{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:P7EXA4BEAH6V2IB65HWIYUCO5F","short_pith_number":"pith:P7EXA4BE","schema_version":"1.0","canonical_sha256":"7fc970702401fd5d203ee9ec8c504ee9775f3704a6252803343c4c9ad8bd39f8","source":{"kind":"arxiv","id":"2406.10876","version":1},"attestation_state":"computed","paper":{"title":"Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.PR"],"primary_cat":"cs.LG","authors_text":"Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett, Julia Ackermann","submitted_at":"2024-06-16T09:59:29Z","abstract_excerpt":"It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer under the curse of dimensionality (COD) in the sense that the number of computational operations of the approximation method grows at least exponentially in the PDE dimension and with such methods it is essentially impossible to approximately solve high-dimensional PDEs even when the fastest currently available computers are used. However, in the last years great progress has been made in this area of research throu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2406.10876","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-06-16T09:59:29Z","cross_cats_sorted":["cs.NA","math.NA","math.PR"],"title_canon_sha256":"e4f0efa35a85281f028c6b55c41f1d587f0261c13e750e877baed7f3ed6cafa8","abstract_canon_sha256":"058ffd1d8cd337891bf8a93805361a4d6e1b623dfc962802e709abc0635dd159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:32:45.609818Z","signature_b64":"pkb7d6ERfxagl2ywizaUqdOMsvPOEy5Ou9dbMP2pBBncKhG5IajxwFhZ0uQr+1V2ZGmqLKrXjkF+yJJDbCwHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fc970702401fd5d203ee9ec8c504ee9775f3704a6252803343c4c9ad8bd39f8","last_reissued_at":"2026-07-05T08:32:45.609408Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:32:45.609408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.PR"],"primary_cat":"cs.LG","authors_text":"Arnulf Jentzen, Benno Kuckuck, Joshua Lee Padgett, Julia Ackermann","submitted_at":"2024-06-16T09:59:29Z","abstract_excerpt":"It is a challenging topic in applied mathematics to solve high-dimensional nonlinear partial differential equations (PDEs). Standard approximation methods for nonlinear PDEs suffer under the curse of dimensionality (COD) in the sense that the number of computational operations of the approximation method grows at least exponentially in the PDE dimension and with such methods it is essentially impossible to approximately solve high-dimensional PDEs even when the fastest currently available computers are used. However, in the last years great progress has been made in this area of research throu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.10876","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/2406.10876/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2406.10876","created_at":"2026-07-05T08:32:45.609466+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.10876v1","created_at":"2026-07-05T08:32:45.609466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.10876","created_at":"2026-07-05T08:32:45.609466+00:00"},{"alias_kind":"pith_short_12","alias_value":"P7EXA4BEAH6V","created_at":"2026-07-05T08:32:45.609466+00:00"},{"alias_kind":"pith_short_16","alias_value":"P7EXA4BEAH6V2IB6","created_at":"2026-07-05T08:32:45.609466+00:00"},{"alias_kind":"pith_short_8","alias_value":"P7EXA4BE","created_at":"2026-07-05T08:32:45.609466+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.22851","citing_title":"Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F","json":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F.json","graph_json":"https://pith.science/api/pith-number/P7EXA4BEAH6V2IB65HWIYUCO5F/graph.json","events_json":"https://pith.science/api/pith-number/P7EXA4BEAH6V2IB65HWIYUCO5F/events.json","paper":"https://pith.science/paper/P7EXA4BE"},"agent_actions":{"view_html":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F","download_json":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F.json","view_paper":"https://pith.science/paper/P7EXA4BE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.10876&json=true","fetch_graph":"https://pith.science/api/pith-number/P7EXA4BEAH6V2IB65HWIYUCO5F/graph.json","fetch_events":"https://pith.science/api/pith-number/P7EXA4BEAH6V2IB65HWIYUCO5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F/action/storage_attestation","attest_author":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F/action/author_attestation","sign_citation":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F/action/citation_signature","submit_replication":"https://pith.science/pith/P7EXA4BEAH6V2IB65HWIYUCO5F/action/replication_record"}},"created_at":"2026-07-05T08:32:45.609466+00:00","updated_at":"2026-07-05T08:32:45.609466+00:00"}