgoIct9XBQ==","signature_status":"signed_v1","signed_at":"2026-06-04T20:13:58.658452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.02261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b6ee79b8fb50cf6eaaf1e99532329019b99f25eb388c8dcfb301c0bc6257976","sha256:9211590edc0964972d285b27545a17a613560b99cfdaae3e405a5bf5fbe3eddc"],"state_sha256":"3f5e9ce907317400b7c451d223dd5ded674c56f3caf96fe98486bfe4d19f03e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OGrea3TX1li2C/b8MWc6qFIa6sj1rak6F6pBOnwtatVaEgv523wawBZvf2uE0FjvDuRYZ2UQcyhSKo/vqfrTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:19:52.902889Z","bundle_sha256":"5875b1dbcfb2203754d9d0a06aef9452774168ee8f2dd4aa18b5b146908a617f"}}