{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ASRYYS337RSA533HBRGHG5Y6FP","short_pith_number":"pith:ASRYYS33","canonical_record":{"source":{"id":"1507.05031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-17T16:50:57Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"bc3d7db60ba97e18e62c282f1f5dcc1c2317098d2a92391d3c9f3755a1a6d3a1","abstract_canon_sha256":"f622f16c9b59447b758cef8e7c983d1ff2b255737065a2f9972d7ca2d9c4c417"},"schema_version":"1.0"},"canonical_sha256":"04a38c4b7bfc640eef670c4c73771e2bd7bde2bf10bdfe4a9de2958d8c872c5d","source":{"kind":"arxiv","id":"1507.05031","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05031","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05031v2","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05031","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ASRYYS337RSA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASRYYS337RSA533H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASRYYS33","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ASRYYS337RSA533HBRGHG5Y6FP","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-17T16:50:57Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"bc3d7db60ba97e18e62c282f1f5dcc1c2317098d2a92391d3c9f3755a1a6d3a1","abstract_canon_sha256":"f622f16c9b59447b758cef8e7c983d1ff2b255737065a2f9972d7ca2d9c4c417"},"schema_version":"1.0"},"canonical_sha256":"04a38c4b7bfc640eef670c4c73771e2bd7bde2bf10bdfe4a9de2958d8c872c5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:45.753303Z","signature_b64":"7FSrsJfJEsWme0IsslpBsoRJFFtSYaMs4KWOnqDqaAd2usDK71cEvZzD0Pp17cb8/eskDZ/NrNo6WkofrEwsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04a38c4b7bfc640eef670c4c73771e2bd7bde2bf10bdfe4a9de2958d8c872c5d","last_reissued_at":"2026-05-18T01:02:45.752917Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:45.752917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05031","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EEuPuWBwrbPUlu1YmpCb3+AVYpaMgIqvcNADefb/aybdfGclQBozmQ9BaOyn5jeBZGVAv6Y7UEc2W/q9vjxSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:24:43.673347Z"},"content_sha256":"16a6b72ee5f4f48b76194a52abe4117b4a17f4be72d1b4d89a3927e56b3abe0c","schema_version":"1.0","event_id":"sha256:16a6b72ee5f4f48b76194a52abe4117b4a17f4be72d1b4d89a3927e56b3abe0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ASRYYS337RSA533HBRGHG5Y6FP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First- and second-order error estimates in Monte Carlo integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"math.NA","authors_text":"F. Versteegen, R. Bakx, R.H.P. Kleiss","submitted_at":"2015-07-17T16:50:57Z","abstract_excerpt":"In Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In contrast to the usual (first-order) error estimator, this second-order estimator can be shown to be not necessarily positive in an actual Monte Carlo computation. We propose an alternative and indicate how this can be computed in linear time without risk of large rounding errors. In addition, we comment on the relatively very slow convergence of the second-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05031","kind":"arxiv","version":2},"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":"2026-05-18T01:02:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2UmDMp+tGg7MrIeug/xYcKcJqjdK5tOqc5X113WO9/Ctu26a31lcmIUGBlf0GJL55y139IrvVN80TypWhN+YAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T11:24:43.673710Z"},"content_sha256":"7dd3e2711fb5e737e2120eff5a69efc3bfa86df28eeaf8aebf3e2a68db2c24ca","schema_version":"1.0","event_id":"sha256:7dd3e2711fb5e737e2120eff5a69efc3bfa86df28eeaf8aebf3e2a68db2c24ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASRYYS337RSA533HBRGHG5Y6FP/bundle.json","state_url":"https://pith.science/pith/ASRYYS337RSA533HBRGHG5Y6FP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASRYYS337RSA533HBRGHG5Y6FP/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":"2026-06-03T11:24:43Z","links":{"resolver":"https://pith.science/pith/ASRYYS337RSA533HBRGHG5Y6FP","bundle":"https://pith.science/pith/ASRYYS337RSA533HBRGHG5Y6FP/bundle.json","state":"https://pith.science/pith/ASRYYS337RSA533HBRGHG5Y6FP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASRYYS337RSA533HBRGHG5Y6FP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ASRYYS337RSA533HBRGHG5Y6FP","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":"f622f16c9b59447b758cef8e7c983d1ff2b255737065a2f9972d7ca2d9c4c417","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-17T16:50:57Z","title_canon_sha256":"bc3d7db60ba97e18e62c282f1f5dcc1c2317098d2a92391d3c9f3755a1a6d3a1"},"schema_version":"1.0","source":{"id":"1507.05031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05031","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05031v2","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05031","created_at":"2026-05-18T01:02:45Z"},{"alias_kind":"pith_short_12","alias_value":"ASRYYS337RSA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASRYYS337RSA533H","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASRYYS33","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:7dd3e2711fb5e737e2120eff5a69efc3bfa86df28eeaf8aebf3e2a68db2c24ca","target":"graph","created_at":"2026-05-18T01:02:45Z","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 Monte Carlo integration an accurate and reliable determination of the numerical intregration error is essential. We point out the need for an independent estimate of the error on this error, for which we present an unbiased estimator. In contrast to the usual (first-order) error estimator, this second-order estimator can be shown to be not necessarily positive in an actual Monte Carlo computation. We propose an alternative and indicate how this can be computed in linear time without risk of large rounding errors. In addition, we comment on the relatively very slow convergence of the second-","authors_text":"F. Versteegen, R. Bakx, R.H.P. Kleiss","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-17T16:50:57Z","title":"First- and second-order error estimates in Monte Carlo integration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05031","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":"sha256:16a6b72ee5f4f48b76194a52abe4117b4a17f4be72d1b4d89a3927e56b3abe0c","target":"record","created_at":"2026-05-18T01:02:45Z","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":"f622f16c9b59447b758cef8e7c983d1ff2b255737065a2f9972d7ca2d9c4c417","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-17T16:50:57Z","title_canon_sha256":"bc3d7db60ba97e18e62c282f1f5dcc1c2317098d2a92391d3c9f3755a1a6d3a1"},"schema_version":"1.0","source":{"id":"1507.05031","kind":"arxiv","version":2}},"canonical_sha256":"04a38c4b7bfc640eef670c4c73771e2bd7bde2bf10bdfe4a9de2958d8c872c5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04a38c4b7bfc640eef670c4c73771e2bd7bde2bf10bdfe4a9de2958d8c872c5d","first_computed_at":"2026-05-18T01:02:45.752917Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:45.752917Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7FSrsJfJEsWme0IsslpBsoRJFFtSYaMs4KWOnqDqaAd2usDK71cEvZzD0Pp17cb8/eskDZ/NrNo6WkofrEwsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:45.753303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a6b72ee5f4f48b76194a52abe4117b4a17f4be72d1b4d89a3927e56b3abe0c","sha256:7dd3e2711fb5e737e2120eff5a69efc3bfa86df28eeaf8aebf3e2a68db2c24ca"],"state_sha256":"63ce7b860d20969994a836a34a37c6f67454fb7177e9a1beda2091d71db74bf2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAik340U/QD0iO0aCMk6di2Ezvj1yiaWDIIH7zl7m5FV7Cktymxh2l/Qm9dhzW0apDzqdKZL6EFcTAfG4n/sAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T11:24:43.675798Z","bundle_sha256":"18f4aa1bb5f8ee89cad597a4f8f2caa1b811b1c6e9a786bcf5cbdaa52a25a0f7"}}