{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GOQOMKDLVGTX2XAHSZKW7BUJO7","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":"2850cc30c70f9abdaf5619c0510138f0cc79376d5572685059e73fa1d4fe5b63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-06T02:44:01Z","title_canon_sha256":"dab01c56c2cf765e76d10cfd4692a4c31984cdf9cb795fb107441dbd7bee07c2"},"schema_version":"1.0","source":{"id":"1702.01487","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01487","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01487v2","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01487","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"GOQOMKDLVGTX","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GOQOMKDLVGTX2XAH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GOQOMKDL","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:4516594f246ef20d1a01cad969617b1644abaed72a9a4987d0d9ec3ea170df47","target":"graph","created_at":"2026-05-18T00:37:54Z","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":"Monte Carlo methods approximate integrals by sample averages of integrand values. The error of Monte Carlo methods may be expressed as a trio identity: the product of the variation of the integrand, the discrepancy of the sampling measure, and the confounding. The trio identity has different versions, depending on whether the integrand is deterministic or Bayesian and whether the sampling measure is deterministic or random. Although the variation and the discrepancy are common in the literature, the confounding is relatively unknown and under-appreciated. Theory and examples are used to show h","authors_text":"Fred J. Hickernell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-06T02:44:01Z","title":"The Trio Identity for Quasi-Monte Carlo Error"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01487","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":"sha256:01dbe78fa85844f69d60ff941d32fb628ad44db8ded705cc7af581d568082b41","target":"record","created_at":"2026-05-18T00:37:54Z","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":"2850cc30c70f9abdaf5619c0510138f0cc79376d5572685059e73fa1d4fe5b63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-06T02:44:01Z","title_canon_sha256":"dab01c56c2cf765e76d10cfd4692a4c31984cdf9cb795fb107441dbd7bee07c2"},"schema_version":"1.0","source":{"id":"1702.01487","kind":"arxiv","version":2}},"canonical_sha256":"33a0e6286ba9a77d5c0796556f868977f8021bf93fedca4541efb08a1b0e9f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33a0e6286ba9a77d5c0796556f868977f8021bf93fedca4541efb08a1b0e9f72","first_computed_at":"2026-05-18T00:37:54.633343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:54.633343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QlVD8jcxAHHvEr9J3969cLkvOKK8U3oJ9xJqhtsddF0Ry8S8S8YnBIyCar+/VZ3w92JA6WP6Je0UNMmILYRsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:54.634051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01487","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01dbe78fa85844f69d60ff941d32fb628ad44db8ded705cc7af581d568082b41","sha256:4516594f246ef20d1a01cad969617b1644abaed72a9a4987d0d9ec3ea170df47"],"state_sha256":"3a2b77329bfd4b3bdcfc5f60e413ceebf88a7d0181cbad5aa9f7871a4f82c2ea"}