{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B2GVBZZVBDRDUJIQZ275W6J2MC","short_pith_number":"pith:B2GVBZZV","canonical_record":{"source":{"id":"1706.06869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:46:47Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"323bd5d14a74e82dadff36d2482fecbc1799ae0003eb1ecec94b750fe0a1822b","abstract_canon_sha256":"1431000f5a2034cfe5cce9829db3cc9d260eecd777bfb38115ef4a3f2e462d80"},"schema_version":"1.0"},"canonical_sha256":"0e8d50e73508e23a2510cebfdb793a60985fa91329b6239a304f39b7a5834a88","source":{"kind":"arxiv","id":"1706.06869","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06869","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06869v1","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06869","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"B2GVBZZVBDRD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B2GVBZZVBDRDUJIQ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B2GVBZZV","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B2GVBZZVBDRDUJIQZ275W6J2MC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:46:47Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"323bd5d14a74e82dadff36d2482fecbc1799ae0003eb1ecec94b750fe0a1822b","abstract_canon_sha256":"1431000f5a2034cfe5cce9829db3cc9d260eecd777bfb38115ef4a3f2e462d80"},"schema_version":"1.0"},"canonical_sha256":"0e8d50e73508e23a2510cebfdb793a60985fa91329b6239a304f39b7a5834a88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:56.693934Z","signature_b64":"d3c/nzVegj5cRTltuh0A2p3TNADTuJGQ/BwHheBwdFZueR2jC4mgJQRXfU/VRO0/QKmWdi8o0CkgYUOXTzxsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e8d50e73508e23a2510cebfdb793a60985fa91329b6239a304f39b7a5834a88","last_reissued_at":"2026-05-18T00:41:56.693484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:56.693484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06869","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":"2026-05-18T00:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ip0zCNm6CB4NDM8yuYQUAXuxAdIz2UUJPGSajdfzTUfWbUlbVe59iBG+xj1IpwWoTXBhEHkTDzYC+8A0z4F6CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:42:07.744110Z"},"content_sha256":"234c30f00deeee5e694ab7e78aecc97e0f0c401369dea4049ff4f9c3413d6732","schema_version":"1.0","event_id":"sha256:234c30f00deeee5e694ab7e78aecc97e0f0c401369dea4049ff4f9c3413d6732"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B2GVBZZVBDRDUJIQZ275W6J2MC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Multilevel Monte Carlo Approximation of Distribution Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Klaus Ritter, Mike B. Giles, Tigran Nagapetyan","submitted_at":"2017-06-21T12:46:47Z","abstract_excerpt":"We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an asymptotic analysis of the error and the cost of the algorithm. Furthermore we construct an adaptive version of the algorithm that does not require any a priori knowledge on weak or strong convergence rates. We apply the adaptive algorithm to smooth path-independent and path-dependent functionals and to stopped exit times of SDEs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06869","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":"2026-05-18T00:41:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+e1exW+nWqAk3ZXePIrv5GU/I7smMOCqI5DwI23XyMyy5Git1SmsJ4uk6eTRn0GEl3nwQLahlYkiew0GoLZ3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:42:07.744472Z"},"content_sha256":"dfc17fe649b08adfd8aba258fff796143d43a817280063abc28b73c47ab46132","schema_version":"1.0","event_id":"sha256:dfc17fe649b08adfd8aba258fff796143d43a817280063abc28b73c47ab46132"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/bundle.json","state_url":"https://pith.science/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/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":"2026-06-20T05:42:07Z","links":{"resolver":"https://pith.science/pith/B2GVBZZVBDRDUJIQZ275W6J2MC","bundle":"https://pith.science/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/bundle.json","state":"https://pith.science/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2GVBZZVBDRDUJIQZ275W6J2MC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B2GVBZZVBDRDUJIQZ275W6J2MC","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":"1431000f5a2034cfe5cce9829db3cc9d260eecd777bfb38115ef4a3f2e462d80","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:46:47Z","title_canon_sha256":"323bd5d14a74e82dadff36d2482fecbc1799ae0003eb1ecec94b750fe0a1822b"},"schema_version":"1.0","source":{"id":"1706.06869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06869","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06869v1","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06869","created_at":"2026-05-18T00:41:56Z"},{"alias_kind":"pith_short_12","alias_value":"B2GVBZZVBDRD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B2GVBZZVBDRDUJIQ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B2GVBZZV","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:dfc17fe649b08adfd8aba258fff796143d43a817280063abc28b73c47ab46132","target":"graph","created_at":"2026-05-18T00:41:56Z","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":"We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an asymptotic analysis of the error and the cost of the algorithm. Furthermore we construct an adaptive version of the algorithm that does not require any a priori knowledge on weak or strong convergence rates. We apply the adaptive algorithm to smooth path-independent and path-dependent functionals and to stopped exit times of SDEs.","authors_text":"Klaus Ritter, Mike B. Giles, Tigran Nagapetyan","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:46:47Z","title":"Adaptive Multilevel Monte Carlo Approximation of Distribution Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06869","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":"sha256:234c30f00deeee5e694ab7e78aecc97e0f0c401369dea4049ff4f9c3413d6732","target":"record","created_at":"2026-05-18T00:41:56Z","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":"1431000f5a2034cfe5cce9829db3cc9d260eecd777bfb38115ef4a3f2e462d80","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-21T12:46:47Z","title_canon_sha256":"323bd5d14a74e82dadff36d2482fecbc1799ae0003eb1ecec94b750fe0a1822b"},"schema_version":"1.0","source":{"id":"1706.06869","kind":"arxiv","version":1}},"canonical_sha256":"0e8d50e73508e23a2510cebfdb793a60985fa91329b6239a304f39b7a5834a88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e8d50e73508e23a2510cebfdb793a60985fa91329b6239a304f39b7a5834a88","first_computed_at":"2026-05-18T00:41:56.693484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:56.693484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d3c/nzVegj5cRTltuh0A2p3TNADTuJGQ/BwHheBwdFZueR2jC4mgJQRXfU/VRO0/QKmWdi8o0CkgYUOXTzxsBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:56.693934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:234c30f00deeee5e694ab7e78aecc97e0f0c401369dea4049ff4f9c3413d6732","sha256:dfc17fe649b08adfd8aba258fff796143d43a817280063abc28b73c47ab46132"],"state_sha256":"2c9fa97add06f9b4e732fa956ee42c0d63a4db86b8e65d88b23bd1cd58ea2671"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrZbmbluQPcJf3OL0NaSIKREe1hb4jaAaRdTpS/FsZJqN6FQ+FktFv9dqspx49ik5t4ZGfo9J0EdTRIZMG4XCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:42:07.746459Z","bundle_sha256":"2422223c7cba66428f4ea840408dfea5cc17ebe3237424986c19c1ef46781713"}}