{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:JCA43TMIOMFGJQ5BAZFXK6E46L","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":"1236db3f5bb5bc64403b7f80441c48c081d649b09d31ec4a12663784180b9447","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-05-28T11:03:35Z","title_canon_sha256":"acd5429976ba0d88458e09a8b0afc870770f683a3155e93774331b779a9c3064"},"schema_version":"1.0","source":{"id":"2205.14398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.14398","created_at":"2026-07-05T04:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"2205.14398v1","created_at":"2026-07-05T04:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.14398","created_at":"2026-07-05T04:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"JCA43TMIOMFG","created_at":"2026-07-05T04:27:17Z"},{"alias_kind":"pith_short_16","alias_value":"JCA43TMIOMFGJQ5B","created_at":"2026-07-05T04:27:17Z"},{"alias_kind":"pith_short_8","alias_value":"JCA43TMI","created_at":"2026-07-05T04:27:17Z"}],"graph_snapshots":[{"event_id":"sha256:ac5fc931096c4ba63742591c4e9b74bc6d03cd420d35601b9c2bc8048f2f3ed9","target":"graph","created_at":"2026-07-05T04:27:17Z","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/2205.14398/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, while the required number of parameters in the networks grow at most polynomially in both dimension $d \\in \\mathbb{N}$ and prescribed reciprocal accuracy $\\varepsilon$. Previously, this has only been proven in the case of semilinear heat equations.","authors_text":"Martin Hutzenthaler, Petru A. Cioica-Licht, P. Tobias Werner","cross_cats":["cs.NA","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-05-28T11:03:35Z","title":"Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.14398","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:eb6d799a240d2f03788fa8beb3a657eda284a37762dc07c20557fad306e4553d","target":"record","created_at":"2026-07-05T04:27:17Z","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":"1236db3f5bb5bc64403b7f80441c48c081d649b09d31ec4a12663784180b9447","cross_cats_sorted":["cs.NA","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-05-28T11:03:35Z","title_canon_sha256":"acd5429976ba0d88458e09a8b0afc870770f683a3155e93774331b779a9c3064"},"schema_version":"1.0","source":{"id":"2205.14398","kind":"arxiv","version":1}},"canonical_sha256":"4881cdcd88730a64c3a1064b75789cf2d5c6a8b6e05074afa899b345b1340fb0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4881cdcd88730a64c3a1064b75789cf2d5c6a8b6e05074afa899b345b1340fb0","first_computed_at":"2026-07-05T04:27:17.093214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:27:17.093214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sm9ebnqXPcl27HOAVorOCuH5SSWt7ouAK4XTAJ1JfS5N5pYuBU2fH2JZHNFfm1TUnovFrOikO2LGc8x0xlzWCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:27:17.093887Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.14398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6d799a240d2f03788fa8beb3a657eda284a37762dc07c20557fad306e4553d","sha256:ac5fc931096c4ba63742591c4e9b74bc6d03cd420d35601b9c2bc8048f2f3ed9"],"state_sha256":"275bbb405e1365253a7a7376f1ae856222c4a15587b5f8753eb6b7bfe63dadf0"}