{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GZN5SRPUJ4AKNULYO3W3E6X3QA","short_pith_number":"pith:GZN5SRPU","schema_version":"1.0","canonical_sha256":"365bd945f44f00a6d17876edb27afb803e14984ccd9e71fa58d7ef0880e8e0a9","source":{"kind":"arxiv","id":"1602.01730","version":3},"attestation_state":"computed","paper":{"title":"The deterministic Kermack-McKendrick model bounds the general stochastic epidemic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Frank G. Ball, Kieran J. Sharkey, Robert R. Wilkinson","submitted_at":"2016-02-04T16:26:19Z","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."},"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":"1602.01730","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-02-04T16:26:19Z","cross_cats_sorted":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"title_canon_sha256":"a152428ba759bfe2676a21c435533d7577e968a74118ab9c557538d3548e6d15","abstract_canon_sha256":"db268f4cfee11b7a10f4aed5ee9b1073cb867ba9a4293b2f3675b47b1d73a3e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:01.408224Z","signature_b64":"tOgxODaTafVYd+E0Ij9sxZRrnwzR0W5T/1e/mc/hlKwxeWppyt1DlyiMf6ZbuCVyyTPcpDYp1jmTiDdrjreEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"365bd945f44f00a6d17876edb27afb803e14984ccd9e71fa58d7ef0880e8e0a9","last_reissued_at":"2026-05-18T00:51:01.407743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:01.407743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The deterministic Kermack-McKendrick model bounds the general stochastic epidemic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.PR","physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Frank G. Ball, Kieran J. Sharkey, Robert R. Wilkinson","submitted_at":"2016-02-04T16:26:19Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01730","kind":"arxiv","version":3},"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":"1602.01730","created_at":"2026-05-18T00:51:01.407830+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.01730v3","created_at":"2026-05-18T00:51:01.407830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.01730","created_at":"2026-05-18T00:51:01.407830+00:00"},{"alias_kind":"pith_short_12","alias_value":"GZN5SRPUJ4AK","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GZN5SRPUJ4AKNULY","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GZN5SRPU","created_at":"2026-05-18T12:30:19.053100+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/GZN5SRPUJ4AKNULYO3W3E6X3QA","json":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA.json","graph_json":"https://pith.science/api/pith-number/GZN5SRPUJ4AKNULYO3W3E6X3QA/graph.json","events_json":"https://pith.science/api/pith-number/GZN5SRPUJ4AKNULYO3W3E6X3QA/events.json","paper":"https://pith.science/paper/GZN5SRPU"},"agent_actions":{"view_html":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA","download_json":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA.json","view_paper":"https://pith.science/paper/GZN5SRPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.01730&json=true","fetch_graph":"https://pith.science/api/pith-number/GZN5SRPUJ4AKNULYO3W3E6X3QA/graph.json","fetch_events":"https://pith.science/api/pith-number/GZN5SRPUJ4AKNULYO3W3E6X3QA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA/action/storage_attestation","attest_author":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA/action/author_attestation","sign_citation":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA/action/citation_signature","submit_replication":"https://pith.science/pith/GZN5SRPUJ4AKNULYO3W3E6X3QA/action/replication_record"}},"created_at":"2026-05-18T00:51:01.407830+00:00","updated_at":"2026-05-18T00:51:01.407830+00:00"}