{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JYYMWB7TVQDAQGULRLKSMDDHXT","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":"a83508763690bae5a4074f90586087d11719b5458d2c357713331be107a62fd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-23T15:52:35Z","title_canon_sha256":"d215008e6f829bc1b41550eb8df28f9ecd51a667f809aed523e1966b5f6547ac"},"schema_version":"1.0","source":{"id":"1403.5764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5764","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5764v1","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5764","created_at":"2026-05-18T02:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"JYYMWB7TVQDA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JYYMWB7TVQDAQGUL","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JYYMWB7T","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:994d6c98fbae8832382afd7c56eba6e55ff594b425eb46c77244a258552ab46b","target":"graph","created_at":"2026-05-18T02:55:48Z","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 generalise the construction of multivariate Hawkes processes to a possibly infinite network of counting processes on a directed graph $\\mathbb G$. The process is constructed as the solution to a system of Poisson driven stochastic differential equations, for which we prove pathwise existence and uniqueness under some reasonable conditions.\n  We next investigate how to approximate a standard $N$-dimensional Hawkes process by a simple inhomogeneous Poisson process in the mean-field framework where each pair of individuals interact in the same way, in the limit $N \\rightarrow \\infty$. In the s","authors_text":"Marc Hoffmann, Nicolas Fournier, Sylvain Delattre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-23T15:52:35Z","title":"High dimensional Hawkes processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5764","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":"sha256:0da3bf2a1a05127489fc85db85d8a37e9902a93659500ba024a7a8dd3b82ceb0","target":"record","created_at":"2026-05-18T02:55:48Z","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":"a83508763690bae5a4074f90586087d11719b5458d2c357713331be107a62fd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-23T15:52:35Z","title_canon_sha256":"d215008e6f829bc1b41550eb8df28f9ecd51a667f809aed523e1966b5f6547ac"},"schema_version":"1.0","source":{"id":"1403.5764","kind":"arxiv","version":1}},"canonical_sha256":"4e30cb07f3ac06081a8b8ad5260c67bcc9637288f053f7e4d7bc4fed1876a357","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e30cb07f3ac06081a8b8ad5260c67bcc9637288f053f7e4d7bc4fed1876a357","first_computed_at":"2026-05-18T02:55:48.948865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:48.948865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SOXMls3zawx17SfFs+tDN5m7kR0SIw+PwGqGYQJo+wDPeYs3cnWVKAEgXik0v70zg14erV58qlYdc4reAM8zBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:48.949423Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0da3bf2a1a05127489fc85db85d8a37e9902a93659500ba024a7a8dd3b82ceb0","sha256:994d6c98fbae8832382afd7c56eba6e55ff594b425eb46c77244a258552ab46b"],"state_sha256":"c1bdc592f00d3886de0e89ddcf379e9c2468ca0c4e0dd0672c67c8909e5c3548"}