{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2KQRLA6HLD6CSK56P3BBGZ3VKG","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":"9252ba3f7266fc587f5f0e1c069207166a86a52d6e7636bfbe968aaa22b96b13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-21T13:27:12Z","title_canon_sha256":"29f0c91bc814699cc585ef83a03d227ca39cec5db64efacb0ce5c3434e202b35"},"schema_version":"1.0","source":{"id":"1606.06560","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06560","created_at":"2026-05-18T00:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06560v1","created_at":"2026-05-18T00:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06560","created_at":"2026-05-18T00:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"2KQRLA6HLD6C","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2KQRLA6HLD6CSK56","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2KQRLA6H","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:cf2cd2fc37bbc971921f49339860027f7678f7c57c9accc233bbeabb4650629b","target":"graph","created_at":"2026-05-18T00:50:37Z","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":"The Crank-Nicolson (short for C-N) scheme for solving {\\it backward stochastic differential equation} (BSDE), driven by Brownian motions, was first developed by the authors W. Zhao, L. Chen and S. Peng [SIAM J. Sci. Comput., 28 (2006), 1563--1581], and numerical experiments showed that the accuracy of this C-N scheme was of second order for solving BSDE. This C-N scheme was extended to solve decoupled {\\it forward-backward stochastic differential equations} (FBSDEs) by W. Zhao, Y. Li and Y. Fu [Sci. China. Math., 57 (2014), 665--686], and it was numerically shown that the accuracy of the exten","authors_text":"Jie Yang, Weidong Zhao, Yang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-21T13:27:12Z","title":"Convergence Error Estimates of the Crank-Nicolson Scheme for Solving Decoupled FBSDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06560","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":"sha256:1c34b2a601629e422a63216f37afb8cbdeb5d74162469d5134ddd0270964f01c","target":"record","created_at":"2026-05-18T00:50:37Z","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":"9252ba3f7266fc587f5f0e1c069207166a86a52d6e7636bfbe968aaa22b96b13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-06-21T13:27:12Z","title_canon_sha256":"29f0c91bc814699cc585ef83a03d227ca39cec5db64efacb0ce5c3434e202b35"},"schema_version":"1.0","source":{"id":"1606.06560","kind":"arxiv","version":1}},"canonical_sha256":"d2a11583c758fc292bbe7ec2136775519a8dd0034508b4011d4f7cc33b158f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2a11583c758fc292bbe7ec2136775519a8dd0034508b4011d4f7cc33b158f54","first_computed_at":"2026-05-18T00:50:37.934367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:37.934367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IMVwwYZr6Tx5L6XBLq+PcF0CjGdndhV9CjMjwBPJLJYSo/mm6ZRlqHGqSf710bGRakZkiQw2J9SGhp4mdqfjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:37.935053Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06560","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c34b2a601629e422a63216f37afb8cbdeb5d74162469d5134ddd0270964f01c","sha256:cf2cd2fc37bbc971921f49339860027f7678f7c57c9accc233bbeabb4650629b"],"state_sha256":"f9948d665aceea7502f151c7f8118a85b4f773f386dd64193956d463a2a2390a"}