{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JH264QZAVH4OBXI3LYTHRFYQWT","short_pith_number":"pith:JH264QZA","canonical_record":{"source":{"id":"1412.0783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-02T05:14:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1233dcb60af1a56ae3c0d4b5c7ebe801e696e15a2ef997765ffe10eb95704136","abstract_canon_sha256":"eefd89050bb0c0386e71dc3e7ebf79f6ddd09417bcf0ab7249bec76c3d626de9"},"schema_version":"1.0"},"canonical_sha256":"49f5ee4320a9f8e0dd1b5e26789710b4ead47eb29a31dc2109bf548b929bc04c","source":{"kind":"arxiv","id":"1412.0783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0783","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0783v1","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0783","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"JH264QZAVH4O","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"JH264QZAVH4OBXI3","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"JH264QZA","created_at":"2026-06-04T16:08:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JH264QZAVH4OBXI3LYTHRFYQWT","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-02T05:14:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"1233dcb60af1a56ae3c0d4b5c7ebe801e696e15a2ef997765ffe10eb95704136","abstract_canon_sha256":"eefd89050bb0c0386e71dc3e7ebf79f6ddd09417bcf0ab7249bec76c3d626de9"},"schema_version":"1.0"},"canonical_sha256":"49f5ee4320a9f8e0dd1b5e26789710b4ead47eb29a31dc2109bf548b929bc04c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T16:08:58.202020Z","signature_b64":"CxeiYR4RAnPT+TGb+xhS7OXZBPNtZOT5ynoBToAWZL0G0houK/rdgBYDUAhddxRF/UXCoApo9csT+KaaD+3HBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49f5ee4320a9f8e0dd1b5e26789710b4ead47eb29a31dc2109bf548b929bc04c","last_reissued_at":"2026-06-04T16:08:58.201519Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T16:08:58.201519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0783","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":"2026-06-04T16:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/2cYwX8/lkofc1qeEomMfEQEMHxuS+bO36Nt8cePMHIe8uGo1tzuKW/lqzAQAaf4pv9KOsyaiPe+u/uh3uIcAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:34:33.244120Z"},"content_sha256":"7ab4b7264d7fa34fc69fb49a89743b91128b84f51e3e782d8120860e2a564cc0","schema_version":"1.0","event_id":"sha256:7ab4b7264d7fa34fc69fb49a89743b91128b84f51e3e782d8120860e2a564cc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JH264QZAVH4OBXI3LYTHRFYQWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Kosuke Suzuki, Ryuichi Ohori, Takashi Goda, Takehito Yoshiki","submitted_at":"2014-12-02T05:14:21Z","abstract_excerpt":"In this paper, we study randomized quasi-Monte Carlo (QMC) integration using digitally shifted digital nets. We express the mean square QMC error of the $n$-th discrete approximation $f_n$ of a function $f\\colon[0,1)^s\\to \\mathbb{R}$ for digitally shifted digital nets in terms of the Walsh coefficients of $f$. We then apply a bound on the Walsh coefficients for sufficiently smooth integrands to obtain a quality measure called Walsh figure of merit for root mean square error, which satisfies a Koksma-Hlawka type inequality on the root mean square error. Through two types of experiments, we conf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0783","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1412.0783/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":"2026-06-04T16:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4u+cIaTi42V6ebxhg5+0+muh67ZWzM37nPt5ezecodpvfFSASgZoSC8EeXFBgbeP/H14vVQxIns7/RemNHrxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:34:33.245020Z"},"content_sha256":"dc9d83538de9fc3e59e8e95ccf87acb0451e46b7f7d8292c7217ea366dc080ba","schema_version":"1.0","event_id":"sha256:dc9d83538de9fc3e59e8e95ccf87acb0451e46b7f7d8292c7217ea366dc080ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JH264QZAVH4OBXI3LYTHRFYQWT/bundle.json","state_url":"https://pith.science/pith/JH264QZAVH4OBXI3LYTHRFYQWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JH264QZAVH4OBXI3LYTHRFYQWT/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":"2026-06-07T21:34:33Z","links":{"resolver":"https://pith.science/pith/JH264QZAVH4OBXI3LYTHRFYQWT","bundle":"https://pith.science/pith/JH264QZAVH4OBXI3LYTHRFYQWT/bundle.json","state":"https://pith.science/pith/JH264QZAVH4OBXI3LYTHRFYQWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JH264QZAVH4OBXI3LYTHRFYQWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JH264QZAVH4OBXI3LYTHRFYQWT","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":"eefd89050bb0c0386e71dc3e7ebf79f6ddd09417bcf0ab7249bec76c3d626de9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-02T05:14:21Z","title_canon_sha256":"1233dcb60af1a56ae3c0d4b5c7ebe801e696e15a2ef997765ffe10eb95704136"},"schema_version":"1.0","source":{"id":"1412.0783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0783","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0783v1","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0783","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"JH264QZAVH4O","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"JH264QZAVH4OBXI3","created_at":"2026-06-04T16:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"JH264QZA","created_at":"2026-06-04T16:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:dc9d83538de9fc3e59e8e95ccf87acb0451e46b7f7d8292c7217ea366dc080ba","target":"graph","created_at":"2026-06-04T16:08:58Z","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/1412.0783/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study randomized quasi-Monte Carlo (QMC) integration using digitally shifted digital nets. We express the mean square QMC error of the $n$-th discrete approximation $f_n$ of a function $f\\colon[0,1)^s\\to \\mathbb{R}$ for digitally shifted digital nets in terms of the Walsh coefficients of $f$. We then apply a bound on the Walsh coefficients for sufficiently smooth integrands to obtain a quality measure called Walsh figure of merit for root mean square error, which satisfies a Koksma-Hlawka type inequality on the root mean square error. Through two types of experiments, we conf","authors_text":"Kosuke Suzuki, Ryuichi Ohori, Takashi Goda, Takehito Yoshiki","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-02T05:14:21Z","title":"The Mean Square Quasi-Monte Carlo Error for Digitally Shifted Digital Nets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0783","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":"sha256:7ab4b7264d7fa34fc69fb49a89743b91128b84f51e3e782d8120860e2a564cc0","target":"record","created_at":"2026-06-04T16:08:58Z","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":"eefd89050bb0c0386e71dc3e7ebf79f6ddd09417bcf0ab7249bec76c3d626de9","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-12-02T05:14:21Z","title_canon_sha256":"1233dcb60af1a56ae3c0d4b5c7ebe801e696e15a2ef997765ffe10eb95704136"},"schema_version":"1.0","source":{"id":"1412.0783","kind":"arxiv","version":1}},"canonical_sha256":"49f5ee4320a9f8e0dd1b5e26789710b4ead47eb29a31dc2109bf548b929bc04c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49f5ee4320a9f8e0dd1b5e26789710b4ead47eb29a31dc2109bf548b929bc04c","first_computed_at":"2026-06-04T16:08:58.201519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T16:08:58.201519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CxeiYR4RAnPT+TGb+xhS7OXZBPNtZOT5ynoBToAWZL0G0houK/rdgBYDUAhddxRF/UXCoApo9csT+KaaD+3HBg==","signature_status":"signed_v1","signed_at":"2026-06-04T16:08:58.202020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ab4b7264d7fa34fc69fb49a89743b91128b84f51e3e782d8120860e2a564cc0","sha256:dc9d83538de9fc3e59e8e95ccf87acb0451e46b7f7d8292c7217ea366dc080ba"],"state_sha256":"efe6c4fd2fa2ba9290b75c5ed294de03f0ba3559c5183beea5e2fefd70f1d001"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LL7QYapUbVmItuMEhbycIduEi3eCR8TQhDcEH7AhJmm7E/Z5fNnPGDY+oUNKzd7t4tx2Do1LakdMWg/3xi/bBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:34:33.249242Z","bundle_sha256":"b8c38536b30efadb9bb794003a7498414bfde236e4dbf4c084e5f559cda55831"}}