{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WE4LB7E2BQ26FHZZMFBZUXX5KQ","short_pith_number":"pith:WE4LB7E2","canonical_record":{"source":{"id":"1608.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-02T14:22:28Z","cross_cats_sorted":[],"title_canon_sha256":"6730ecded275980052c2a39e9fcc19f19e701a80461a071196cc41bcff53e600","abstract_canon_sha256":"600dc2cb19733467e31b8344dbf7bac1118caaed24f689e5f88f3d24e9a37690"},"schema_version":"1.0"},"canonical_sha256":"b138b0fc9a0c35e29f3961439a5efd542d935afcbd5d1e4a4ff72c0711d48d53","source":{"kind":"arxiv","id":"1608.00832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00832","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00832v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00832","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"WE4LB7E2BQ26","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WE4LB7E2BQ26FHZZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WE4LB7E2","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WE4LB7E2BQ26FHZZMFBZUXX5KQ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-02T14:22:28Z","cross_cats_sorted":[],"title_canon_sha256":"6730ecded275980052c2a39e9fcc19f19e701a80461a071196cc41bcff53e600","abstract_canon_sha256":"600dc2cb19733467e31b8344dbf7bac1118caaed24f689e5f88f3d24e9a37690"},"schema_version":"1.0"},"canonical_sha256":"b138b0fc9a0c35e29f3961439a5efd542d935afcbd5d1e4a4ff72c0711d48d53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:00.845966Z","signature_b64":"dU++T+Jg7BDnpbOo5dEDjHCOhA92be5nWscpOY0gBKBCOSxtTNPHo3q3bc8iDtdITVLWhlpgCrFkeN53xKrzAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b138b0fc9a0c35e29f3961439a5efd542d935afcbd5d1e4a4ff72c0711d48d53","last_reissued_at":"2026-05-18T01:10:00.845303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:00.845303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00832","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gc+GD6sfvjVj1cOe3TJwrnd6y573+dIPuSBK8vqHMhGwdT8M+5z0f+5g/Rg8M7/MHdogoIc89pkr7lDPMsP5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:55:01.499479Z"},"content_sha256":"0033c14bef349b9d9e6014da7f595e4ba2545e3bcf735cbe6be8cebbe21c2144","schema_version":"1.0","event_id":"sha256:0033c14bef349b9d9e6014da7f595e4ba2545e3bcf735cbe6be8cebbe21c2144"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WE4LB7E2BQ26FHZZMFBZUXX5KQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anthony Le Cavil (ENSTA ParisTech UMA, D), EDF R, Francesco Russo (ENSTA ParisTech UMA), Nadia Oudjane (FiME Lab","submitted_at":"2016-08-02T14:22:28Z","abstract_excerpt":"We discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00832","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":"2026-05-18T01:10:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6Tt3fhi6dkwBfJ/JVGTV8pn7cYJptOdJnzXAuwwV0Wzk/C/UsgPlyxrnQNuLPImT5pEstaTiXuTD7o6QQKvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:55:01.500127Z"},"content_sha256":"27455fedcdecdfd0ef25edc65c9765d04738a805648508e0df7f555cde54b079","schema_version":"1.0","event_id":"sha256:27455fedcdecdfd0ef25edc65c9765d04738a805648508e0df7f555cde54b079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/bundle.json","state_url":"https://pith.science/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/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":"2026-06-04T04:55:01Z","links":{"resolver":"https://pith.science/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ","bundle":"https://pith.science/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/bundle.json","state":"https://pith.science/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WE4LB7E2BQ26FHZZMFBZUXX5KQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WE4LB7E2BQ26FHZZMFBZUXX5KQ","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":"600dc2cb19733467e31b8344dbf7bac1118caaed24f689e5f88f3d24e9a37690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-02T14:22:28Z","title_canon_sha256":"6730ecded275980052c2a39e9fcc19f19e701a80461a071196cc41bcff53e600"},"schema_version":"1.0","source":{"id":"1608.00832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00832","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00832v1","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00832","created_at":"2026-05-18T01:10:00Z"},{"alias_kind":"pith_short_12","alias_value":"WE4LB7E2BQ26","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WE4LB7E2BQ26FHZZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WE4LB7E2","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:27455fedcdecdfd0ef25edc65c9765d04738a805648508e0df7f555cde54b079","target":"graph","created_at":"2026-05-18T01:10:00Z","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 discuss numerical aspects related to a new class of nonlinear Stochastic Differential Equations in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE.","authors_text":"Anthony Le Cavil (ENSTA ParisTech UMA, D), EDF R, Francesco Russo (ENSTA ParisTech UMA), Nadia Oudjane (FiME Lab","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-02T14:22:28Z","title":"Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00832","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":"sha256:0033c14bef349b9d9e6014da7f595e4ba2545e3bcf735cbe6be8cebbe21c2144","target":"record","created_at":"2026-05-18T01:10:00Z","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":"600dc2cb19733467e31b8344dbf7bac1118caaed24f689e5f88f3d24e9a37690","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-02T14:22:28Z","title_canon_sha256":"6730ecded275980052c2a39e9fcc19f19e701a80461a071196cc41bcff53e600"},"schema_version":"1.0","source":{"id":"1608.00832","kind":"arxiv","version":1}},"canonical_sha256":"b138b0fc9a0c35e29f3961439a5efd542d935afcbd5d1e4a4ff72c0711d48d53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b138b0fc9a0c35e29f3961439a5efd542d935afcbd5d1e4a4ff72c0711d48d53","first_computed_at":"2026-05-18T01:10:00.845303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:00.845303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dU++T+Jg7BDnpbOo5dEDjHCOhA92be5nWscpOY0gBKBCOSxtTNPHo3q3bc8iDtdITVLWhlpgCrFkeN53xKrzAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:00.845966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0033c14bef349b9d9e6014da7f595e4ba2545e3bcf735cbe6be8cebbe21c2144","sha256:27455fedcdecdfd0ef25edc65c9765d04738a805648508e0df7f555cde54b079"],"state_sha256":"2c85ea9c8a57dcb9b1ce31f8c692d5cf48b6ad54a53a1b6558b0593574edd5fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bGJZaHJ6M6UHXFIKfLEPbo/pSjNfBE3UKd5hQqrANlx0ron6F2oQMmvgCW0tWvqqXx135kGkKymUarel10ZhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:55:01.503615Z","bundle_sha256":"daa833d7acb9f22665c459e67b685786f870f92da4ada4f713b372f0c3fea181"}}