{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GHCM4KWXYTT7GO53MK5VZIH7YF","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":"9b8480735342ae243e590a1087ce44ab75d11cad469bac193b61d70f32b0eba9","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-08T11:18:27Z","title_canon_sha256":"70ab0e1f59cd7f322c29c0776b25c6a0ed7969192c9a46aa2dc56f240c70cc40"},"schema_version":"1.0","source":{"id":"1911.03188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.03188","created_at":"2026-07-05T00:18:00Z"},{"alias_kind":"arxiv_version","alias_value":"1911.03188v1","created_at":"2026-07-05T00:18:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.03188","created_at":"2026-07-05T00:18:00Z"},{"alias_kind":"pith_short_12","alias_value":"GHCM4KWXYTT7","created_at":"2026-07-05T00:18:00Z"},{"alias_kind":"pith_short_16","alias_value":"GHCM4KWXYTT7GO53","created_at":"2026-07-05T00:18:00Z"},{"alias_kind":"pith_short_8","alias_value":"GHCM4KWX","created_at":"2026-07-05T00:18:00Z"}],"graph_snapshots":[{"event_id":"sha256:3af49ba2cd53d993d2764722c847ff0b2e8cf8c06bc04adca8dbf005e9b84806","target":"graph","created_at":"2026-07-05T00:18:00Z","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/1911.03188/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numerical approximation schemes studied in the scientific literature suffer under the curse of dimensionality in the sense that the number of computational operations needed to compute an approximation with an error of size at most $ \\varepsilon > 0 $ grows at least exponentially in the PDE dimension $ d \\in \\mathbb{N} $ or in the reciprocal of $ \\varepsilon $. Recently, so-called full-history recursive multilevel Picard (","authors_text":"Arnulf Jentzen, Michael B. Giles, Timo Welti","cross_cats":["cs.NA","math.AP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-08T11:18:27Z","title":"Generalised multilevel Picard approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.03188","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:e79b67d8ec83eb433ae1faee9deca86e9250030f9fa8b38a5e7987f1cdb7243c","target":"record","created_at":"2026-07-05T00:18:00Z","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":"9b8480735342ae243e590a1087ce44ab75d11cad469bac193b61d70f32b0eba9","cross_cats_sorted":["cs.NA","math.AP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-11-08T11:18:27Z","title_canon_sha256":"70ab0e1f59cd7f322c29c0776b25c6a0ed7969192c9a46aa2dc56f240c70cc40"},"schema_version":"1.0","source":{"id":"1911.03188","kind":"arxiv","version":1}},"canonical_sha256":"31c4ce2ad7c4e7f33bbb62bb5ca0ffc15a714b30fcc2aa5c7f6ffb2d77ae8964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31c4ce2ad7c4e7f33bbb62bb5ca0ffc15a714b30fcc2aa5c7f6ffb2d77ae8964","first_computed_at":"2026-07-05T00:18:00.387032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:18:00.387032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bKABqpMKovyhoOQyyMtcgqrSakraOEsng0inO4OgkuPJEwYOSIrbVZDoBgWIeyF+Jx8mbThehadovOifWu18Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:18:00.387383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.03188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e79b67d8ec83eb433ae1faee9deca86e9250030f9fa8b38a5e7987f1cdb7243c","sha256:3af49ba2cd53d993d2764722c847ff0b2e8cf8c06bc04adca8dbf005e9b84806"],"state_sha256":"a67a74dda32f943cdd21b2dd40aec14bc0a8b1cbfe1766dfe5c197a6a4284759"}