{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:D7GZWIDA6OOWKEDYQLHJOVNLZA","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":"7a9e395065b19d18352990e8b46d9188bfc7ae66a169e09b6b50c2122d2a4f7d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-12-10T19:21:05Z","title_canon_sha256":"cfd5453d4b38ef9318131b35394de22bec26639c5893a8d15ebdfb74d4f5ef14"},"schema_version":"1.0","source":{"id":"1212.2172","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2172","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2172v3","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2172","created_at":"2026-05-18T03:04:22Z"},{"alias_kind":"pith_short_12","alias_value":"D7GZWIDA6OOW","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"D7GZWIDA6OOWKEDY","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"D7GZWIDA","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:8d32dc2e3c873852bdaf24c4ff6c4139d88d25e868331c9850a95b5e61a596ec","target":"graph","created_at":"2026-05-18T03:04:22Z","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 consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this ``deterministic'' representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.","authors_text":"Istvan Z. Kiss, Kieran J. Sharkey, Peter L. Simon, Robert R. Wilkinson","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-12-10T19:21:05Z","title":"Exact equations for SIR epidemics on tree graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2172","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":"sha256:9aa67dc1d0f995d957e3ca3198215ecf09c8135616d09777c4c323210fc92545","target":"record","created_at":"2026-05-18T03:04:22Z","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":"7a9e395065b19d18352990e8b46d9188bfc7ae66a169e09b6b50c2122d2a4f7d","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2012-12-10T19:21:05Z","title_canon_sha256":"cfd5453d4b38ef9318131b35394de22bec26639c5893a8d15ebdfb74d4f5ef14"},"schema_version":"1.0","source":{"id":"1212.2172","kind":"arxiv","version":3}},"canonical_sha256":"1fcd9b2060f39d65107882ce9755abc82e36718ebf9ab43a81e872260f0558c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fcd9b2060f39d65107882ce9755abc82e36718ebf9ab43a81e872260f0558c6","first_computed_at":"2026-05-18T03:04:22.599938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:22.599938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j53ATvQ1xyIPQVr/VuAWzVfg3WyW5NDO7ZmTGcjcYDGrD0tHlIDElqS+UzdsiYg02fNxZ2LkZf7qfF4f8BljDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:22.600330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2172","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9aa67dc1d0f995d957e3ca3198215ecf09c8135616d09777c4c323210fc92545","sha256:8d32dc2e3c873852bdaf24c4ff6c4139d88d25e868331c9850a95b5e61a596ec"],"state_sha256":"7bea2e010db7fe7dace50f6f40ae3900bc3a497517ac2127f5823929e86c7be4"}