{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GZN5SRPUJ4AKNULYO3W3E6X3QA","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":"db268f4cfee11b7a10f4aed5ee9b1073cb867ba9a4293b2f3675b47b1d73a3e0","cross_cats_sorted":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-02-04T16:26:19Z","title_canon_sha256":"a152428ba759bfe2676a21c435533d7577e968a74118ab9c557538d3548e6d15"},"schema_version":"1.0","source":{"id":"1602.01730","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.01730","created_at":"2026-05-18T00:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1602.01730v3","created_at":"2026-05-18T00:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01730","created_at":"2026-05-18T00:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"GZN5SRPUJ4AK","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZN5SRPUJ4AKNULY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZN5SRPU","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:0fc73235ebbe11e4d6fc4dc7e5564c11aad42d87bbd7d87146b421dc14fa3ae7","target":"graph","created_at":"2026-05-18T00:51:01Z","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 prove that, for Poisson transmission and recovery processes, the classic Susceptible $\\to$ Infected $\\to$ Recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time $t>0$, a strict lower bound on the expected number of suscpetibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.","authors_text":"Frank G. Ball, Kieran J. Sharkey, Robert R. Wilkinson","cross_cats":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-02-04T16:26:19Z","title":"The deterministic Kermack-McKendrick model bounds the general stochastic epidemic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01730","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":"sha256:777e7af4b7b739a1b1d9c954ac9a7352e6b438239bd52db826de4190600acf4b","target":"record","created_at":"2026-05-18T00:51:01Z","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":"db268f4cfee11b7a10f4aed5ee9b1073cb867ba9a4293b2f3675b47b1d73a3e0","cross_cats_sorted":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-02-04T16:26:19Z","title_canon_sha256":"a152428ba759bfe2676a21c435533d7577e968a74118ab9c557538d3548e6d15"},"schema_version":"1.0","source":{"id":"1602.01730","kind":"arxiv","version":3}},"canonical_sha256":"365bd945f44f00a6d17876edb27afb803e14984ccd9e71fa58d7ef0880e8e0a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"365bd945f44f00a6d17876edb27afb803e14984ccd9e71fa58d7ef0880e8e0a9","first_computed_at":"2026-05-18T00:51:01.407743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:01.407743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOgxODaTafVYd+E0Ij9sxZRrnwzR0W5T/1e/mc/hlKwxeWppyt1DlyiMf6ZbuCVyyTPcpDYp1jmTiDdrjreEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:01.408224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.01730","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:777e7af4b7b739a1b1d9c954ac9a7352e6b438239bd52db826de4190600acf4b","sha256:0fc73235ebbe11e4d6fc4dc7e5564c11aad42d87bbd7d87146b421dc14fa3ae7"],"state_sha256":"e4fcd604066c53a9afe20f815030b036ffd1e988079b8b16cb695543c33c2d54"}