{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I3RDXMVXAU5VAKLV2TTUMHUPIQ","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":"642d1fa503ce53517302070a596723fb932220d1bb6344fc75929e09614b1dc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-02T16:51:54Z","title_canon_sha256":"71a0c38461abc4727fc1bb7948c968b17cd9ea0c750d295055ddd636ffb582fc"},"schema_version":"1.0","source":{"id":"1704.00328","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.00328","created_at":"2026-05-18T00:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1704.00328v2","created_at":"2026-05-18T00:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00328","created_at":"2026-05-18T00:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"I3RDXMVXAU5V","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I3RDXMVXAU5VAKLV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I3RDXMVX","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:009cd1a1ccaef6e5c001961ed5184b72468b0eb1be3dcef608628adc6f9e7e99","target":"graph","created_at":"2026-05-18T00:23:21Z","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":"We study semi-linear elliptic PDEs with polynomial non-linearity and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives, we extend previous results in the literature by showing that our probabilistic representation provides a solution to the PDE without assuming its existence. In the general case, we derive a new representation of the solution by using marked branching diffusion processes and automatic differentiation formulas to account for the non-linear gradient term. In b","authors_text":"Ankush Agarwal, Julien Claisse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-02T16:51:54Z","title":"Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00328","kind":"arxiv","version":2},"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":"sha256:7ec38e0d5bd90b33efd64b3d45535e71356330792a609c07d32cd4600c4d7e5f","target":"record","created_at":"2026-05-18T00:23:21Z","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":"642d1fa503ce53517302070a596723fb932220d1bb6344fc75929e09614b1dc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-02T16:51:54Z","title_canon_sha256":"71a0c38461abc4727fc1bb7948c968b17cd9ea0c750d295055ddd636ffb582fc"},"schema_version":"1.0","source":{"id":"1704.00328","kind":"arxiv","version":2}},"canonical_sha256":"46e23bb2b7053b502975d4e7461e8f4414435ada15a53ff8515e87c344303cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e23bb2b7053b502975d4e7461e8f4414435ada15a53ff8515e87c344303cdf","first_computed_at":"2026-05-18T00:23:21.406433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:21.406433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K+eNklU66v9dOw4tYkxRVAHsviVcpNA4OcQJJF7T7xwJmveHBaQgiK8qKYg5vkNqm5AUTOWBkRIHohlW8xxGDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:21.407127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.00328","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ec38e0d5bd90b33efd64b3d45535e71356330792a609c07d32cd4600c4d7e5f","sha256:009cd1a1ccaef6e5c001961ed5184b72468b0eb1be3dcef608628adc6f9e7e99"],"state_sha256":"1f5dd92feff49e1d1df89d8fae09c5e0d5e8e300723d5a606c06b4d6e1e0aa1a"}