{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PYYQTYXLBZVRN2FIA6EHP3S2EC","short_pith_number":"pith:PYYQTYXL","schema_version":"1.0","canonical_sha256":"7e3109e2eb0e6b16e8a8078877ee5a20978afadb9def2134cdb103fcc50a60b4","source":{"kind":"arxiv","id":"1903.06066","version":1},"attestation_state":"computed","paper":{"title":"Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Arnulf Jentzen, Diyora Salimova, Felix Lindner, Martin Hutzenthaler, Matteo Beccari, Ryan Kurniawan","submitted_at":"2019-03-14T15:13:31Z","abstract_excerpt":"The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing nonlinearities. It remained an open question whether such a divergence phenomenon also holds in the case of stochastic partial differential equations with superlinearly growing nonlinearities such as stochastic Allen-Cahn equations. In this work we solve this problem by proving that full-discrete exponential Euler and full-discrete linear-implic"},"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":"1903.06066","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-14T15:13:31Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d83278322d19e550e685f8dfbd7c7093f73f591af6557331358e515dc0009ca3","abstract_canon_sha256":"8e0e3eb18754b0f2d18df89e6c9517de986061f84e476c2138244345f6aaee99"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:15.463859Z","signature_b64":"rh1CdL7u7Nlco2kguBAFikR3RCXDlotFAUclpDBdhP5DzB34ORX7/G7EWf4DMJxnPjBoRcmug5CfuyGTd9RMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e3109e2eb0e6b16e8a8078877ee5a20978afadb9def2134cdb103fcc50a60b4","last_reissued_at":"2026-05-17T23:51:15.463241Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:15.463241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Arnulf Jentzen, Diyora Salimova, Felix Lindner, Martin Hutzenthaler, Matteo Beccari, Ryan Kurniawan","submitted_at":"2019-03-14T15:13:31Z","abstract_excerpt":"The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing nonlinearities. It remained an open question whether such a divergence phenomenon also holds in the case of stochastic partial differential equations with superlinearly growing nonlinearities such as stochastic Allen-Cahn equations. In this work we solve this problem by proving that full-discrete exponential Euler and full-discrete linear-implic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06066","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":""},"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":"1903.06066","created_at":"2026-05-17T23:51:15.463327+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.06066v1","created_at":"2026-05-17T23:51:15.463327+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06066","created_at":"2026-05-17T23:51:15.463327+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYYQTYXLBZVR","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYYQTYXLBZVRN2FI","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYYQTYXL","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2406.03058","citing_title":"Higher order approximation of nonlinear SPDEs with additive space-time white noise","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC","json":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC.json","graph_json":"https://pith.science/api/pith-number/PYYQTYXLBZVRN2FIA6EHP3S2EC/graph.json","events_json":"https://pith.science/api/pith-number/PYYQTYXLBZVRN2FIA6EHP3S2EC/events.json","paper":"https://pith.science/paper/PYYQTYXL"},"agent_actions":{"view_html":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC","download_json":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC.json","view_paper":"https://pith.science/paper/PYYQTYXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.06066&json=true","fetch_graph":"https://pith.science/api/pith-number/PYYQTYXLBZVRN2FIA6EHP3S2EC/graph.json","fetch_events":"https://pith.science/api/pith-number/PYYQTYXLBZVRN2FIA6EHP3S2EC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC/action/storage_attestation","attest_author":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC/action/author_attestation","sign_citation":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC/action/citation_signature","submit_replication":"https://pith.science/pith/PYYQTYXLBZVRN2FIA6EHP3S2EC/action/replication_record"}},"created_at":"2026-05-17T23:51:15.463327+00:00","updated_at":"2026-05-17T23:51:15.463327+00:00"}