{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:2SZMRUFZQW5IFAETJEZO7KLPMA","short_pith_number":"pith:2SZMRUFZ","canonical_record":{"source":{"id":"1903.10353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-03-22T12:23:00Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"0bd17776b225a287f578c7a92dcfd587f3e832ff67a2519bee147a7aff879b9c","abstract_canon_sha256":"a4f63bad0c8fdff4388dcaee6692918d5ff2bfd7c17fcb6c288ca4ee6b87e90a"},"schema_version":"1.0"},"canonical_sha256":"d4b2c8d0b985ba8280934932efa96f6018e9bb622aeb6fe84317c08bab0926f4","source":{"kind":"arxiv","id":"1903.10353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10353","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10353v1","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10353","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"2SZMRUFZQW5I","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2SZMRUFZQW5IFAET","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2SZMRUFZ","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:2SZMRUFZQW5IFAETJEZO7KLPMA","target":"record","payload":{"canonical_record":{"source":{"id":"1903.10353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-03-22T12:23:00Z","cross_cats_sorted":["stat.ME"],"title_canon_sha256":"0bd17776b225a287f578c7a92dcfd587f3e832ff67a2519bee147a7aff879b9c","abstract_canon_sha256":"a4f63bad0c8fdff4388dcaee6692918d5ff2bfd7c17fcb6c288ca4ee6b87e90a"},"schema_version":"1.0"},"canonical_sha256":"d4b2c8d0b985ba8280934932efa96f6018e9bb622aeb6fe84317c08bab0926f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:29.737925Z","signature_b64":"EX29BAsfOYZoZL8dWdB0hza9Ukj6CSJSBAST+p3u85RCrWgGekh9MavhQRDdZQkR6PJfZlsSZN5ngGSbaDU5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4b2c8d0b985ba8280934932efa96f6018e9bb622aeb6fe84317c08bab0926f4","last_reissued_at":"2026-05-17T23:50:29.737156Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:29.737156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.10353","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":"2026-05-17T23:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gG1e4i5F57mIHvNPg9tJMZ+2W7oovTdsyIOM+u5Icbk/iHWTPzeblViS67OHnPYDz0SNkCF+0LXQl3+i8YGtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:14:39.165712Z"},"content_sha256":"4e27470a9c4d2c5ca0276314f2b0caa25e3c6769b88ff43ea6f974132a62b026","schema_version":"1.0","event_id":"sha256:4e27470a9c4d2c5ca0276314f2b0caa25e3c6769b88ff43ea6f974132a62b026"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:2SZMRUFZQW5IFAETJEZO7KLPMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The basic reproduction number, $R_0$, in structured populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME"],"primary_cat":"q-bio.PE","authors_text":"Peter Neal, Thitiya Theparod","submitted_at":"2019-03-22T12:23:00Z","abstract_excerpt":"In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household mod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10353","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"66t0H2t2oh43orv8cFePg5LHqix9kjrqCcezKluv4u6L0JTFGlcrWIBjko04oLTaj30MItbIERrCc+bjbWKFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:14:39.166053Z"},"content_sha256":"feabc52c12c77c11eddf59f038d4ecf1366d0bc0415f014700aac0b4165f7ae0","schema_version":"1.0","event_id":"sha256:feabc52c12c77c11eddf59f038d4ecf1366d0bc0415f014700aac0b4165f7ae0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/bundle.json","state_url":"https://pith.science/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/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":"2026-06-24T04:14:39Z","links":{"resolver":"https://pith.science/pith/2SZMRUFZQW5IFAETJEZO7KLPMA","bundle":"https://pith.science/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/bundle.json","state":"https://pith.science/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2SZMRUFZQW5IFAETJEZO7KLPMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2SZMRUFZQW5IFAETJEZO7KLPMA","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":"a4f63bad0c8fdff4388dcaee6692918d5ff2bfd7c17fcb6c288ca4ee6b87e90a","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-03-22T12:23:00Z","title_canon_sha256":"0bd17776b225a287f578c7a92dcfd587f3e832ff67a2519bee147a7aff879b9c"},"schema_version":"1.0","source":{"id":"1903.10353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10353","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10353v1","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10353","created_at":"2026-05-17T23:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"2SZMRUFZQW5I","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"2SZMRUFZQW5IFAET","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"2SZMRUFZ","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:feabc52c12c77c11eddf59f038d4ecf1366d0bc0415f014700aac0b4165f7ae0","target":"graph","created_at":"2026-05-17T23:50:29Z","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":"In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, $R_0$, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both $SIR$ and $SIS$ epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household mod","authors_text":"Peter Neal, Thitiya Theparod","cross_cats":["stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-03-22T12:23:00Z","title":"The basic reproduction number, $R_0$, in structured populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10353","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":"sha256:4e27470a9c4d2c5ca0276314f2b0caa25e3c6769b88ff43ea6f974132a62b026","target":"record","created_at":"2026-05-17T23:50:29Z","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":"a4f63bad0c8fdff4388dcaee6692918d5ff2bfd7c17fcb6c288ca4ee6b87e90a","cross_cats_sorted":["stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-03-22T12:23:00Z","title_canon_sha256":"0bd17776b225a287f578c7a92dcfd587f3e832ff67a2519bee147a7aff879b9c"},"schema_version":"1.0","source":{"id":"1903.10353","kind":"arxiv","version":1}},"canonical_sha256":"d4b2c8d0b985ba8280934932efa96f6018e9bb622aeb6fe84317c08bab0926f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4b2c8d0b985ba8280934932efa96f6018e9bb622aeb6fe84317c08bab0926f4","first_computed_at":"2026-05-17T23:50:29.737156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:29.737156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EX29BAsfOYZoZL8dWdB0hza9Ukj6CSJSBAST+p3u85RCrWgGekh9MavhQRDdZQkR6PJfZlsSZN5ngGSbaDU5AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:29.737925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e27470a9c4d2c5ca0276314f2b0caa25e3c6769b88ff43ea6f974132a62b026","sha256:feabc52c12c77c11eddf59f038d4ecf1366d0bc0415f014700aac0b4165f7ae0"],"state_sha256":"820cd38f9558c26a021bf4321ee596f3a7ddb064054a5b1e054f4d19064402f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2ILZz5huZbKXYjoVhUUujovYloemi/9BKhj9WbXJhnFCJn0sFDUNqO9972sAP9KWVX7Dl8pGpUExasafWJ5Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:14:39.168011Z","bundle_sha256":"12181cc6d414b45f377daa49cc187672fe1cf2c44030b59e74f7cb998355fffa"}}