{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FQJWZYCHHWA2PRZRPKQA4FVVKQ","short_pith_number":"pith:FQJWZYCH","canonical_record":{"source":{"id":"1510.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-19T18:58:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bfeacc9b464ddf45f8e1fc40534d59ec67749531e4b83bad774f37e67a8abb9a","abstract_canon_sha256":"0f6f61c82d3c78b9a9507ce1af45cf5c3f13612806d128b7caadc3bb4a1202f6"},"schema_version":"1.0"},"canonical_sha256":"2c136ce0473d81a7c7317aa00e16b55438e4761c8a53847ff85844d5b9f7176a","source":{"kind":"arxiv","id":"1510.05620","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05620","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05620v2","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05620","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"FQJWZYCHHWA2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FQJWZYCHHWA2PRZR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FQJWZYCH","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FQJWZYCHHWA2PRZRPKQA4FVVKQ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-19T18:58:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"bfeacc9b464ddf45f8e1fc40534d59ec67749531e4b83bad774f37e67a8abb9a","abstract_canon_sha256":"0f6f61c82d3c78b9a9507ce1af45cf5c3f13612806d128b7caadc3bb4a1202f6"},"schema_version":"1.0"},"canonical_sha256":"2c136ce0473d81a7c7317aa00e16b55438e4761c8a53847ff85844d5b9f7176a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:43.108279Z","signature_b64":"dyFWqi/ODSz9+MMxmy+9HTL6Tp16pCA1ynuTItLSty8x8wJFwAUNrJx/FEZHwOG2X6PG4h68b4wb2LhHMt4JDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c136ce0473d81a7c7317aa00e16b55438e4761c8a53847ff85844d5b9f7176a","last_reissued_at":"2026-05-18T00:48:43.107833Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:43.107833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05620","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzlU0JLRi1vOMKzJxQXuYzi1ZUXA0+leiItr2XAKmNEKuxRRYad3W1ofNVr/ZLgW50juzR/pbp67AMZZ02JnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:56:29.237586Z"},"content_sha256":"1b68559841407be5b5af2210059ca60dae4aac10e1257368de4768ed430174dd","schema_version":"1.0","event_id":"sha256:1b68559841407be5b5af2210059ca60dae4aac10e1257368de4768ed430174dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FQJWZYCHHWA2PRZRPKQA4FVVKQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field limit of generalized Hawkes processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Julien Chevallier (JAD)","submitted_at":"2015-10-19T18:58:41Z","abstract_excerpt":"We generalize multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a system of n mean-field interacting age-dependent Hawkes processes. We prove that such a system can be approximated by independent and identically distributed age dependent point processes interacting with their own mean intensity. This result generalizes the study performed by Delattre, Fournier and Hoffmann (2015). In continuity with the work of Chevallier e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05620","kind":"arxiv","version":2},"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":"2026-05-18T00:48:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dz98KKat0437A8r7c5j7KvqSYQ0FJiF+aGvBEASvhnHv28on/RY6h5uhoT9MUfkNtFridcmXlLX0vdMDUTN1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:56:29.237938Z"},"content_sha256":"f3e844d8c4062f4e84a36002f44d8c5445cac47bc1e21ae12238d75eff87c60e","schema_version":"1.0","event_id":"sha256:f3e844d8c4062f4e84a36002f44d8c5445cac47bc1e21ae12238d75eff87c60e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/bundle.json","state_url":"https://pith.science/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/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":"2026-06-24T18:56:29Z","links":{"resolver":"https://pith.science/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ","bundle":"https://pith.science/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/bundle.json","state":"https://pith.science/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQJWZYCHHWA2PRZRPKQA4FVVKQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FQJWZYCHHWA2PRZRPKQA4FVVKQ","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":"0f6f61c82d3c78b9a9507ce1af45cf5c3f13612806d128b7caadc3bb4a1202f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-19T18:58:41Z","title_canon_sha256":"bfeacc9b464ddf45f8e1fc40534d59ec67749531e4b83bad774f37e67a8abb9a"},"schema_version":"1.0","source":{"id":"1510.05620","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05620","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05620v2","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05620","created_at":"2026-05-18T00:48:43Z"},{"alias_kind":"pith_short_12","alias_value":"FQJWZYCHHWA2","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FQJWZYCHHWA2PRZR","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FQJWZYCH","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:f3e844d8c4062f4e84a36002f44d8c5445cac47bc1e21ae12238d75eff87c60e","target":"graph","created_at":"2026-05-18T00:48:43Z","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 multivariate Hawkes processes mainly by including a dependence with respect to the age of the process, i.e. the delay since the last point. Within this class, we investigate the limit behaviour, when n goes to infinity, of a system of n mean-field interacting age-dependent Hawkes processes. We prove that such a system can be approximated by independent and identically distributed age dependent point processes interacting with their own mean intensity. This result generalizes the study performed by Delattre, Fournier and Hoffmann (2015). In continuity with the work of Chevallier e","authors_text":"Julien Chevallier (JAD)","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-19T18:58:41Z","title":"Mean-field limit of generalized Hawkes processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05620","kind":"arxiv","version":2},"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":"sha256:1b68559841407be5b5af2210059ca60dae4aac10e1257368de4768ed430174dd","target":"record","created_at":"2026-05-18T00:48:43Z","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":"0f6f61c82d3c78b9a9507ce1af45cf5c3f13612806d128b7caadc3bb4a1202f6","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-19T18:58:41Z","title_canon_sha256":"bfeacc9b464ddf45f8e1fc40534d59ec67749531e4b83bad774f37e67a8abb9a"},"schema_version":"1.0","source":{"id":"1510.05620","kind":"arxiv","version":2}},"canonical_sha256":"2c136ce0473d81a7c7317aa00e16b55438e4761c8a53847ff85844d5b9f7176a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c136ce0473d81a7c7317aa00e16b55438e4761c8a53847ff85844d5b9f7176a","first_computed_at":"2026-05-18T00:48:43.107833Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:43.107833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dyFWqi/ODSz9+MMxmy+9HTL6Tp16pCA1ynuTItLSty8x8wJFwAUNrJx/FEZHwOG2X6PG4h68b4wb2LhHMt4JDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:43.108279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05620","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b68559841407be5b5af2210059ca60dae4aac10e1257368de4768ed430174dd","sha256:f3e844d8c4062f4e84a36002f44d8c5445cac47bc1e21ae12238d75eff87c60e"],"state_sha256":"25fa1c990d447a9629cd9a9eadc7f73307c85d78fde34eaad312eb6e50fa41ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tSAqflfUakTA7LBTw++ZuonMkIR2/2Ax9LXHhel4Rls6ozkexDrDUkgBgL4QG6vA9uwLyi3S/VtjPOmMW2YBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:56:29.239917Z","bundle_sha256":"094fa84f47e3152d141b78fadb8c958cb5c866be9fc213b56439cac907b5ef5c"}}