{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VYVFHJRDC7BZM2AULHLUFRGXGG","short_pith_number":"pith:VYVFHJRD","canonical_record":{"source":{"id":"1710.10933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T13:38:58Z","cross_cats_sorted":[],"title_canon_sha256":"93261501c96ad391bf3ec90d4c597faf5cde7ef26014df2c3582888053e1847f","abstract_canon_sha256":"87eaadc02cf92ece864c9686533085619a1c3d0a397b8052ea258cd749f3ed0a"},"schema_version":"1.0"},"canonical_sha256":"ae2a53a62317c396681459d742c4d7319d5437ad179bf0baaf9445ca63bc5bb2","source":{"kind":"arxiv","id":"1710.10933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10933","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10933v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10933","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"VYVFHJRDC7BZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYVFHJRDC7BZM2AU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYVFHJRD","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VYVFHJRDC7BZM2AULHLUFRGXGG","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T13:38:58Z","cross_cats_sorted":[],"title_canon_sha256":"93261501c96ad391bf3ec90d4c597faf5cde7ef26014df2c3582888053e1847f","abstract_canon_sha256":"87eaadc02cf92ece864c9686533085619a1c3d0a397b8052ea258cd749f3ed0a"},"schema_version":"1.0"},"canonical_sha256":"ae2a53a62317c396681459d742c4d7319d5437ad179bf0baaf9445ca63bc5bb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:46.064065Z","signature_b64":"8GG9ydkMBeuGJS3GVaE89woIN0SwdHPJWNPjPEERSK8pvL8cxHkIh5BmUYkL91etK8/FXEIAqq7nhnfrExO3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae2a53a62317c396681459d742c4d7319d5437ad179bf0baaf9445ca63bc5bb2","last_reissued_at":"2026-05-18T00:31:46.063375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:46.063375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10933","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":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OT2CU9/uoxGrl5o8M5RPbl5ShwqLyepZfg9pclAIF3KNzGXTl28j7bx942OjOcXTBPcRzqLMq1obCOn3GomUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:35:34.767293Z"},"content_sha256":"632b0531862764eadad1ec0b80cc982de995073ac7b1a65c98b3a51bfa10507c","schema_version":"1.0","event_id":"sha256:632b0531862764eadad1ec0b80cc982de995073ac7b1a65c98b3a51bfa10507c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VYVFHJRDC7BZM2AULHLUFRGXGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical approximation of general Lipschitz BSDEs with branching processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Bouchard (CEREMADE), Xavier Warin (EDF R\\&D), Xiaolu Tan (CEREMADE)","submitted_at":"2017-10-30T13:38:58Z","abstract_excerpt":"We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Converg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10933","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":"2026-05-18T00:31:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2inu1eTSsm2ZfUKHIdub6WMG1/G92VQRfA1KiCZ8t2qgcQXvFYBys8IlK0bwcz/xOjtlKxNuinYscPO2MHMpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:35:34.767660Z"},"content_sha256":"8391927e66a69ef8f723073ed261d7478c3fe45896603a2a39f665fc9608206b","schema_version":"1.0","event_id":"sha256:8391927e66a69ef8f723073ed261d7478c3fe45896603a2a39f665fc9608206b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/bundle.json","state_url":"https://pith.science/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/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":"2026-06-03T17:35:34Z","links":{"resolver":"https://pith.science/pith/VYVFHJRDC7BZM2AULHLUFRGXGG","bundle":"https://pith.science/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/bundle.json","state":"https://pith.science/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYVFHJRDC7BZM2AULHLUFRGXGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VYVFHJRDC7BZM2AULHLUFRGXGG","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":"87eaadc02cf92ece864c9686533085619a1c3d0a397b8052ea258cd749f3ed0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T13:38:58Z","title_canon_sha256":"93261501c96ad391bf3ec90d4c597faf5cde7ef26014df2c3582888053e1847f"},"schema_version":"1.0","source":{"id":"1710.10933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10933","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10933v1","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10933","created_at":"2026-05-18T00:31:46Z"},{"alias_kind":"pith_short_12","alias_value":"VYVFHJRDC7BZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VYVFHJRDC7BZM2AU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VYVFHJRD","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:8391927e66a69ef8f723073ed261d7478c3fe45896603a2a39f665fc9608206b","target":"graph","created_at":"2026-05-18T00:31:46Z","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 extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in [3], this requires a localization procedure that uses a priori estimates on the true solution, so as to ensure the well-posedness of the involved Picard iteration scheme, and the global convergence of the algorithm. When, the nonlinearity depends on the gradient, the later needs to be controlled as well. This is done by using a face-lifting procedure. Converg","authors_text":"Bruno Bouchard (CEREMADE), Xavier Warin (EDF R\\&D), Xiaolu Tan (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T13:38:58Z","title":"Numerical approximation of general Lipschitz BSDEs with branching processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10933","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":"sha256:632b0531862764eadad1ec0b80cc982de995073ac7b1a65c98b3a51bfa10507c","target":"record","created_at":"2026-05-18T00:31:46Z","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":"87eaadc02cf92ece864c9686533085619a1c3d0a397b8052ea258cd749f3ed0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-30T13:38:58Z","title_canon_sha256":"93261501c96ad391bf3ec90d4c597faf5cde7ef26014df2c3582888053e1847f"},"schema_version":"1.0","source":{"id":"1710.10933","kind":"arxiv","version":1}},"canonical_sha256":"ae2a53a62317c396681459d742c4d7319d5437ad179bf0baaf9445ca63bc5bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae2a53a62317c396681459d742c4d7319d5437ad179bf0baaf9445ca63bc5bb2","first_computed_at":"2026-05-18T00:31:46.063375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:46.063375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8GG9ydkMBeuGJS3GVaE89woIN0SwdHPJWNPjPEERSK8pvL8cxHkIh5BmUYkL91etK8/FXEIAqq7nhnfrExO3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:46.064065Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:632b0531862764eadad1ec0b80cc982de995073ac7b1a65c98b3a51bfa10507c","sha256:8391927e66a69ef8f723073ed261d7478c3fe45896603a2a39f665fc9608206b"],"state_sha256":"88065bcbe535b39a116ed330d0d196228b3e97e0439e6e1c19098c0720ef6409"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ivbm/R6z9e2RcQp/koYxcQc/ESyOKhAsyPZ9115eZ1/+8EpL9KGQaEt/X95qfdWRx0nX8ELKqwEI7zuWhdbeAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:35:34.769860Z","bundle_sha256":"28e363b21b17e4083e17a6822779fb8989ce4523d7eed6d1a78ec4b1ca866e5b"}}