{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RHJDTFKAUUOAG3URWKLPA4LUYA","short_pith_number":"pith:RHJDTFKA","canonical_record":{"source":{"id":"1612.07002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T07:59:15Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"6415e023dceb909232f76adc24e0a901cd93a2c079b0baf32ee99eb26f186bef","abstract_canon_sha256":"47c828746e807817570831a0f11b78c68bf825893bc8ee9be091dda9bcd5c13e"},"schema_version":"1.0"},"canonical_sha256":"89d2399540a51c036e91b296f07174c00f7b0039e3d3012ed57e503c18eb57e0","source":{"kind":"arxiv","id":"1612.07002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07002","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07002v1","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07002","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"RHJDTFKAUUOA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHJDTFKAUUOAG3UR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHJDTFKA","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RHJDTFKAUUOAG3URWKLPA4LUYA","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T07:59:15Z","cross_cats_sorted":["stat.CO"],"title_canon_sha256":"6415e023dceb909232f76adc24e0a901cd93a2c079b0baf32ee99eb26f186bef","abstract_canon_sha256":"47c828746e807817570831a0f11b78c68bf825893bc8ee9be091dda9bcd5c13e"},"schema_version":"1.0"},"canonical_sha256":"89d2399540a51c036e91b296f07174c00f7b0039e3d3012ed57e503c18eb57e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:56.155760Z","signature_b64":"MLuSAw67o7TtZLfXD5y6XOhYgHFo3W7xyAZ1khgmyeDGusggQSUPZHy+9V9njeIx/dl+F/g5wPSRThPTCBbeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d2399540a51c036e91b296f07174c00f7b0039e3d3012ed57e503c18eb57e0","last_reissued_at":"2026-05-18T00:43:56.155278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:56.155278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07002","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":"2026-05-18T00:43:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Us0ZaiZ5hL3/h0PeMHjNj4WAS1z+CcJtbbR31/x7mc0zKRLOLKvwciCVAY/rAMBR+TH9UWdfjj411+T/N/PgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:44:02.393911Z"},"content_sha256":"33e9557b47c42cc38ffa663f07594da23d43243ad1d37de246ced12206b55f24","schema_version":"1.0","event_id":"sha256:33e9557b47c42cc38ffa663f07594da23d43243ad1d37de246ced12206b55f24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RHJDTFKAUUOAG3URWKLPA4LUYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A subset multicanonical Monte Carlo method for simulating rare failure events","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.CO"],"primary_cat":"math.NA","authors_text":"Jinglai Li, Xinjuan Chen","submitted_at":"2016-12-21T07:59:15Z","abstract_excerpt":"Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\\leq10^{-10}$). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07002","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":"2026-05-18T00:43:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z5/ht9C90dUCoowvENwGnkK8R6E2DexBypHS+tu9w6jntCqale8ZMSDq4Y2ygZ6z+UEOxJWhHu6AIlWH0lTSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T09:44:02.394501Z"},"content_sha256":"9a21a38e2c90a2768ee8c8f3acad1b1487c640661cfdff2953bda8e8644bd93c","schema_version":"1.0","event_id":"sha256:9a21a38e2c90a2768ee8c8f3acad1b1487c640661cfdff2953bda8e8644bd93c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/bundle.json","state_url":"https://pith.science/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/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":"2026-05-25T09:44:02Z","links":{"resolver":"https://pith.science/pith/RHJDTFKAUUOAG3URWKLPA4LUYA","bundle":"https://pith.science/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/bundle.json","state":"https://pith.science/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHJDTFKAUUOAG3URWKLPA4LUYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RHJDTFKAUUOAG3URWKLPA4LUYA","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":"47c828746e807817570831a0f11b78c68bf825893bc8ee9be091dda9bcd5c13e","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T07:59:15Z","title_canon_sha256":"6415e023dceb909232f76adc24e0a901cd93a2c079b0baf32ee99eb26f186bef"},"schema_version":"1.0","source":{"id":"1612.07002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07002","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07002v1","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07002","created_at":"2026-05-18T00:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"RHJDTFKAUUOA","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RHJDTFKAUUOAG3UR","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RHJDTFKA","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:9a21a38e2c90a2768ee8c8f3acad1b1487c640661cfdff2953bda8e8644bd93c","target":"graph","created_at":"2026-05-18T00:43:56Z","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":"Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\\leq10^{-10}$). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in","authors_text":"Jinglai Li, Xinjuan Chen","cross_cats":["stat.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T07:59:15Z","title":"A subset multicanonical Monte Carlo method for simulating rare failure events"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07002","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":"sha256:33e9557b47c42cc38ffa663f07594da23d43243ad1d37de246ced12206b55f24","target":"record","created_at":"2026-05-18T00:43:56Z","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":"47c828746e807817570831a0f11b78c68bf825893bc8ee9be091dda9bcd5c13e","cross_cats_sorted":["stat.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-12-21T07:59:15Z","title_canon_sha256":"6415e023dceb909232f76adc24e0a901cd93a2c079b0baf32ee99eb26f186bef"},"schema_version":"1.0","source":{"id":"1612.07002","kind":"arxiv","version":1}},"canonical_sha256":"89d2399540a51c036e91b296f07174c00f7b0039e3d3012ed57e503c18eb57e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d2399540a51c036e91b296f07174c00f7b0039e3d3012ed57e503c18eb57e0","first_computed_at":"2026-05-18T00:43:56.155278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:56.155278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MLuSAw67o7TtZLfXD5y6XOhYgHFo3W7xyAZ1khgmyeDGusggQSUPZHy+9V9njeIx/dl+F/g5wPSRThPTCBbeBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:56.155760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33e9557b47c42cc38ffa663f07594da23d43243ad1d37de246ced12206b55f24","sha256:9a21a38e2c90a2768ee8c8f3acad1b1487c640661cfdff2953bda8e8644bd93c"],"state_sha256":"8edb83246a386fcffcc231de1d23911a1b3bc8378d22b897144258ae6807661c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QW3LT1X9ZwRG4daAC0BklMD3uepYOtWLoNPn8oFml1znD1XfMJCD5GBNl1djmEXgKwLwi1bJc5Xqe4rJHM3NCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T09:44:02.398148Z","bundle_sha256":"d4aa2fc4f0ef7f964f168da2a7fd3cffb2d061dea57b5342f218d5baa2b81f53"}}