{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G7E3NJDPCT644TZGMHDWEJKGZY","short_pith_number":"pith:G7E3NJDP","canonical_record":{"source":{"id":"1808.02173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-08-07T01:17:10Z","cross_cats_sorted":["math.PR","q-fin.MF"],"title_canon_sha256":"7fdac941b696b0fd359f0782ebe8fe4354883a60033d40139f18eb1dec22645e","abstract_canon_sha256":"e0d55c95a7712a5c851bfd3cd16a176ccf3c9bb319627feff64ab35b999b1a8e"},"schema_version":"1.0"},"canonical_sha256":"37c9b6a46f14fdce4f2661c7622546ce3fa03d048c8cf4fef376653c61180f03","source":{"kind":"arxiv","id":"1808.02173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02173","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02173v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02173","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"G7E3NJDPCT64","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G7E3NJDPCT644TZG","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G7E3NJDP","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G7E3NJDPCT644TZGMHDWEJKGZY","target":"record","payload":{"canonical_record":{"source":{"id":"1808.02173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-08-07T01:17:10Z","cross_cats_sorted":["math.PR","q-fin.MF"],"title_canon_sha256":"7fdac941b696b0fd359f0782ebe8fe4354883a60033d40139f18eb1dec22645e","abstract_canon_sha256":"e0d55c95a7712a5c851bfd3cd16a176ccf3c9bb319627feff64ab35b999b1a8e"},"schema_version":"1.0"},"canonical_sha256":"37c9b6a46f14fdce4f2661c7622546ce3fa03d048c8cf4fef376653c61180f03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:47.369047Z","signature_b64":"6oB9CRRMvZGtFRpqA9d8Jp3J3I4zQdElpsfJtgXBBtF3aCD3Y1edn4wNMlhJh9a8MVBIiShINKbqtDNgXNoaCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37c9b6a46f14fdce4f2661c7622546ce3fa03d048c8cf4fef376653c61180f03","last_reissued_at":"2026-05-18T00:08:47.368395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:47.368395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.02173","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bibg/XKr+vu1P7HVLAiXz4yYWl2qiuWGqePsaIjoJjO/ZyXKUjV4ds1hCdj29KJdexaj4vjZ6nJxJ+eASdB3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:14:46.179114Z"},"content_sha256":"60a6da96d70863e10eb34a55c9af67a7d62196bc9da72e3c0e85782241bce335","schema_version":"1.0","event_id":"sha256:60a6da96d70863e10eb34a55c9af67a7d62196bc9da72e3c0e85782241bce335"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G7E3NJDPCT644TZGMHDWEJKGZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapted $\\theta$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.PR","q-fin.MF"],"primary_cat":"math.NA","authors_text":"Chang-Ho Rim, Chol-Kyu Pak, Mun-Chol KiM","submitted_at":"2018-08-07T01:17:10Z","abstract_excerpt":"In this paper we propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\\theta$-scheme, we reduce truncation errors by taking $\\theta$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02173","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2x6yfLIBRsRw7q+gjnUTINzMBjoKHkoMQHq4V9IyF7V4q5qACO5aXOdebNC718JZ7Hb87nMCli9Q/S5N9FM3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T20:14:46.179465Z"},"content_sha256":"a8b622d969d799e88970cf0e2ecd0eea39f98cac37da3fc2bc0d149e96f6b853","schema_version":"1.0","event_id":"sha256:a8b622d969d799e88970cf0e2ecd0eea39f98cac37da3fc2bc0d149e96f6b853"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7E3NJDPCT644TZGMHDWEJKGZY/bundle.json","state_url":"https://pith.science/pith/G7E3NJDPCT644TZGMHDWEJKGZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7E3NJDPCT644TZGMHDWEJKGZY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T20:14:46Z","links":{"resolver":"https://pith.science/pith/G7E3NJDPCT644TZGMHDWEJKGZY","bundle":"https://pith.science/pith/G7E3NJDPCT644TZGMHDWEJKGZY/bundle.json","state":"https://pith.science/pith/G7E3NJDPCT644TZGMHDWEJKGZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7E3NJDPCT644TZGMHDWEJKGZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G7E3NJDPCT644TZGMHDWEJKGZY","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":"e0d55c95a7712a5c851bfd3cd16a176ccf3c9bb319627feff64ab35b999b1a8e","cross_cats_sorted":["math.PR","q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-08-07T01:17:10Z","title_canon_sha256":"7fdac941b696b0fd359f0782ebe8fe4354883a60033d40139f18eb1dec22645e"},"schema_version":"1.0","source":{"id":"1808.02173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.02173","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"arxiv_version","alias_value":"1808.02173v1","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02173","created_at":"2026-05-18T00:08:47Z"},{"alias_kind":"pith_short_12","alias_value":"G7E3NJDPCT64","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G7E3NJDPCT644TZG","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G7E3NJDP","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:a8b622d969d799e88970cf0e2ecd0eea39f98cac37da3fc2bc0d149e96f6b853","target":"graph","created_at":"2026-05-18T00:08:47Z","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 propose a new kind of high order numerical scheme for backward stochastic differential equations(BSDEs). Unlike the traditional $\\theta$-scheme, we reduce truncation errors by taking $\\theta$ carefully for every subinterval according to the characteristics of integrands. We give error estimates of this nonlinear scheme and verify the order of scheme through a typical numerical experiment.","authors_text":"Chang-Ho Rim, Chol-Kyu Pak, Mun-Chol KiM","cross_cats":["math.PR","q-fin.MF"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-08-07T01:17:10Z","title":"Adapted $\\theta$-Scheme and Its Error Estimates for Backward Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02173","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":"sha256:60a6da96d70863e10eb34a55c9af67a7d62196bc9da72e3c0e85782241bce335","target":"record","created_at":"2026-05-18T00:08:47Z","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":"e0d55c95a7712a5c851bfd3cd16a176ccf3c9bb319627feff64ab35b999b1a8e","cross_cats_sorted":["math.PR","q-fin.MF"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2018-08-07T01:17:10Z","title_canon_sha256":"7fdac941b696b0fd359f0782ebe8fe4354883a60033d40139f18eb1dec22645e"},"schema_version":"1.0","source":{"id":"1808.02173","kind":"arxiv","version":1}},"canonical_sha256":"37c9b6a46f14fdce4f2661c7622546ce3fa03d048c8cf4fef376653c61180f03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37c9b6a46f14fdce4f2661c7622546ce3fa03d048c8cf4fef376653c61180f03","first_computed_at":"2026-05-18T00:08:47.368395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:47.368395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6oB9CRRMvZGtFRpqA9d8Jp3J3I4zQdElpsfJtgXBBtF3aCD3Y1edn4wNMlhJh9a8MVBIiShINKbqtDNgXNoaCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:47.369047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.02173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60a6da96d70863e10eb34a55c9af67a7d62196bc9da72e3c0e85782241bce335","sha256:a8b622d969d799e88970cf0e2ecd0eea39f98cac37da3fc2bc0d149e96f6b853"],"state_sha256":"911a32228ed453a19bf167a8cb7a2cbaf946b2d167e1f1a6771d09238b3a8264"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hOoL756db5FWoHJeesarRu11Jf6O8sA/cFabjGuaoKwIF8mEjyA3Bc9x0nw3hra8z8eXLZffxuvqC9wHE6V2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T20:14:46.181543Z","bundle_sha256":"6661069ef5355e0ef3e67650d6e808f73fed45026da78706209d45f25108294c"}}