{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NS7HLRI5B77WDDPM7V5M7ZFN4B","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":"661db3f49f8736d66d1157d76e71de1dc3757b29aa7ffdd808a38d5fa97920cc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-07T11:38:08Z","title_canon_sha256":"8ceeb3543d8178b2f66e4e73396297032d61fe318f933e3ad6e6ee7a02182750"},"schema_version":"1.0","source":{"id":"1608.02204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.02204","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.02204v1","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.02204","created_at":"2026-05-18T01:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"NS7HLRI5B77W","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NS7HLRI5B77WDDPM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NS7HLRI5","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:a7cebb5e0c0268c8358b159814d7e997c85074147d81314696987f18d992cf05","target":"graph","created_at":"2026-05-18T01:09:40Z","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 study, we concern the multidimensional viscosity solutions theory of a kind of semi-linear partial differential equations (PDEs). A new definition of viscosity solution for this multidimensional semi-linear PDEs which is related to a type of multidimensional backward stochastic differential equations (BSDEs) is given. Further more, we establish the existence and uniqueness results for the viscosity solution of this semi-linear PDEs via the comparison theorem of the related BSDEs and a smooth approximation technique.","authors_text":"Shuzhen Yang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-07T11:38:08Z","title":"Multidimensional viscosity solutions theory of semi-linear partial differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.02204","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:e7c1d9dacae9a25f619f2be6b3a90021ba158c010289c70a396dba6c8091a57e","target":"record","created_at":"2026-05-18T01:09:40Z","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":"661db3f49f8736d66d1157d76e71de1dc3757b29aa7ffdd808a38d5fa97920cc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-08-07T11:38:08Z","title_canon_sha256":"8ceeb3543d8178b2f66e4e73396297032d61fe318f933e3ad6e6ee7a02182750"},"schema_version":"1.0","source":{"id":"1608.02204","kind":"arxiv","version":1}},"canonical_sha256":"6cbe75c51d0fff618decfd7acfe4ade04d7c30fdf3e69df392da6595e6886013","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cbe75c51d0fff618decfd7acfe4ade04d7c30fdf3e69df392da6595e6886013","first_computed_at":"2026-05-18T01:09:40.741915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:40.741915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KxgOkPG9zUiAi7kTOezwZzQReri1+5mRZGy4vDQqZ6Y+K3t7yicbjAdg5JbVNKc+NvxkL/Eu8XrP0MfMDijxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:40.742544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.02204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7c1d9dacae9a25f619f2be6b3a90021ba158c010289c70a396dba6c8091a57e","sha256:a7cebb5e0c0268c8358b159814d7e997c85074147d81314696987f18d992cf05"],"state_sha256":"2bc854cf9c2b61306294cbab2d9d04e7d43392e20fddbd074e779051cb7a0627"}