{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NKBMZQQEOKZZ34F3THLM4KGWWV","short_pith_number":"pith:NKBMZQQE","canonical_record":{"source":{"id":"1709.05963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-18T14:16:06Z","cross_cats_sorted":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"title_canon_sha256":"435d7d0a17291ade91f00ae53c6cad04dd985a8953c21fb9a08e48ff44a3b0af","abstract_canon_sha256":"5b4c5f6e66e9f53b292b6074cc526a3cfcf652c6143d9e737dc2477146a4c504"},"schema_version":"1.0"},"canonical_sha256":"6a82ccc20472b39df0bb99d6ce28d6b56f27274e82ae4e5ca83d9091a7acb590","source":{"kind":"arxiv","id":"1709.05963","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05963","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05963v1","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05963","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"NKBMZQQEOKZZ","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_16","alias_value":"NKBMZQQEOKZZ34F3","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_8","alias_value":"NKBMZQQE","created_at":"2026-06-04T19:10:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NKBMZQQEOKZZ34F3THLM4KGWWV","target":"record","payload":{"canonical_record":{"source":{"id":"1709.05963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-18T14:16:06Z","cross_cats_sorted":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"title_canon_sha256":"435d7d0a17291ade91f00ae53c6cad04dd985a8953c21fb9a08e48ff44a3b0af","abstract_canon_sha256":"5b4c5f6e66e9f53b292b6074cc526a3cfcf652c6143d9e737dc2477146a4c504"},"schema_version":"1.0"},"canonical_sha256":"6a82ccc20472b39df0bb99d6ce28d6b56f27274e82ae4e5ca83d9091a7acb590","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T19:10:59.663640Z","signature_b64":"Cx5YrYaashXtqHvOIDHMKGGCevCA33PGkP59manlVGPgelXFYkbwLuEJwINJOHVeMW2wd4ubu494ryEKaKCAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a82ccc20472b39df0bb99d6ce28d6b56f27274e82ae4e5ca83d9091a7acb590","last_reissued_at":"2026-06-04T19:10:59.663228Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T19:10:59.663228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.05963","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":"2026-06-04T19:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YjLrEI0JCTE28Vghq9V9MiXpG6QRhzB8Z6H9wUb5BmptGmRkfvOnqqi6NV1kbWcZifCSab9mJdQ+vH5D3un2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:41:24.413049Z"},"content_sha256":"742281e8cc9e93db45a81a9479b30451c74612fc7297dcf12071eb2fcdf24717","schema_version":"1.0","event_id":"sha256:742281e8cc9e93db45a81a9479b30451c74612fc7297dcf12071eb2fcdf24717"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NKBMZQQEOKZZ34F3THLM4KGWWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"primary_cat":"math.NA","authors_text":"Arnulf Jentzen, Christian Beck, Weinan E","submitted_at":"2017-09-18T14:16:06Z","abstract_excerpt":"High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05963","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1709.05963/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":"2026-06-04T19:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5DQ4Rk+LP/z7UFd1iWwCamGo/mHq//zu0HP50Ed1saKcqTMtExD8ohm7VVVS6YGFOaRJHQPOigjB2B8r5BaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T05:41:24.413437Z"},"content_sha256":"b1c7df99858603b71f84edded290e010ba39c9133942263c0f4ccbcff84d8988","schema_version":"1.0","event_id":"sha256:b1c7df99858603b71f84edded290e010ba39c9133942263c0f4ccbcff84d8988"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/bundle.json","state_url":"https://pith.science/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/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":"2026-07-05T05:41:24Z","links":{"resolver":"https://pith.science/pith/NKBMZQQEOKZZ34F3THLM4KGWWV","bundle":"https://pith.science/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/bundle.json","state":"https://pith.science/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NKBMZQQEOKZZ34F3THLM4KGWWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NKBMZQQEOKZZ34F3THLM4KGWWV","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":"5b4c5f6e66e9f53b292b6074cc526a3cfcf652c6143d9e737dc2477146a4c504","cross_cats_sorted":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-18T14:16:06Z","title_canon_sha256":"435d7d0a17291ade91f00ae53c6cad04dd985a8953c21fb9a08e48ff44a3b0af"},"schema_version":"1.0","source":{"id":"1709.05963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05963","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05963v1","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05963","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"NKBMZQQEOKZZ","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_16","alias_value":"NKBMZQQEOKZZ34F3","created_at":"2026-06-04T19:10:59Z"},{"alias_kind":"pith_short_8","alias_value":"NKBMZQQE","created_at":"2026-06-04T19:10:59Z"}],"graph_snapshots":[{"event_id":"sha256:b1c7df99858603b71f84edded290e010ba39c9133942263c0f4ccbcff84d8988","target":"graph","created_at":"2026-06-04T19:10:59Z","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/1709.05963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model.","authors_text":"Arnulf Jentzen, Christian Beck, Weinan E","cross_cats":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-18T14:16:06Z","title":"Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05963","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":"sha256:742281e8cc9e93db45a81a9479b30451c74612fc7297dcf12071eb2fcdf24717","target":"record","created_at":"2026-06-04T19:10:59Z","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":"5b4c5f6e66e9f53b292b6074cc526a3cfcf652c6143d9e737dc2477146a4c504","cross_cats_sorted":["cs.LG","cs.NA","cs.NE","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-09-18T14:16:06Z","title_canon_sha256":"435d7d0a17291ade91f00ae53c6cad04dd985a8953c21fb9a08e48ff44a3b0af"},"schema_version":"1.0","source":{"id":"1709.05963","kind":"arxiv","version":1}},"canonical_sha256":"6a82ccc20472b39df0bb99d6ce28d6b56f27274e82ae4e5ca83d9091a7acb590","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a82ccc20472b39df0bb99d6ce28d6b56f27274e82ae4e5ca83d9091a7acb590","first_computed_at":"2026-06-04T19:10:59.663228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T19:10:59.663228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cx5YrYaashXtqHvOIDHMKGGCevCA33PGkP59manlVGPgelXFYkbwLuEJwINJOHVeMW2wd4ubu494ryEKaKCAAA==","signature_status":"signed_v1","signed_at":"2026-06-04T19:10:59.663640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:742281e8cc9e93db45a81a9479b30451c74612fc7297dcf12071eb2fcdf24717","sha256:b1c7df99858603b71f84edded290e010ba39c9133942263c0f4ccbcff84d8988"],"state_sha256":"1af7963459bb680cff7e4dc24a58e72b1909d5b3d7682b43e082f0ee349f2770"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfIdIwoT1PtDeqLpIK/YXzcbqpkkTka1ukSkHd6AvzG3Z0kt1UEEF28sbIm5S8XXj3U/JzjK0CcQqVYzTHhHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T05:41:24.415409Z","bundle_sha256":"dc764e785abacd1ba02f4cf6d01d196fbbdfbb79cc534f0e900d22c220faa40c"}}