{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XOIZQVPT566GS5ACRQZUNLZHYF","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":"b2d0328421f97e05319e65d4e5b9c02fa408d57db9686792345a08f10c4458c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-09T20:27:58Z","title_canon_sha256":"642a92e14e2b4035bfbc0352e39676b5d47f7c0edf468da10b7a03885d0acfc8"},"schema_version":"1.0","source":{"id":"1311.2207","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.2207","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"arxiv_version","alias_value":"1311.2207v1","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.2207","created_at":"2026-05-18T03:07:33Z"},{"alias_kind":"pith_short_12","alias_value":"XOIZQVPT566G","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XOIZQVPT566GS5AC","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XOIZQVPT","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c73c5b31caa88f49f289cab97ebccb250607482f4e3e7bf52db0d99bb304d8a0","target":"graph","created_at":"2026-05-18T03:07:33Z","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"},"paper":{"abstract_excerpt":"In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By applying a spectral Galerkin method for spatial discretization and a numerical scheme in time introduced by Jentzen $\\&$ Kloeden, we obtain the rate of path-wise convergence in the uniform topology. The main assumptions are either uniform bounds on the spectral Galerkin approximation or uniform bounds on the numerical data. Numerical examples illustrate the theor","authors_text":"Dirk Bl\\\"omker, Minoo Kamrani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-09T20:27:58Z","title":"Numerical Solution of Stochastic Partial Differential Equations with Correlated Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2207","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:af42419dd4b09e5d4d29ecb88fa0e7460db6bcccfd0bfb531f82f44ded95dca4","target":"record","created_at":"2026-05-18T03:07:33Z","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":"b2d0328421f97e05319e65d4e5b9c02fa408d57db9686792345a08f10c4458c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-09T20:27:58Z","title_canon_sha256":"642a92e14e2b4035bfbc0352e39676b5d47f7c0edf468da10b7a03885d0acfc8"},"schema_version":"1.0","source":{"id":"1311.2207","kind":"arxiv","version":1}},"canonical_sha256":"bb919855f3efbc6974028c3346af27c154d2e9810fb84295fb61f03ace874c22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb919855f3efbc6974028c3346af27c154d2e9810fb84295fb61f03ace874c22","first_computed_at":"2026-05-18T03:07:33.257948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:33.257948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gs3MJt4HXCTFfnDKjQiobkyMbhNcB/VgxRtBBQOIuD19TALPa6UJXZSrpqqlb70zUM6kPEzEZIYq/vPLnpO1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:33.258555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.2207","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af42419dd4b09e5d4d29ecb88fa0e7460db6bcccfd0bfb531f82f44ded95dca4","sha256:c73c5b31caa88f49f289cab97ebccb250607482f4e3e7bf52db0d99bb304d8a0"],"state_sha256":"a34454840978f1af59df8037dbab83ad7ca16d8288e33a39825368e6941ce0e8"}