{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6ZNC4LIK5ROE2TAGPIPZ63RRNL","short_pith_number":"pith:6ZNC4LIK","canonical_record":{"source":{"id":"1302.4624","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T14:44:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9223638dba7fb084f514e6a862fc078fe1c1b3afad64a0b87640413ae3ca5519","abstract_canon_sha256":"5ce02039acb474d5e3516a51258a46c4496e717772dd1b83355b39f9f618f2b3"},"schema_version":"1.0"},"canonical_sha256":"f65a2e2d0aec5c4d4c067a1f9f6e316ae83a5ca26c2a4ab9c40bfc490671ed4d","source":{"kind":"arxiv","id":"1302.4624","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4624","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4624v3","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4624","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"6ZNC4LIK5ROE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZNC4LIK5ROE2TAG","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZNC4LIK","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6ZNC4LIK5ROE2TAGPIPZ63RRNL","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4624","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T14:44:40Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"9223638dba7fb084f514e6a862fc078fe1c1b3afad64a0b87640413ae3ca5519","abstract_canon_sha256":"5ce02039acb474d5e3516a51258a46c4496e717772dd1b83355b39f9f618f2b3"},"schema_version":"1.0"},"canonical_sha256":"f65a2e2d0aec5c4d4c067a1f9f6e316ae83a5ca26c2a4ab9c40bfc490671ed4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:36.992133Z","signature_b64":"pZmtK9c9vSkNcMJUEc0fgGTMIT0wXD3cKkgztQIYA5nI8whX2eUKdCjT3Ng7AkF9s/CvhyxwDaODtxLImpl4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f65a2e2d0aec5c4d4c067a1f9f6e316ae83a5ca26c2a4ab9c40bfc490671ed4d","last_reissued_at":"2026-05-18T03:10:36.991565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:36.991565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4624","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"US3KPyejKatyBcN+dOxJkVuxvIg7bbYfFfJyRIJESKlIoygV9TmCAMviRqzLDXWE4Pmol86SUxYo63oEM+JzDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:43:59.836051Z"},"content_sha256":"d79a0bbdebdc63440455b68805b308df16871249b7c2e2a20bf0fa221b112bbd","schema_version":"1.0","event_id":"sha256:d79a0bbdebdc63440455b68805b308df16871249b7c2e2a20bf0fa221b112bbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6ZNC4LIK5ROE2TAGPIPZ63RRNL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical algorithm for a class of BSDEs via branching process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NA","authors_text":"Nizar Touzi, Pierre Henry-Labordere, Xiaolu Tan","submitted_at":"2013-02-19T14:44:40Z","abstract_excerpt":"We generalize the algorithm for semi-linear parabolic PDEs in Henry-Labord\\`ere (2012) to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren, Keller, Touzi and Zhang (2012) and extended in Ekren, Touzi and Zhang (2013)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4624","kind":"arxiv","version":3},"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":"2026-05-18T03:10:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tG906al39zX8O/o38Dz97oAXMCNkdSVj2gjzrpQUuAcdHHHF2r2lubuQhQkEDRp4TFgxx8h/D8usMqs5HuUTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:43:59.836448Z"},"content_sha256":"4d14478cb85c263490abdc98c95c528aca1f17dddccad6fc28bf000a80c95fda","schema_version":"1.0","event_id":"sha256:4d14478cb85c263490abdc98c95c528aca1f17dddccad6fc28bf000a80c95fda"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/bundle.json","state_url":"https://pith.science/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/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":"2026-05-26T08:43:59Z","links":{"resolver":"https://pith.science/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL","bundle":"https://pith.science/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/bundle.json","state":"https://pith.science/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZNC4LIK5ROE2TAGPIPZ63RRNL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZNC4LIK5ROE2TAGPIPZ63RRNL","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":"5ce02039acb474d5e3516a51258a46c4496e717772dd1b83355b39f9f618f2b3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T14:44:40Z","title_canon_sha256":"9223638dba7fb084f514e6a862fc078fe1c1b3afad64a0b87640413ae3ca5519"},"schema_version":"1.0","source":{"id":"1302.4624","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4624","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4624v3","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4624","created_at":"2026-05-18T03:10:36Z"},{"alias_kind":"pith_short_12","alias_value":"6ZNC4LIK5ROE","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZNC4LIK5ROE2TAG","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZNC4LIK","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:4d14478cb85c263490abdc98c95c528aca1f17dddccad6fc28bf000a80c95fda","target":"graph","created_at":"2026-05-18T03:10:36Z","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 generalize the algorithm for semi-linear parabolic PDEs in Henry-Labord\\`ere (2012) to the non-Markovian case for a class of Backward SDEs (BSDEs). By simulating the branching process, the algorithm does not need any backward regression. To prove that the numerical algorithm converges to the solution of BSDEs, we use the notion of viscosity solution of path dependent PDEs introduced by Ekren, Keller, Touzi and Zhang (2012) and extended in Ekren, Touzi and Zhang (2013).","authors_text":"Nizar Touzi, Pierre Henry-Labordere, Xiaolu Tan","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T14:44:40Z","title":"A numerical algorithm for a class of BSDEs via branching process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4624","kind":"arxiv","version":3},"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:d79a0bbdebdc63440455b68805b308df16871249b7c2e2a20bf0fa221b112bbd","target":"record","created_at":"2026-05-18T03:10:36Z","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":"5ce02039acb474d5e3516a51258a46c4496e717772dd1b83355b39f9f618f2b3","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-02-19T14:44:40Z","title_canon_sha256":"9223638dba7fb084f514e6a862fc078fe1c1b3afad64a0b87640413ae3ca5519"},"schema_version":"1.0","source":{"id":"1302.4624","kind":"arxiv","version":3}},"canonical_sha256":"f65a2e2d0aec5c4d4c067a1f9f6e316ae83a5ca26c2a4ab9c40bfc490671ed4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f65a2e2d0aec5c4d4c067a1f9f6e316ae83a5ca26c2a4ab9c40bfc490671ed4d","first_computed_at":"2026-05-18T03:10:36.991565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:36.991565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZmtK9c9vSkNcMJUEc0fgGTMIT0wXD3cKkgztQIYA5nI8whX2eUKdCjT3Ng7AkF9s/CvhyxwDaODtxLImpl4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:36.992133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4624","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d79a0bbdebdc63440455b68805b308df16871249b7c2e2a20bf0fa221b112bbd","sha256:4d14478cb85c263490abdc98c95c528aca1f17dddccad6fc28bf000a80c95fda"],"state_sha256":"306722cda7e16e2314ade132a133410cbd6c4aa94c740d646a0f5df09f7a1e4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SU7YqEOSOf4av0VgdoR4ixnZXplVbzYchva2vh/MW/9hZvNYMIEOaU2eJDB7k4rAKTxoI/f05g7fdrDfv0D1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:43:59.839474Z","bundle_sha256":"61d36935790d244137b871944289b9e5cac86daaae8f8a5dffec9b920a847341"}}