{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q3YXPLNVW27KMJ6IZNITAYKILO","short_pith_number":"pith:Q3YXPLNV","canonical_record":{"source":{"id":"1411.1151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-05T04:59:22Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"7398f4cd6f3daacfd7c3ca80467b2971d6db74973b97dc58f861374fcb1174be","abstract_canon_sha256":"3308b53d880697356830966f4124e9bd92a244fb448ac00a6b9b5ee4e3515f7a"},"schema_version":"1.0"},"canonical_sha256":"86f177adb5b6bea627c8cb513061485b8f3f67a89ff36d0e6669f0c29439eb43","source":{"kind":"arxiv","id":"1411.1151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1151","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1151v1","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1151","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"Q3YXPLNVW27K","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3YXPLNVW27KMJ6I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3YXPLNV","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q3YXPLNVW27KMJ6IZNITAYKILO","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-05T04:59:22Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"7398f4cd6f3daacfd7c3ca80467b2971d6db74973b97dc58f861374fcb1174be","abstract_canon_sha256":"3308b53d880697356830966f4124e9bd92a244fb448ac00a6b9b5ee4e3515f7a"},"schema_version":"1.0"},"canonical_sha256":"86f177adb5b6bea627c8cb513061485b8f3f67a89ff36d0e6669f0c29439eb43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:36.182361Z","signature_b64":"kQpQvx5LgA8Pg25oN2CwTG2N4L4XbWafZCx+k00f2Jp1Xfmchm5EKw0SPSfuTAoadC5wbtyeFkb+l2PBzsXQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f177adb5b6bea627c8cb513061485b8f3f67a89ff36d0e6669f0c29439eb43","last_reissued_at":"2026-05-18T02:38:36.181754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:36.181754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1151","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":"2026-05-18T02:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fI8sHSYOu+mOVvZ/aB/j2sUpEtQbNCcxyr1VWmHub4qFzSK71GL+xLus6b6/2Jocwh5pRS346JmnqqlpCYnnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:49:20.604610Z"},"content_sha256":"202309f3cb1633eea900c3bc9ef9a6f39a28735096f3ec6be346a51a2f13be5a","schema_version":"1.0","event_id":"sha256:202309f3cb1633eea900c3bc9ef9a6f39a28735096f3ec6be346a51a2f13be5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q3YXPLNVW27KMJ6IZNITAYKILO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Guaranteed Monte Carlo Methods for Bernoulli Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"math.NA","authors_text":"Fred J. Hickernell, Lan Jiang","submitted_at":"2014-11-05T04:59:22Z","abstract_excerpt":"Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to model success (failure) of complex systems. Here $Y=1$ denotes a success (failure), and $p=\\mathbb{E}(Y)$ denotes the probability of that success (failure). Another application of Bernoulli random variables is $Y=\\mathbb{1}_{R}(\\boldsymbol{X})$, where then $p$ is the probability of $\\boldsymbol{X}$ lying in the region $R$. This article explores how estimate $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1151","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":""},"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":"2026-05-18T02:38:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xjoj5xr1nBrDQjbgI36kzpS+ps8U++FTfqw1NBsYGxEYlhT6tzWcscjMVIJVOmFqrMbF44gBuIQ34eAwY2vJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:49:20.604962Z"},"content_sha256":"e9b9b7b3313abd3f65ddd59df8f0980521d683107b2b7bda42e5ca253f0ee622","schema_version":"1.0","event_id":"sha256:e9b9b7b3313abd3f65ddd59df8f0980521d683107b2b7bda42e5ca253f0ee622"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/bundle.json","state_url":"https://pith.science/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/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":"2026-05-30T07:49:20Z","links":{"resolver":"https://pith.science/pith/Q3YXPLNVW27KMJ6IZNITAYKILO","bundle":"https://pith.science/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/bundle.json","state":"https://pith.science/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3YXPLNVW27KMJ6IZNITAYKILO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q3YXPLNVW27KMJ6IZNITAYKILO","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":"3308b53d880697356830966f4124e9bd92a244fb448ac00a6b9b5ee4e3515f7a","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-05T04:59:22Z","title_canon_sha256":"7398f4cd6f3daacfd7c3ca80467b2971d6db74973b97dc58f861374fcb1174be"},"schema_version":"1.0","source":{"id":"1411.1151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1151","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1151v1","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1151","created_at":"2026-05-18T02:38:36Z"},{"alias_kind":"pith_short_12","alias_value":"Q3YXPLNVW27K","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3YXPLNVW27KMJ6I","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3YXPLNV","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e9b9b7b3313abd3f65ddd59df8f0980521d683107b2b7bda42e5ca253f0ee622","target":"graph","created_at":"2026-05-18T02:38:36Z","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":"Simple Monte Carlo is a versatile computational method with a convergence rate of $O(n^{-1/2})$. It can be used to estimate the means of random variables whose distributions are unknown. Bernoulli random variables, $Y$, are widely used to model success (failure) of complex systems. Here $Y=1$ denotes a success (failure), and $p=\\mathbb{E}(Y)$ denotes the probability of that success (failure). Another application of Bernoulli random variables is $Y=\\mathbb{1}_{R}(\\boldsymbol{X})$, where then $p$ is the probability of $\\boldsymbol{X}$ lying in the region $R$. This article explores how estimate $","authors_text":"Fred J. Hickernell, Lan Jiang","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-05T04:59:22Z","title":"Guaranteed Monte Carlo Methods for Bernoulli Random Variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1151","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":"sha256:202309f3cb1633eea900c3bc9ef9a6f39a28735096f3ec6be346a51a2f13be5a","target":"record","created_at":"2026-05-18T02:38:36Z","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":"3308b53d880697356830966f4124e9bd92a244fb448ac00a6b9b5ee4e3515f7a","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-11-05T04:59:22Z","title_canon_sha256":"7398f4cd6f3daacfd7c3ca80467b2971d6db74973b97dc58f861374fcb1174be"},"schema_version":"1.0","source":{"id":"1411.1151","kind":"arxiv","version":1}},"canonical_sha256":"86f177adb5b6bea627c8cb513061485b8f3f67a89ff36d0e6669f0c29439eb43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86f177adb5b6bea627c8cb513061485b8f3f67a89ff36d0e6669f0c29439eb43","first_computed_at":"2026-05-18T02:38:36.181754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:36.181754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQpQvx5LgA8Pg25oN2CwTG2N4L4XbWafZCx+k00f2Jp1Xfmchm5EKw0SPSfuTAoadC5wbtyeFkb+l2PBzsXQCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:36.182361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:202309f3cb1633eea900c3bc9ef9a6f39a28735096f3ec6be346a51a2f13be5a","sha256:e9b9b7b3313abd3f65ddd59df8f0980521d683107b2b7bda42e5ca253f0ee622"],"state_sha256":"76a664d533e9f971ec015f5ac4d3aa3e3d2eb3025b8b35aa94993ef48c66c14f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vNzj10btgwfi81t+t7FJmmWI8i1Oj7OsHU+xdCWtcRshqMmAhVdOWaXq36s2aasmXwcma/S/a7ogRmchj44BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:49:20.606918Z","bundle_sha256":"2afe93237547a48cd3366bff4afe804676f3e3988f804eed43ada5d8bc143824"}}