{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HWCICTRWSKB7UDYFOU2L3LTAXJ","short_pith_number":"pith:HWCICTRW","canonical_record":{"source":{"id":"2311.11730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-11-20T12:50:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c67178858eef9b820fdfb548195047604983e96cf457aa0edd9eebb4a068c16a","abstract_canon_sha256":"c878fe3a166fcb1376d52390a2b4e2815c77a5fda001eeb1469cb234c6661db3"},"schema_version":"1.0"},"canonical_sha256":"3d84814e369283fa0f057534bdae60ba6c1f338b0badd2d56fbb5546241b84d4","source":{"kind":"arxiv","id":"2311.11730","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.11730","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"2311.11730v1","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.11730","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"HWCICTRWSKB7","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_16","alias_value":"HWCICTRWSKB7UDYF","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_8","alias_value":"HWCICTRW","created_at":"2026-07-05T07:14:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HWCICTRWSKB7UDYFOU2L3LTAXJ","target":"record","payload":{"canonical_record":{"source":{"id":"2311.11730","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-11-20T12:50:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c67178858eef9b820fdfb548195047604983e96cf457aa0edd9eebb4a068c16a","abstract_canon_sha256":"c878fe3a166fcb1376d52390a2b4e2815c77a5fda001eeb1469cb234c6661db3"},"schema_version":"1.0"},"canonical_sha256":"3d84814e369283fa0f057534bdae60ba6c1f338b0badd2d56fbb5546241b84d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:14:38.282594Z","signature_b64":"FQl+v5dbbameAJMfMQGbFVhbZ05CChaWDkh5cEi71viFjaAvBZGSA1m8WMzhznBE+eR2mPhAw1LbGSOXl5HdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d84814e369283fa0f057534bdae60ba6c1f338b0badd2d56fbb5546241b84d4","last_reissued_at":"2026-07-05T07:14:38.282159Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:14:38.282159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.11730","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":"2026-07-05T07:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QyM9Irikf5mUwgsjk3ux32D8djwdMicxdCZRxMe1M1PahIJ5te4+p+30vz2bQx5xAnAwo0Dn9I3B9ASot39ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:03.221794Z"},"content_sha256":"77a16c6b8a4ab30f0b4c66059e957a18cbe420ba9940385e8d5b7cead83fe982","schema_version":"1.0","event_id":"sha256:77a16c6b8a4ab30f0b4c66059e957a18cbe420ba9940385e8d5b7cead83fe982"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HWCICTRWSKB7UDYFOU2L3LTAXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing properties for multivariate Hawkes processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Felix Cheysson (LAMA), Ousmane Boly (AGM - UMR 8088), Thi Hien Nguyen (AGM - UMR 8088)","submitted_at":"2023-11-20T12:50:28Z","abstract_excerpt":"Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the proof to the multivariate case. We illustrate these properties by establishing a functional central limit theorem for multivariate Hawkes processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.11730","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.11730/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNHga0dG8BrZkkKxQ1oqP8P/GfDZTPA/t+0cj6ponsQuKeyCWhTEaBingpvQO6PoeW0O4S8ptgLqwxdSZINJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T11:24:03.222740Z"},"content_sha256":"0ba36df6adb78eb9eb280729b9f14668c8b7d8b54d67c6d47dff583382969e67","schema_version":"1.0","event_id":"sha256:0ba36df6adb78eb9eb280729b9f14668c8b7d8b54d67c6d47dff583382969e67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/bundle.json","state_url":"https://pith.science/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/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":"2026-08-08T11:24:03Z","links":{"resolver":"https://pith.science/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ","bundle":"https://pith.science/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/bundle.json","state":"https://pith.science/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWCICTRWSKB7UDYFOU2L3LTAXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HWCICTRWSKB7UDYFOU2L3LTAXJ","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":"c878fe3a166fcb1376d52390a2b4e2815c77a5fda001eeb1469cb234c6661db3","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-11-20T12:50:28Z","title_canon_sha256":"c67178858eef9b820fdfb548195047604983e96cf457aa0edd9eebb4a068c16a"},"schema_version":"1.0","source":{"id":"2311.11730","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.11730","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"2311.11730v1","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.11730","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"HWCICTRWSKB7","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_16","alias_value":"HWCICTRWSKB7UDYF","created_at":"2026-07-05T07:14:38Z"},{"alias_kind":"pith_short_8","alias_value":"HWCICTRW","created_at":"2026-07-05T07:14:38Z"}],"graph_snapshots":[{"event_id":"sha256:0ba36df6adb78eb9eb280729b9f14668c8b7d8b54d67c6d47dff583382969e67","target":"graph","created_at":"2026-07-05T07:14:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.11730/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Properties of strong mixing have been established for the stationary linear Hawkes process in the univariate case, and can serve as a basis for statistical applications. In this paper, we provide the technical arguments needed to extend the proof to the multivariate case. We illustrate these properties by establishing a functional central limit theorem for multivariate Hawkes processes.","authors_text":"Felix Cheysson (LAMA), Ousmane Boly (AGM - UMR 8088), Thi Hien Nguyen (AGM - UMR 8088)","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-11-20T12:50:28Z","title":"Mixing properties for multivariate Hawkes processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.11730","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":"sha256:77a16c6b8a4ab30f0b4c66059e957a18cbe420ba9940385e8d5b7cead83fe982","target":"record","created_at":"2026-07-05T07:14:38Z","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":"c878fe3a166fcb1376d52390a2b4e2815c77a5fda001eeb1469cb234c6661db3","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2023-11-20T12:50:28Z","title_canon_sha256":"c67178858eef9b820fdfb548195047604983e96cf457aa0edd9eebb4a068c16a"},"schema_version":"1.0","source":{"id":"2311.11730","kind":"arxiv","version":1}},"canonical_sha256":"3d84814e369283fa0f057534bdae60ba6c1f338b0badd2d56fbb5546241b84d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d84814e369283fa0f057534bdae60ba6c1f338b0badd2d56fbb5546241b84d4","first_computed_at":"2026-07-05T07:14:38.282159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:14:38.282159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FQl+v5dbbameAJMfMQGbFVhbZ05CChaWDkh5cEi71viFjaAvBZGSA1m8WMzhznBE+eR2mPhAw1LbGSOXl5HdDg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:14:38.282594Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.11730","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77a16c6b8a4ab30f0b4c66059e957a18cbe420ba9940385e8d5b7cead83fe982","sha256:0ba36df6adb78eb9eb280729b9f14668c8b7d8b54d67c6d47dff583382969e67"],"state_sha256":"9018b39cde7c918d728012801d03413986880f7f186d8f1c58103c8ee7ade592"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9/+9ldBfl6YdkxVd3v9Vymu9o+Gvw1w0VCDzJe5WSANGll6OqCj00T4/ndeH6Pl7JuleF4yYy48wn6f7EPpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T11:24:03.228167Z","bundle_sha256":"e53c2890d501f76ac34bdd15a5cb3ecd3ed28c02f8eb482d4bc6f9decf10219c"}}