{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:UNHFPCQ6EHFWBWEDFMFCLTFLZV","short_pith_number":"pith:UNHFPCQ6","canonical_record":{"source":{"id":"1206.5889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-26T06:15:10Z","cross_cats_sorted":[],"title_canon_sha256":"40a05a0a531253cce2e87292077a051762e4a23b7ea4b401fb37943fd53bfe3a","abstract_canon_sha256":"e1adeea7d8ae03a232e87641b5c26a57f787f2ba297772501eac9024731641c0"},"schema_version":"1.0"},"canonical_sha256":"a34e578a1e21cb60d8832b0a25ccabcd4e0db7f156d7595d10cec5194e28e3c0","source":{"kind":"arxiv","id":"1206.5889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5889","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5889v1","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5889","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"pith_short_12","alias_value":"UNHFPCQ6EHFW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNHFPCQ6EHFWBWED","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNHFPCQ6","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:UNHFPCQ6EHFWBWEDFMFCLTFLZV","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5889","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-26T06:15:10Z","cross_cats_sorted":[],"title_canon_sha256":"40a05a0a531253cce2e87292077a051762e4a23b7ea4b401fb37943fd53bfe3a","abstract_canon_sha256":"e1adeea7d8ae03a232e87641b5c26a57f787f2ba297772501eac9024731641c0"},"schema_version":"1.0"},"canonical_sha256":"a34e578a1e21cb60d8832b0a25ccabcd4e0db7f156d7595d10cec5194e28e3c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:37.825775Z","signature_b64":"Y0ZmrFX/NzgG3dcPz1RZBm+yNNTIQtffomlSo4suwk1EWi5vEQRcWe5zPrzFWfcWB7OZ957DL7Sk6fCV84ayAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a34e578a1e21cb60d8832b0a25ccabcd4e0db7f156d7595d10cec5194e28e3c0","last_reissued_at":"2026-05-18T03:52:37.824962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:37.824962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5889","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":"2026-05-18T03:52:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8QPSpljpShDxfW1+52yOSVej9NTFKz9wYAJBqZ45hvgRSBJQ2A9EZ/Utils0FYm9Kbz4uaXKUdtRZE7a/MxDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:18:34.989625Z"},"content_sha256":"eb6c12da19f826345041a66bb1ec9fe8f8eb34321f333736477b07d67d02b39d","schema_version":"1.0","event_id":"sha256:eb6c12da19f826345041a66bb1ec9fe8f8eb34321f333736477b07d67d02b39d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:UNHFPCQ6EHFWBWEDFMFCLTFLZV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Backward Stochastic Differential Equations Driven by G-Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mingshang Hu, Shaolin Ji, Shige Peng, Yongsheng Song","submitted_at":"2012-06-26T06:15:10Z","abstract_excerpt":"In this paper, we study backward stochastic differential equations driven by a G-Brownian motion. The solution of such new type of BSDE is a triple (Y,Z,K) where K is a decreasing G-martingale. Under a Lipschitz condition for generator f and g in Y and Z. The existence and uniqueness of the solution (Y,Z,K) is proved. Although the methods used in the proof and the related estimates are quite different from the classical proof for BSDEs, stochastic calculus in G-framework plays a central role."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5889","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":"2026-05-18T03:52:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i3l8bSELBAs60n5dcc7i1Bz48XbjKGPa3vC5uBmhYbxS+O74Htz3aD2XY0xmHuM/Qg7jfpfGOmv9FCPxQQDJCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T23:18:34.990272Z"},"content_sha256":"bae057e5c2c6d89e92956267c41b4c3f29920f5a667576c5494dac34cfe2e9e6","schema_version":"1.0","event_id":"sha256:bae057e5c2c6d89e92956267c41b4c3f29920f5a667576c5494dac34cfe2e9e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/bundle.json","state_url":"https://pith.science/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/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":"2026-05-21T23:18:34Z","links":{"resolver":"https://pith.science/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV","bundle":"https://pith.science/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/bundle.json","state":"https://pith.science/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UNHFPCQ6EHFWBWEDFMFCLTFLZV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UNHFPCQ6EHFWBWEDFMFCLTFLZV","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":"e1adeea7d8ae03a232e87641b5c26a57f787f2ba297772501eac9024731641c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-26T06:15:10Z","title_canon_sha256":"40a05a0a531253cce2e87292077a051762e4a23b7ea4b401fb37943fd53bfe3a"},"schema_version":"1.0","source":{"id":"1206.5889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5889","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5889v1","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5889","created_at":"2026-05-18T03:52:37Z"},{"alias_kind":"pith_short_12","alias_value":"UNHFPCQ6EHFW","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UNHFPCQ6EHFWBWED","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UNHFPCQ6","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:bae057e5c2c6d89e92956267c41b4c3f29920f5a667576c5494dac34cfe2e9e6","target":"graph","created_at":"2026-05-18T03:52:37Z","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":"In this paper, we study backward stochastic differential equations driven by a G-Brownian motion. The solution of such new type of BSDE is a triple (Y,Z,K) where K is a decreasing G-martingale. Under a Lipschitz condition for generator f and g in Y and Z. The existence and uniqueness of the solution (Y,Z,K) is proved. Although the methods used in the proof and the related estimates are quite different from the classical proof for BSDEs, stochastic calculus in G-framework plays a central role.","authors_text":"Mingshang Hu, Shaolin Ji, Shige Peng, Yongsheng Song","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-26T06:15:10Z","title":"Backward Stochastic Differential Equations Driven by G-Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5889","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:eb6c12da19f826345041a66bb1ec9fe8f8eb34321f333736477b07d67d02b39d","target":"record","created_at":"2026-05-18T03:52:37Z","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":"e1adeea7d8ae03a232e87641b5c26a57f787f2ba297772501eac9024731641c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-06-26T06:15:10Z","title_canon_sha256":"40a05a0a531253cce2e87292077a051762e4a23b7ea4b401fb37943fd53bfe3a"},"schema_version":"1.0","source":{"id":"1206.5889","kind":"arxiv","version":1}},"canonical_sha256":"a34e578a1e21cb60d8832b0a25ccabcd4e0db7f156d7595d10cec5194e28e3c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a34e578a1e21cb60d8832b0a25ccabcd4e0db7f156d7595d10cec5194e28e3c0","first_computed_at":"2026-05-18T03:52:37.824962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:37.824962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0ZmrFX/NzgG3dcPz1RZBm+yNNTIQtffomlSo4suwk1EWi5vEQRcWe5zPrzFWfcWB7OZ957DL7Sk6fCV84ayAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:37.825775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6c12da19f826345041a66bb1ec9fe8f8eb34321f333736477b07d67d02b39d","sha256:bae057e5c2c6d89e92956267c41b4c3f29920f5a667576c5494dac34cfe2e9e6"],"state_sha256":"11b982f92fa0c55b8bf547acbafcc6fb68a799e57afab7adf1cf76dd6b6c9353"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2/owhsETpDyaVKUWqQeoiJk3n42bzjPmPbjvfoFbf1QqHr0tGTRY0Y/VYdsJrFlT59LJHv73q3IBFJxHvYqAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T23:18:34.993084Z","bundle_sha256":"820ae3abf4394ad0e721267fb05ab5fbdd1ec6b49d55b18207d7ea9733de2213"}}