{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IHOX7GVJN5QFCEMOQ2MWKDIGHV","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":"39021a004bfc13fd43678fc9fcec25ecae701901c7dd1f93f7d066130e0e1ea5","cross_cats_sorted":["math.NA","math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-02T01:39:35Z","title_canon_sha256":"32e21b9bff9a3e7a87a2b5868860cedaea6486a61c86892ec118f21664a8abdf"},"schema_version":"1.0","source":{"id":"1406.0230","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.0230","created_at":"2026-05-18T02:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1406.0230v2","created_at":"2026-05-18T02:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0230","created_at":"2026-05-18T02:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"IHOX7GVJN5QF","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IHOX7GVJN5QFCEMO","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IHOX7GVJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:dec74e31f03b34d0fa02a6fb4f12084f38f89b53603aa158b0e56792e3a07603","target":"graph","created_at":"2026-05-18T02:40:53Z","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":"In this paper we prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma--Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. Furthermore, we discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure into a sequence with low discrepancy with respect to a general measure","authors_text":"Christoph Aistleitner, Josef Dick","cross_cats":["math.NA","math.NT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-02T01:39:35Z","title":"Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0230","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":"sha256:57da09cd004a86ee1920b9d4d27f686b68f8fa57a1d642eb5e9c0c82df2919ea","target":"record","created_at":"2026-05-18T02:40:53Z","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":"39021a004bfc13fd43678fc9fcec25ecae701901c7dd1f93f7d066130e0e1ea5","cross_cats_sorted":["math.NA","math.NT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-02T01:39:35Z","title_canon_sha256":"32e21b9bff9a3e7a87a2b5868860cedaea6486a61c86892ec118f21664a8abdf"},"schema_version":"1.0","source":{"id":"1406.0230","kind":"arxiv","version":2}},"canonical_sha256":"41dd7f9aa96f6051118e8699650d063d7232b3224f6345dc07d081f79ec43c42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41dd7f9aa96f6051118e8699650d063d7232b3224f6345dc07d081f79ec43c42","first_computed_at":"2026-05-18T02:40:53.898213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:53.898213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kp2QXNhqh2hYi5XOYLV/BidNEK7jJqxW3YIFel8O2A6BCtivWffaGDDHu8MlBzqyqZVVsHCSy2DYkZ3sOlxfBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:53.898826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.0230","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57da09cd004a86ee1920b9d4d27f686b68f8fa57a1d642eb5e9c0c82df2919ea","sha256:dec74e31f03b34d0fa02a6fb4f12084f38f89b53603aa158b0e56792e3a07603"],"state_sha256":"4831b04d642052a8bea874c1b1324e48bb8737bf6767dc14d99dbd2f904e5edc"}