{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EDFDPZ4U2VHSMT5INZ5XEJ5ZM4","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":"32a4ccbcb4c62c05afaeb3e71695803acc6f0428c5300f2fe5c3e84f26fd92b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-20T15:17:27Z","title_canon_sha256":"a05fdb40441f78c33912a5934631ed180a38704eb5f8a2738261e1c635891d0e"},"schema_version":"1.0","source":{"id":"1809.07669","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07669","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07669v3","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07669","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_12","alias_value":"EDFDPZ4U2VHS","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_16","alias_value":"EDFDPZ4U2VHSMT5I","created_at":"2026-07-05T03:21:03Z"},{"alias_kind":"pith_short_8","alias_value":"EDFDPZ4U","created_at":"2026-07-05T03:21:03Z"}],"graph_snapshots":[{"event_id":"sha256:7f9f10949d089f49f06fa1ca12811db7ba69b50c42951e716ef07c6798e61751","target":"graph","created_at":"2026-07-05T03:21:03Z","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/1809.07669/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze approximation rates by deep ReLU networks of a class of multi-variate solutions of Kolmogorov equations which arise in option pricing. Key technical devices are deep ReLU architectures capable of efficiently approximating tensor products. Combining this with results concerning the approximation of well behaved (i.e. fulfilling some smoothness properties) univariate functions, this provides insights into rates of deep ReLU approximation of multi-variate functions with tensor structures. We apply this in particular to the model problem given by the price of a European maximum option o","authors_text":"Arnulf Jentzen, Christoph Schwab, Dennis Elbr\\\"achter, Philipp Grohs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-20T15:17:27Z","title":"DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07669","kind":"arxiv","version":3},"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":"sha256:4b6b026add1b2a494e1cba30bb6c9436194f042d1789354fff899388b4d37d09","target":"record","created_at":"2026-07-05T03:21:03Z","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":"32a4ccbcb4c62c05afaeb3e71695803acc6f0428c5300f2fe5c3e84f26fd92b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-20T15:17:27Z","title_canon_sha256":"a05fdb40441f78c33912a5934631ed180a38704eb5f8a2738261e1c635891d0e"},"schema_version":"1.0","source":{"id":"1809.07669","kind":"arxiv","version":3}},"canonical_sha256":"20ca37e794d54f264fa86e7b7227b967187c8552637e1b436711aebe78c766cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ca37e794d54f264fa86e7b7227b967187c8552637e1b436711aebe78c766cd","first_computed_at":"2026-07-05T03:21:03.511823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:21:03.511823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CTPo82pQXqjL4s6Rr3EtLdsHykyitObKWAjaYYFi2Jy2ZlBmF/p9MjqbpheAY5rwtL6xbTiwJkfjzhjNDAeBBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:21:03.512202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07669","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b6b026add1b2a494e1cba30bb6c9436194f042d1789354fff899388b4d37d09","sha256:7f9f10949d089f49f06fa1ca12811db7ba69b50c42951e716ef07c6798e61751"],"state_sha256":"392d9ed222107d3b8c6d3c76d8be45459267ad3da883248e47b2fe0efd2e306c"}