{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JRJFRURTX6JT7D5UC3GS5EONBL","short_pith_number":"pith:JRJFRURT","schema_version":"1.0","canonical_sha256":"4c5258d233bf933f8fb416cd2e91cd0ac651541f8b04a14bb7b2e8a890b83ba2","source":{"kind":"arxiv","id":"1101.1611","version":1},"attestation_state":"computed","paper":{"title":"Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Saichev, D. Sornette","submitted_at":"2011-01-08T18:17:14Z","abstract_excerpt":"We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which past activity triggers future activity. The term \"multivariate\" refers to the property that events come in different types, with possibly different intra- and inter-triggering abilities. We develop the general formalism of the multivariate generating moment function for the cumulative number of first-generation and of all generation events triggered by a giv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1101.1611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-01-08T18:17:14Z","cross_cats_sorted":["physics.geo-ph"],"title_canon_sha256":"b5ce1d4ccd4bc1e93cc912c1763e73ed7bb8399e1d2f95131e26e6e2b96e1eb0","abstract_canon_sha256":"8f28e2821c06cb00fd4e3a9736c564790613bb21bb327fcd9435431016a7d009"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:32.734576Z","signature_b64":"HnRzBpA+kDu9dpegzySBRqbpbk/alDibg9VG5EAfVL0XlJn3vQAsfpyztKbqPFi2ONJzVBECJrvH3XtWZefGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c5258d233bf933f8fb416cd2e91cd0ac651541f8b04a14bb7b2e8a890b83ba2","last_reissued_at":"2026-05-18T02:44:32.734174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:32.734174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hierarchy of Temporal Responses of Multivariate Self-Excited Epidemic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.geo-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Saichev, D. Sornette","submitted_at":"2011-01-08T18:17:14Z","abstract_excerpt":"We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which past activity triggers future activity. The term \"multivariate\" refers to the property that events come in different types, with possibly different intra- and inter-triggering abilities. We develop the general formalism of the multivariate generating moment function for the cumulative number of first-generation and of all generation events triggered by a giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1611","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.1611","created_at":"2026-05-18T02:44:32.734232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.1611v1","created_at":"2026-05-18T02:44:32.734232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1611","created_at":"2026-05-18T02:44:32.734232+00:00"},{"alias_kind":"pith_short_12","alias_value":"JRJFRURTX6JT","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JRJFRURTX6JT7D5U","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JRJFRURT","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL","json":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL.json","graph_json":"https://pith.science/api/pith-number/JRJFRURTX6JT7D5UC3GS5EONBL/graph.json","events_json":"https://pith.science/api/pith-number/JRJFRURTX6JT7D5UC3GS5EONBL/events.json","paper":"https://pith.science/paper/JRJFRURT"},"agent_actions":{"view_html":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL","download_json":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL.json","view_paper":"https://pith.science/paper/JRJFRURT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.1611&json=true","fetch_graph":"https://pith.science/api/pith-number/JRJFRURTX6JT7D5UC3GS5EONBL/graph.json","fetch_events":"https://pith.science/api/pith-number/JRJFRURTX6JT7D5UC3GS5EONBL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL/action/storage_attestation","attest_author":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL/action/author_attestation","sign_citation":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL/action/citation_signature","submit_replication":"https://pith.science/pith/JRJFRURTX6JT7D5UC3GS5EONBL/action/replication_record"}},"created_at":"2026-05-18T02:44:32.734232+00:00","updated_at":"2026-05-18T02:44:32.734232+00:00"}