{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7MKNXNNZ42KOS62C3AUVNNERJ4","short_pith_number":"pith:7MKNXNNZ","canonical_record":{"source":{"id":"1409.2342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T13:46:43Z","cross_cats_sorted":[],"title_canon_sha256":"578fb2a1cda506e7c042af9cb88dcbb208567c1216539ae8bfc415f6848d7a85","abstract_canon_sha256":"e900aa3c25e0a6ff11c8b305e78e873dadf46fea5b47363f0c67a389f06b3077"},"schema_version":"1.0"},"canonical_sha256":"fb14dbb5b9e694e97b42d82956b4914f10bb17f5c016c2d6dc5e56534049bf88","source":{"kind":"arxiv","id":"1409.2342","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2342","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2342v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2342","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"7MKNXNNZ42KO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7MKNXNNZ42KOS62C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7MKNXNNZ","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7MKNXNNZ42KOS62C3AUVNNERJ4","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2342","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T13:46:43Z","cross_cats_sorted":[],"title_canon_sha256":"578fb2a1cda506e7c042af9cb88dcbb208567c1216539ae8bfc415f6848d7a85","abstract_canon_sha256":"e900aa3c25e0a6ff11c8b305e78e873dadf46fea5b47363f0c67a389f06b3077"},"schema_version":"1.0"},"canonical_sha256":"fb14dbb5b9e694e97b42d82956b4914f10bb17f5c016c2d6dc5e56534049bf88","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:47.000557Z","signature_b64":"ZMbs0aXLk8/c20fQDf/Rppl1LJ7Hc7Ol8HnUoDwvcoDs6Z3FtLCOi7TWioT10hLd6NrFwOXOhwCWYqvGHQuaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb14dbb5b9e694e97b42d82956b4914f10bb17f5c016c2d6dc5e56534049bf88","last_reissued_at":"2026-05-18T02:30:47.000050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:47.000050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2342","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":"2026-05-18T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0eCnMJ3S5aHIpqkaJtoQy3JZ9pbkFOgkKyjq0AdhY9xsLNbVqMHfNWTX4evnNGjNVauBJ4xOASACNAZQ9TXnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:26:12.061513Z"},"content_sha256":"3c637aeb95c7a916de7aa5897937756dc73ac808fdeec97f694640316d610d54","schema_version":"1.0","event_id":"sha256:3c637aeb95c7a916de7aa5897937756dc73ac808fdeec97f694640316d610d54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7MKNXNNZ42KOS62C3AUVNNERJ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improving MLMC for SDEs with application to the Langevin equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eike H. Mueller, Rob Scheichl, Tony Shardlow","submitted_at":"2014-09-08T13:46:43Z","abstract_excerpt":"This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis to circumvent the need for a strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2342","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":"2026-05-18T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBEzgT6c20gx605P+3PTDhwZtiZ6HxM8UkBLuShL1T88kSOsxDjT2GxPF7Du0F5dXU8WtZN/6md77R9AHvikBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:26:12.061858Z"},"content_sha256":"753ede2699cba1b73fa3d9d43162831ec1a6ed09ba81f5a8f003be6176a16963","schema_version":"1.0","event_id":"sha256:753ede2699cba1b73fa3d9d43162831ec1a6ed09ba81f5a8f003be6176a16963"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/bundle.json","state_url":"https://pith.science/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/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":"2026-05-31T08:26:12Z","links":{"resolver":"https://pith.science/pith/7MKNXNNZ42KOS62C3AUVNNERJ4","bundle":"https://pith.science/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/bundle.json","state":"https://pith.science/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7MKNXNNZ42KOS62C3AUVNNERJ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7MKNXNNZ42KOS62C3AUVNNERJ4","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":"e900aa3c25e0a6ff11c8b305e78e873dadf46fea5b47363f0c67a389f06b3077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T13:46:43Z","title_canon_sha256":"578fb2a1cda506e7c042af9cb88dcbb208567c1216539ae8bfc415f6848d7a85"},"schema_version":"1.0","source":{"id":"1409.2342","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2342","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2342v2","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2342","created_at":"2026-05-18T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"7MKNXNNZ42KO","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7MKNXNNZ42KOS62C","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7MKNXNNZ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:753ede2699cba1b73fa3d9d43162831ec1a6ed09ba81f5a8f003be6176a16963","target":"graph","created_at":"2026-05-18T02:30:47Z","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":"This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the Multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis to circumvent the need for a strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussia","authors_text":"Eike H. Mueller, Rob Scheichl, Tony Shardlow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T13:46:43Z","title":"Improving MLMC for SDEs with application to the Langevin equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2342","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":"sha256:3c637aeb95c7a916de7aa5897937756dc73ac808fdeec97f694640316d610d54","target":"record","created_at":"2026-05-18T02:30:47Z","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":"e900aa3c25e0a6ff11c8b305e78e873dadf46fea5b47363f0c67a389f06b3077","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-09-08T13:46:43Z","title_canon_sha256":"578fb2a1cda506e7c042af9cb88dcbb208567c1216539ae8bfc415f6848d7a85"},"schema_version":"1.0","source":{"id":"1409.2342","kind":"arxiv","version":2}},"canonical_sha256":"fb14dbb5b9e694e97b42d82956b4914f10bb17f5c016c2d6dc5e56534049bf88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb14dbb5b9e694e97b42d82956b4914f10bb17f5c016c2d6dc5e56534049bf88","first_computed_at":"2026-05-18T02:30:47.000050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:47.000050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZMbs0aXLk8/c20fQDf/Rppl1LJ7Hc7Ol8HnUoDwvcoDs6Z3FtLCOi7TWioT10hLd6NrFwOXOhwCWYqvGHQuaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:47.000557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2342","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c637aeb95c7a916de7aa5897937756dc73ac808fdeec97f694640316d610d54","sha256:753ede2699cba1b73fa3d9d43162831ec1a6ed09ba81f5a8f003be6176a16963"],"state_sha256":"76293e9c9e3586a0c4482293c5acef7480079a21fd21368830c2199cd93061f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dDlQiSlJy2AdtTQ3BMSsvrq10G289YNaP1cO2RdeF62c1UQ8AqtEh8QSUp7T91E9yzsx1NhL50wdtE6ZJnsiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:26:12.063816Z","bundle_sha256":"2f2d90e947497b4198d696edd97302012e7c6df4ae9b462f311328ad3faea3b9"}}