{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MXODPTVVVHGC777R46FNJHSIIU","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":"efc4d9a3a78a4d4ce723e97c8163bc2195c67a2bba58a66a87f2a58a38437226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-08T06:49:26Z","title_canon_sha256":"c8212eaa126b6686d17d2b32187b001d85b31d38d6000f360df37d9805079ad5"},"schema_version":"1.0","source":{"id":"1604.02239","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02239","created_at":"2026-05-18T01:17:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02239v1","created_at":"2026-05-18T01:17:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02239","created_at":"2026-05-18T01:17:28Z"},{"alias_kind":"pith_short_12","alias_value":"MXODPTVVVHGC","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MXODPTVVVHGC777R","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MXODPTVV","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:1ed00425e8130d4d043f1f69beee4d02fa39f82961b78b8930f0743e879ad999","target":"graph","created_at":"2026-05-18T01:17:28Z","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 type of viscosity solutions for fully nonlinear path dependent PDEs. By restricting to certain pseudo Markovian structure, we remove the uniform non- degeneracy condition imposed in our earlier works [9, 10]. We establish the comparison principle under natural and mild conditions. Moreover, as applications we apply our results to two important classes of PPDEs: the stochastic HJB equations and the path dependent Isaacs equations, induced from the stochastic optimization with random coefficients and the path dependent zero sum game problem, respectively.","authors_text":"Ibrahim Ekren, Jianfeng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-08T06:49:26Z","title":"Pseudo Markovian Viscosity Solutions of Fully Nonlinear Degenerate PPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02239","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":"sha256:67bb90b9a8c80e244065dd3e1d590a278c3d6e019fc93b1b0ac7acae979c9415","target":"record","created_at":"2026-05-18T01:17:28Z","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":"efc4d9a3a78a4d4ce723e97c8163bc2195c67a2bba58a66a87f2a58a38437226","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-08T06:49:26Z","title_canon_sha256":"c8212eaa126b6686d17d2b32187b001d85b31d38d6000f360df37d9805079ad5"},"schema_version":"1.0","source":{"id":"1604.02239","kind":"arxiv","version":1}},"canonical_sha256":"65dc37ceb5a9cc2ffff1e78ad49e484507e31dbdf2d367e80c52bda784a18959","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65dc37ceb5a9cc2ffff1e78ad49e484507e31dbdf2d367e80c52bda784a18959","first_computed_at":"2026-05-18T01:17:28.145578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:28.145578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hGW1Hu2ldluOav6zigrTWmqQR7e6dqNRW1oMahFxrHrH3Yr7C9XAwjBoJC7P7CPO4kA5WdhF//sOQ4P8IsXrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:28.146069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02239","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67bb90b9a8c80e244065dd3e1d590a278c3d6e019fc93b1b0ac7acae979c9415","sha256:1ed00425e8130d4d043f1f69beee4d02fa39f82961b78b8930f0743e879ad999"],"state_sha256":"05a7b01de1babf0b23bd724038fc8c34b83945259f47f7656f8678097dd17aa5"}