{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7ZPZKRDOETRD5NF7LAKMRNQGB7","short_pith_number":"pith:7ZPZKRDO","canonical_record":{"source":{"id":"1407.6086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-23T01:33:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"53d2ea50eb24ba6b31ced7164109ffb9e4f712c3b7b1efed57933206cbf96dc1","abstract_canon_sha256":"df5cf0d43485ef3ee1d7f8e18e612f045b1e907a96edf368069a0a4372a3fc38"},"schema_version":"1.0"},"canonical_sha256":"fe5f95446e24e23eb4bf5814c8b6060fd0d9a100b3b9c4afa8880f47798f0314","source":{"kind":"arxiv","id":"1407.6086","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6086","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6086v3","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6086","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"7ZPZKRDOETRD","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"7ZPZKRDOETRD5NF7","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"7ZPZKRDO","created_at":"2026-06-04T16:08:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7ZPZKRDOETRD5NF7LAKMRNQGB7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6086","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-23T01:33:48Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"53d2ea50eb24ba6b31ced7164109ffb9e4f712c3b7b1efed57933206cbf96dc1","abstract_canon_sha256":"df5cf0d43485ef3ee1d7f8e18e612f045b1e907a96edf368069a0a4372a3fc38"},"schema_version":"1.0"},"canonical_sha256":"fe5f95446e24e23eb4bf5814c8b6060fd0d9a100b3b9c4afa8880f47798f0314","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T16:08:40.510260Z","signature_b64":"EwMSQxNM5dzhWakXxkVGaoT7tu2C4BXOOl6LJmQx/hQif7boKYFLS4IJ6xwEz9r02eSOfSfWKiwuW2ZNkV3kBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe5f95446e24e23eb4bf5814c8b6060fd0d9a100b3b9c4afa8880f47798f0314","last_reissued_at":"2026-06-04T16:08:40.509658Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T16:08:40.509658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6086","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":"2026-06-04T16:08:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9qCKdRWj/rgthEYSGpyqnxcAcIgxuKZ6OB6BNeIacTmc5M4K8cEGPJ4LPfPli8yV06v3GKgw2UA6QR23bdtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:11:49.073216Z"},"content_sha256":"297bf3ddc32ecc0f2962a0487fff264759f236e07a0e58a19d8b60192c67443d","schema_version":"1.0","event_id":"sha256:297bf3ddc32ecc0f2962a0487fff264759f236e07a0e58a19d8b60192c67443d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7ZPZKRDOETRD5NF7LAKMRNQGB7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Kosuke Suzuki, Takashi Goda, Takehito Yoshiki","submitted_at":"2014-07-23T01:33:48Z","abstract_excerpt":"In this paper we study quasi-Monte Carlo integration of smooth functions using digital nets. We fold digital nets over $\\mathbb{Z}_{b}$ by means of the $b$-adic tent transformation, which has recently been introduced by the authors, and employ such \\emph{folded digital nets} as quadrature points. We first analyze the worst-case error of quasi-Monte Carlo rules using folded digital nets in reproducing kernel Hilbert spaces. Here we need to permit digital nets with \"infinite digit expansions,\" which are beyond the scope of the classical definition of digital nets. We overcome this issue by consi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6086","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1407.6086/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":"2026-06-04T16:08:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4skCnq1C2C+cN/F6NgcS+kC8Cv4cUvoGWPTks8tZ8VX+UN2VAPY4egxTE5B2V049AgeluXlIfs2l0nqi4iQcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T21:11:49.073989Z"},"content_sha256":"ea598e08ca06db376783e4a9ff3f725c8810a970b86cabfa307efa8a63f21b41","schema_version":"1.0","event_id":"sha256:ea598e08ca06db376783e4a9ff3f725c8810a970b86cabfa307efa8a63f21b41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/bundle.json","state_url":"https://pith.science/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/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":"2026-06-08T21:11:49Z","links":{"resolver":"https://pith.science/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7","bundle":"https://pith.science/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/bundle.json","state":"https://pith.science/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7ZPZKRDOETRD5NF7LAKMRNQGB7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7ZPZKRDOETRD5NF7LAKMRNQGB7","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":"df5cf0d43485ef3ee1d7f8e18e612f045b1e907a96edf368069a0a4372a3fc38","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-23T01:33:48Z","title_canon_sha256":"53d2ea50eb24ba6b31ced7164109ffb9e4f712c3b7b1efed57933206cbf96dc1"},"schema_version":"1.0","source":{"id":"1407.6086","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6086","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6086v3","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6086","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_12","alias_value":"7ZPZKRDOETRD","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_16","alias_value":"7ZPZKRDOETRD5NF7","created_at":"2026-06-04T16:08:40Z"},{"alias_kind":"pith_short_8","alias_value":"7ZPZKRDO","created_at":"2026-06-04T16:08:40Z"}],"graph_snapshots":[{"event_id":"sha256:ea598e08ca06db376783e4a9ff3f725c8810a970b86cabfa307efa8a63f21b41","target":"graph","created_at":"2026-06-04T16:08:40Z","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/1407.6086/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study quasi-Monte Carlo integration of smooth functions using digital nets. We fold digital nets over $\\mathbb{Z}_{b}$ by means of the $b$-adic tent transformation, which has recently been introduced by the authors, and employ such \\emph{folded digital nets} as quadrature points. We first analyze the worst-case error of quasi-Monte Carlo rules using folded digital nets in reproducing kernel Hilbert spaces. Here we need to permit digital nets with \"infinite digit expansions,\" which are beyond the scope of the classical definition of digital nets. We overcome this issue by consi","authors_text":"Kosuke Suzuki, Takashi Goda, Takehito Yoshiki","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-23T01:33:48Z","title":"Digital nets with infinite digit expansions and construction of folded digital nets for quasi-Monte Carlo integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6086","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":"sha256:297bf3ddc32ecc0f2962a0487fff264759f236e07a0e58a19d8b60192c67443d","target":"record","created_at":"2026-06-04T16:08:40Z","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":"df5cf0d43485ef3ee1d7f8e18e612f045b1e907a96edf368069a0a4372a3fc38","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-07-23T01:33:48Z","title_canon_sha256":"53d2ea50eb24ba6b31ced7164109ffb9e4f712c3b7b1efed57933206cbf96dc1"},"schema_version":"1.0","source":{"id":"1407.6086","kind":"arxiv","version":3}},"canonical_sha256":"fe5f95446e24e23eb4bf5814c8b6060fd0d9a100b3b9c4afa8880f47798f0314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe5f95446e24e23eb4bf5814c8b6060fd0d9a100b3b9c4afa8880f47798f0314","first_computed_at":"2026-06-04T16:08:40.509658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T16:08:40.509658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EwMSQxNM5dzhWakXxkVGaoT7tu2C4BXOOl6LJmQx/hQif7boKYFLS4IJ6xwEz9r02eSOfSfWKiwuW2ZNkV3kBw==","signature_status":"signed_v1","signed_at":"2026-06-04T16:08:40.510260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6086","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:297bf3ddc32ecc0f2962a0487fff264759f236e07a0e58a19d8b60192c67443d","sha256:ea598e08ca06db376783e4a9ff3f725c8810a970b86cabfa307efa8a63f21b41"],"state_sha256":"3b366f73322f4d5eaa70c7c361b443f084a38709f3eda90a15156f1dd6cefa89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0Ns3eJ3DZCpWZ+mDNLARnAkMsx7n9uOdHOzqeViMgstggvo+ZNuZUp2L8pHyA8tCT/h5sf8+mgM0A0bSqcZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T21:11:49.077768Z","bundle_sha256":"e639a993ac29bb1e7a3bd1218926e8f1d16caa189fb6430e98ff3d5f83e2c501"}}