{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EIR54H2NF7V7O4JWUTYNSVYAMA","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":"16e53a81ac5323a542088bb531b422a27f840449a1d1cf3418b8eb10911b98bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-19T08:37:38Z","title_canon_sha256":"b0f88cc4f08dc8fda1e80fd11ee610724a7a49916740f9f795e013c7fd361b5e"},"schema_version":"1.0","source":{"id":"1303.4510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4510","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4510v1","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4510","created_at":"2026-05-18T03:30:26Z"},{"alias_kind":"pith_short_12","alias_value":"EIR54H2NF7V7","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EIR54H2NF7V7O4JW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EIR54H2N","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:ff7265fb19c023af5f3cc3cffabb5d08f09874182567e7822ad6dacaae69ced3","target":"graph","created_at":"2026-05-18T03:30:26Z","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 the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of It\\^o stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order one and order two conditions for the coefficients of explicit stochastic Runge-Kutta methods are solved and the solution space of the possible coefficients is analyzed. A full classification of the coefficients for such stochastic Runge-Kutta schemes of order one and two with minimal stage numbers is calculated. Further, ","authors_text":"Andreas R\\\"o{\\ss}ler, Kristian Debrabant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-19T08:37:38Z","title":"Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4510","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":"sha256:5237a965791e03613e217421332e3f8c861931ab4eae9821b8027ddf18e8d83e","target":"record","created_at":"2026-05-18T03:30:26Z","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":"16e53a81ac5323a542088bb531b422a27f840449a1d1cf3418b8eb10911b98bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-03-19T08:37:38Z","title_canon_sha256":"b0f88cc4f08dc8fda1e80fd11ee610724a7a49916740f9f795e013c7fd361b5e"},"schema_version":"1.0","source":{"id":"1303.4510","kind":"arxiv","version":1}},"canonical_sha256":"2223de1f4d2febf77136a4f0d95700601394c93cc39d71f36f481062a6b599d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2223de1f4d2febf77136a4f0d95700601394c93cc39d71f36f481062a6b599d5","first_computed_at":"2026-05-18T03:30:26.967900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:26.967900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+6HyKNVais29EBbKZnlBNrLS5RSL/2RjOQQphN+Nrp8XkQpJnVyczIquQl1K9HXs/oxjauK86P1KYX9IrHO7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:26.968406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5237a965791e03613e217421332e3f8c861931ab4eae9821b8027ddf18e8d83e","sha256:ff7265fb19c023af5f3cc3cffabb5d08f09874182567e7822ad6dacaae69ced3"],"state_sha256":"ac7eb47cbfae71402a6d305bc768c3fa0e31985997915c019d8eda956a5ad7da"}