{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FROMKJ64KLE6CYDHHKAUCQUKZ7","short_pith_number":"pith:FROMKJ64","canonical_record":{"source":{"id":"2202.02717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-02-06T06:33:15Z","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"title_canon_sha256":"1ec646fc7bc6aa76a1c0d6884e380c0d4b82fd5a9f88c010d76b728050b81934","abstract_canon_sha256":"c03876cd370a06e0772fb02d47cef3b20d3adcec911741e1d544cca92e3e9682"},"schema_version":"1.0"},"canonical_sha256":"2c5cc527dc52c9e160673a8141428acfdd2d3201f27b1cabbc128668a621ef2d","source":{"kind":"arxiv","id":"2202.02717","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.02717","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2202.02717v2","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.02717","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"FROMKJ64KLE6","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"FROMKJ64KLE6CYDH","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"FROMKJ64","created_at":"2026-07-05T09:24:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FROMKJ64KLE6CYDHHKAUCQUKZ7","target":"record","payload":{"canonical_record":{"source":{"id":"2202.02717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-02-06T06:33:15Z","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"title_canon_sha256":"1ec646fc7bc6aa76a1c0d6884e380c0d4b82fd5a9f88c010d76b728050b81934","abstract_canon_sha256":"c03876cd370a06e0772fb02d47cef3b20d3adcec911741e1d544cca92e3e9682"},"schema_version":"1.0"},"canonical_sha256":"2c5cc527dc52c9e160673a8141428acfdd2d3201f27b1cabbc128668a621ef2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:24:14.460798Z","signature_b64":"ZKfyn3+K04eEuTvn740uZLLpqUhCa2dehpNAceSFMgu8GzliC/Xb+pGtznlXvic5Of0fS7NXHB9F/c32NMkyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c5cc527dc52c9e160673a8141428acfdd2d3201f27b1cabbc128668a621ef2d","last_reissued_at":"2026-07-05T09:24:14.460249Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:24:14.460249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.02717","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":"2026-07-05T09:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e2jG86+dTinHggYG+ho6hwB5yiqK97SOkzRiUHWeJktukwo4kcqeFYWV/BPF/7vNtwhMqhSKVBz1eG40lgxtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:09:55.028633Z"},"content_sha256":"2ff8e0b816205d067d0a5d37da7bb950e17a79c4443f0e5f960c72341c04da38","schema_version":"1.0","event_id":"sha256:2ff8e0b816205d067d0a5d37da7bb950e17a79c4443f0e5f960c72341c04da38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FROMKJ64KLE6CYDHHKAUCQUKZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.PR"],"primary_cat":"math.NA","authors_text":"Arnulf Jentzen, Marvin S. M\\\"uller, Philippe von Wurstemberger, Sebastian Becker","submitted_at":"2022-02-06T06:33:15Z","abstract_excerpt":"In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of Monte Carlo (MC) simulations. To obtain a good approximation the MC sample size usually needs to be considerably large resulting in a long computing time to obtain a single approximation. In this paper we introduce a new approximation strategy for parametric approximation problems including the parametric financial pricing problems described above. A central as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02717","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.02717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RrplpYjMPFaSKXg6K9R61Ft2Nly/XjKJ4xEnt2EG8TRyTMohEt4kS9hebYYq6mhCIFzNYqiszoHH0BxK1do+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:09:55.029501Z"},"content_sha256":"fbcf8e7e1bfd128c9d9fe0caf7883ae9201b0be9b809b7a8cb0c886e6187a5c3","schema_version":"1.0","event_id":"sha256:fbcf8e7e1bfd128c9d9fe0caf7883ae9201b0be9b809b7a8cb0c886e6187a5c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/bundle.json","state_url":"https://pith.science/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/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":"2026-08-04T15:09:55Z","links":{"resolver":"https://pith.science/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7","bundle":"https://pith.science/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/bundle.json","state":"https://pith.science/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FROMKJ64KLE6CYDHHKAUCQUKZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FROMKJ64KLE6CYDHHKAUCQUKZ7","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":"c03876cd370a06e0772fb02d47cef3b20d3adcec911741e1d544cca92e3e9682","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-02-06T06:33:15Z","title_canon_sha256":"1ec646fc7bc6aa76a1c0d6884e380c0d4b82fd5a9f88c010d76b728050b81934"},"schema_version":"1.0","source":{"id":"2202.02717","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.02717","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2202.02717v2","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.02717","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"FROMKJ64KLE6","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"FROMKJ64KLE6CYDH","created_at":"2026-07-05T09:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"FROMKJ64","created_at":"2026-07-05T09:24:14Z"}],"graph_snapshots":[{"event_id":"sha256:fbcf8e7e1bfd128c9d9fe0caf7883ae9201b0be9b809b7a8cb0c886e6187a5c3","target":"graph","created_at":"2026-07-05T09:24:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.02717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of Monte Carlo (MC) simulations. To obtain a good approximation the MC sample size usually needs to be considerably large resulting in a long computing time to obtain a single approximation. In this paper we introduce a new approximation strategy for parametric approximation problems including the parametric financial pricing problems described above. A central as","authors_text":"Arnulf Jentzen, Marvin S. M\\\"uller, Philippe von Wurstemberger, Sebastian Becker","cross_cats":["cs.NA","math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-02-06T06:33:15Z","title":"Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02717","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":"sha256:2ff8e0b816205d067d0a5d37da7bb950e17a79c4443f0e5f960c72341c04da38","target":"record","created_at":"2026-07-05T09:24:14Z","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":"c03876cd370a06e0772fb02d47cef3b20d3adcec911741e1d544cca92e3e9682","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-02-06T06:33:15Z","title_canon_sha256":"1ec646fc7bc6aa76a1c0d6884e380c0d4b82fd5a9f88c010d76b728050b81934"},"schema_version":"1.0","source":{"id":"2202.02717","kind":"arxiv","version":2}},"canonical_sha256":"2c5cc527dc52c9e160673a8141428acfdd2d3201f27b1cabbc128668a621ef2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c5cc527dc52c9e160673a8141428acfdd2d3201f27b1cabbc128668a621ef2d","first_computed_at":"2026-07-05T09:24:14.460249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:24:14.460249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZKfyn3+K04eEuTvn740uZLLpqUhCa2dehpNAceSFMgu8GzliC/Xb+pGtznlXvic5Of0fS7NXHB9F/c32NMkyAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:24:14.460798Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.02717","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ff8e0b816205d067d0a5d37da7bb950e17a79c4443f0e5f960c72341c04da38","sha256:fbcf8e7e1bfd128c9d9fe0caf7883ae9201b0be9b809b7a8cb0c886e6187a5c3"],"state_sha256":"08521df6e6412f63386ebf6645b41c623175cebe655c77ad4eb2bfa16be106cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+9PW07yDnq4uALvJaRfdVQWci3alT2PBmxBSruEEyYIWy2Sx4DN3GAu8PZWkzIGf5chQ0y7eMuz2ZLw8XWbHBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:09:55.072601Z","bundle_sha256":"06e319d6b7dcb698d745d31e6c44095043a572239c92276ede7e9ee4d251c827"}}