{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XC42BXWDG23GHCB4OUZACH435M","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":"7c93654d3523c6da4dd32b5234458e6c578fa761991931648263a99f8e12b0ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-04T23:20:01Z","title_canon_sha256":"ab9fdc22ed59ca9ca76e233a37a3a4a9a68be84908a05f78c425d3afae323320"},"schema_version":"1.0","source":{"id":"1805.01962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01962","created_at":"2026-05-17T23:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01962v3","created_at":"2026-05-17T23:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01962","created_at":"2026-05-17T23:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"XC42BXWDG23G","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XC42BXWDG23GHCB4","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XC42BXWD","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:8ae52bcb3f99a4af73255ba4a6cec0045057512e179faa73ee2d4a07729ad24a","target":"graph","created_at":"2026-05-17T23:40:24Z","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 propose a particle system of diffusion processes coupled through a chain-like network structure described by an infinite-dimensional, nonlinear stochastic differential equation of McKean-Vlasov type. It has both (i) a local chain interaction and (ii) a mean-field interaction. It can be approximated by a limit of finite particle systems, as the number of particles goes to infinity. Due to the local chain interaction, propagation of chaos does not necessarily hold. Furthermore, we exhibit a dichotomy of presence or absence of mean-field interaction, and we discuss the problem of detecting its","authors_text":"Jean-Pierre Fouque, Nils Detering, Tomoyuki Ichiba","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-04T23:20:01Z","title":"Directed Chain Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01962","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":"sha256:50c905c7b6e226cfaa2c2088b5bd6a53461ffceba37eca2ae9c4a2faa1bf05af","target":"record","created_at":"2026-05-17T23:40:24Z","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":"7c93654d3523c6da4dd32b5234458e6c578fa761991931648263a99f8e12b0ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-04T23:20:01Z","title_canon_sha256":"ab9fdc22ed59ca9ca76e233a37a3a4a9a68be84908a05f78c425d3afae323320"},"schema_version":"1.0","source":{"id":"1805.01962","kind":"arxiv","version":3}},"canonical_sha256":"b8b9a0dec336b663883c7532011f9beb2375bc8c04f500cd79e92fbcc409f3c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8b9a0dec336b663883c7532011f9beb2375bc8c04f500cd79e92fbcc409f3c5","first_computed_at":"2026-05-17T23:40:24.170083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:24.170083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V9iQ9/VBsP9RCLFT1H4X8OMgsIX7q5uPIjpMIO3N+bGllCshJGJuUyFOUHo3E9MmSlY3dACQiIeg4Dym0hINBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:24.170759Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50c905c7b6e226cfaa2c2088b5bd6a53461ffceba37eca2ae9c4a2faa1bf05af","sha256:8ae52bcb3f99a4af73255ba4a6cec0045057512e179faa73ee2d4a07729ad24a"],"state_sha256":"5e07f57e2709dbc9de29c4af4c96bc9f7c8300b77d766438a37c36b3bfb22711"}