{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5TLFU3Y72FM7XGFX3XYE3YJYX3","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":"11bb9101866747c7c05d74111d634817fe058d8636f98903ed643408af7b0812","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T00:05:21Z","title_canon_sha256":"77d3dc51e87400c080be606a18bd600ddb643621745378f9a80befa29b1f9740"},"schema_version":"1.0","source":{"id":"1907.04209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.04209","created_at":"2026-05-17T23:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1907.04209v1","created_at":"2026-05-17T23:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.04209","created_at":"2026-05-17T23:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"5TLFU3Y72FM7","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"5TLFU3Y72FM7XGFX","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"5TLFU3Y7","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:3360bf6bdb0051730d026be39dddda7d33dad3c63bd8e8ed0ee8d1c9f57992ab","target":"graph","created_at":"2026-05-17T23:41:03Z","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 the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than white noises. Two types of FBS{\\Delta}Ss are investigated. The first one is described by a partially coupled forward-backward stochastic difference equation (FBS{\\Delta}E) and the second one is described by a fully coupled FBS{\\Delta}E. By adopting an appropriate representation of the product rule and an appropriate formulation of the backward stochastic diff","authors_text":"Haodong Liu, Shailin Ji","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T00:05:21Z","title":"Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04209","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:d1b540e287700839a01d8cac14b75266c4b9652a696d699869a689065d484f9d","target":"record","created_at":"2026-05-17T23:41:03Z","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":"11bb9101866747c7c05d74111d634817fe058d8636f98903ed643408af7b0812","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-07-06T00:05:21Z","title_canon_sha256":"77d3dc51e87400c080be606a18bd600ddb643621745378f9a80befa29b1f9740"},"schema_version":"1.0","source":{"id":"1907.04209","kind":"arxiv","version":1}},"canonical_sha256":"ecd65a6f1fd159fb98b7ddf04de138bec1fcec9084fa6c811dadd5ce2ef760ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecd65a6f1fd159fb98b7ddf04de138bec1fcec9084fa6c811dadd5ce2ef760ff","first_computed_at":"2026-05-17T23:41:03.007074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:03.007074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9F0hNJ+RXu71b4k7P5Sbhki843CoKBS6/WwtjhYIh+x/9SvAMdvvcKpCEeQwFf8tbvAPFQcMgpvTe+56ld9fDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:03.007640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.04209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1b540e287700839a01d8cac14b75266c4b9652a696d699869a689065d484f9d","sha256:3360bf6bdb0051730d026be39dddda7d33dad3c63bd8e8ed0ee8d1c9f57992ab"],"state_sha256":"129234ab32237ccf30acc785b2c9d1a5ba22d52ac1bd1d7aefb4b13c1be1979e"}