{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SE2PY5AFP7UVRZNBGHZEQ7VL7M","short_pith_number":"pith:SE2PY5AF","canonical_record":{"source":{"id":"1410.3538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-13T23:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"513a6fd5353d96b7e4248180c60c22b29364ffbb1c299353560c02fe17d429de","abstract_canon_sha256":"dde639bf090e5950cd11a428193f57b1c3a19071bc153f3229358482e8688714"},"schema_version":"1.0"},"canonical_sha256":"9134fc74057fe958e5a131f2487eabfb06297e2f3dea7fd0ff75c29510513a8b","source":{"kind":"arxiv","id":"1410.3538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3538","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3538v1","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3538","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"SE2PY5AFP7UV","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SE2PY5AFP7UVRZNB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SE2PY5AF","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SE2PY5AFP7UVRZNBGHZEQ7VL7M","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-13T23:45:38Z","cross_cats_sorted":[],"title_canon_sha256":"513a6fd5353d96b7e4248180c60c22b29364ffbb1c299353560c02fe17d429de","abstract_canon_sha256":"dde639bf090e5950cd11a428193f57b1c3a19071bc153f3229358482e8688714"},"schema_version":"1.0"},"canonical_sha256":"9134fc74057fe958e5a131f2487eabfb06297e2f3dea7fd0ff75c29510513a8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:09.559309Z","signature_b64":"Nz6Y4EuRaldDkLUCJfHVJJYi660syKu+LS34O2okF3aLHCex4yH+JM+3VNQKF5/zKM5+6AAqbIdKXMvMVOy2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9134fc74057fe958e5a131f2487eabfb06297e2f3dea7fd0ff75c29510513a8b","last_reissued_at":"2026-05-18T02:40:09.558855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:09.558855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3538","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":"2026-05-18T02:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t+PKyIxujVW07QNLTtx4vb8nIkKYZC/uHZxTBahgppOVWU3pD48Z+BE1d1MALIsgexSHxnIM+BrvTsAko1H+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:46:18.985434Z"},"content_sha256":"69bf2e1bfd746eec6d9cff9c4aee9cb85b17bcf6412011fefea707821602a1a3","schema_version":"1.0","event_id":"sha256:69bf2e1bfd746eec6d9cff9c4aee9cb85b17bcf6412011fefea707821602a1a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SE2PY5AFP7UVRZNBGHZEQ7VL7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamic Programming Principle for Stochastic Recursive Optimal Control Problem under G-framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mingshang Hu, Shaolin Ji","submitted_at":"2014-10-13T23:45:38Z","abstract_excerpt":"In this paper, we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related fully nonlinear HJB equation in the framework of G-expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3538","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":"2026-05-18T02:40:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1j+0HUmjpsmzxTxW1YsTbWHZMbgCCzQNIyunDX09rYY7eK7TzSMTDOLhxD/ehPxPbW/Uj4/kBXLTdAbREzy7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T08:46:18.985807Z"},"content_sha256":"17639c39efde170948e0f1156d042ea1657a07ce84a810503b6d189e02600f2e","schema_version":"1.0","event_id":"sha256:17639c39efde170948e0f1156d042ea1657a07ce84a810503b6d189e02600f2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/bundle.json","state_url":"https://pith.science/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/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":"2026-06-11T08:46:18Z","links":{"resolver":"https://pith.science/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M","bundle":"https://pith.science/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/bundle.json","state":"https://pith.science/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SE2PY5AFP7UVRZNBGHZEQ7VL7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SE2PY5AFP7UVRZNBGHZEQ7VL7M","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":"dde639bf090e5950cd11a428193f57b1c3a19071bc153f3229358482e8688714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-13T23:45:38Z","title_canon_sha256":"513a6fd5353d96b7e4248180c60c22b29364ffbb1c299353560c02fe17d429de"},"schema_version":"1.0","source":{"id":"1410.3538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3538","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3538v1","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3538","created_at":"2026-05-18T02:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"SE2PY5AFP7UV","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SE2PY5AFP7UVRZNB","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SE2PY5AF","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:17639c39efde170948e0f1156d042ea1657a07ce84a810503b6d189e02600f2e","target":"graph","created_at":"2026-05-18T02:40:09Z","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 a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related fully nonlinear HJB equation in the framework of G-expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.","authors_text":"Mingshang Hu, Shaolin Ji","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-13T23:45:38Z","title":"Dynamic Programming Principle for Stochastic Recursive Optimal Control Problem under G-framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3538","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":"sha256:69bf2e1bfd746eec6d9cff9c4aee9cb85b17bcf6412011fefea707821602a1a3","target":"record","created_at":"2026-05-18T02:40:09Z","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":"dde639bf090e5950cd11a428193f57b1c3a19071bc153f3229358482e8688714","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-10-13T23:45:38Z","title_canon_sha256":"513a6fd5353d96b7e4248180c60c22b29364ffbb1c299353560c02fe17d429de"},"schema_version":"1.0","source":{"id":"1410.3538","kind":"arxiv","version":1}},"canonical_sha256":"9134fc74057fe958e5a131f2487eabfb06297e2f3dea7fd0ff75c29510513a8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9134fc74057fe958e5a131f2487eabfb06297e2f3dea7fd0ff75c29510513a8b","first_computed_at":"2026-05-18T02:40:09.558855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:09.558855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nz6Y4EuRaldDkLUCJfHVJJYi660syKu+LS34O2okF3aLHCex4yH+JM+3VNQKF5/zKM5+6AAqbIdKXMvMVOy2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:09.559309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69bf2e1bfd746eec6d9cff9c4aee9cb85b17bcf6412011fefea707821602a1a3","sha256:17639c39efde170948e0f1156d042ea1657a07ce84a810503b6d189e02600f2e"],"state_sha256":"a49b1eba3f3e328f42820c4c70e3f7cf1ac883830afc17e57ed8db6e90515368"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mXLCcGYty9h2BYyf0DtdzjZk5Oz2VZknk01lS3Xk0b5p6uyKduOZPVQwssqBVkAQJKXU+0fxNlz8yGJTyEqgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T08:46:18.987858Z","bundle_sha256":"f505bb651c90aa2501033762ae8152b9cdc6960ba60ff3037d163265ac731aba"}}