{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3XZ75ITXB4AS35FJY6A4CM3JR3","short_pith_number":"pith:3XZ75ITX","canonical_record":{"source":{"id":"1710.06984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-19T02:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"00009c9cd0b8624a571fc073bec36c8f6381dabe66943b4f76a42a8e55e3fa76","abstract_canon_sha256":"40eb7491fed31dce4a718675b7725b364192b84d15f1282adca7b2ed26648136"},"schema_version":"1.0"},"canonical_sha256":"ddf3fea2770f012df4a9c781c133698ee36397a6434aec2c6c64cca52b96af1f","source":{"kind":"arxiv","id":"1710.06984","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06984","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06984v2","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06984","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"3XZ75ITXB4AS","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3XZ75ITXB4AS35FJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3XZ75ITX","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3XZ75ITXB4AS35FJY6A4CM3JR3","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06984","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-19T02:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"00009c9cd0b8624a571fc073bec36c8f6381dabe66943b4f76a42a8e55e3fa76","abstract_canon_sha256":"40eb7491fed31dce4a718675b7725b364192b84d15f1282adca7b2ed26648136"},"schema_version":"1.0"},"canonical_sha256":"ddf3fea2770f012df4a9c781c133698ee36397a6434aec2c6c64cca52b96af1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:47.073661Z","signature_b64":"QRfKXNjoykRuWnPrZM+dM1LJM+rkMrukhq4XewNJrBhaucKf+/C5LWzzh3WD9MfNX6hrjpDoXrVfhs9t3mGBCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddf3fea2770f012df4a9c781c133698ee36397a6434aec2c6c64cca52b96af1f","last_reissued_at":"2026-05-17T23:41:47.072928Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:47.072928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06984","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2JtKz0h/psMS/egRZraH/HkNUkuX+0HSdW22xWn/JBIDvgI66kxpG1OIpZpIs+f/MyYDYq/vGwl5VvsUPXvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:56:55.734484Z"},"content_sha256":"2450d34ddcec9959a31782b20dd27be4e155eef12343ee5e81304891f6889bb1","schema_version":"1.0","event_id":"sha256:2450d34ddcec9959a31782b20dd27be4e155eef12343ee5e81304891f6889bb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3XZ75ITXB4AS35FJY6A4CM3JR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global stability of the multi-strain Kermack-McKendrick (renewal) epidemic model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Daniel G. Cocks, Emma S. McBryde, Michael T. Meehan","submitted_at":"2017-10-19T02:03:50Z","abstract_excerpt":"We extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain $R_{0j}$ represents a sharp threshold parameter such that when $R_{0j} \\leq 1$ for all $j$ each strain dies out and the infection-free equilibrium is globally asymptotically stable; whereas for $R_{01} \\equiv \\mathrm{max}_j\\, R_{0j} > 1$ the endemic equilibrium point $\\bar{P}^1$, at which only the fittest strain (i.e. strain 1) remains in circulation, become"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06984","kind":"arxiv","version":2},"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":"2026-05-17T23:41:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBMbG1IyBypUcyYN5P5Fo1q5RmMCjHM+nCWXzowiffe/efY6EVmjogPw98cGxaX6K0cC8g17fUC2mwCe+kTtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:56:55.735068Z"},"content_sha256":"0a5b5987893c95a45f95793c1db8f736d466767d65aa68672c35df1a25d10c94","schema_version":"1.0","event_id":"sha256:0a5b5987893c95a45f95793c1db8f736d466767d65aa68672c35df1a25d10c94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/bundle.json","state_url":"https://pith.science/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/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":"2026-05-18T21:56:55Z","links":{"resolver":"https://pith.science/pith/3XZ75ITXB4AS35FJY6A4CM3JR3","bundle":"https://pith.science/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/bundle.json","state":"https://pith.science/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3XZ75ITXB4AS35FJY6A4CM3JR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3XZ75ITXB4AS35FJY6A4CM3JR3","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":"40eb7491fed31dce4a718675b7725b364192b84d15f1282adca7b2ed26648136","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-19T02:03:50Z","title_canon_sha256":"00009c9cd0b8624a571fc073bec36c8f6381dabe66943b4f76a42a8e55e3fa76"},"schema_version":"1.0","source":{"id":"1710.06984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06984","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06984v2","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06984","created_at":"2026-05-17T23:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"3XZ75ITXB4AS","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3XZ75ITXB4AS35FJ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3XZ75ITX","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:0a5b5987893c95a45f95793c1db8f736d466767d65aa68672c35df1a25d10c94","target":"graph","created_at":"2026-05-17T23:41:47Z","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 extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain $R_{0j}$ represents a sharp threshold parameter such that when $R_{0j} \\leq 1$ for all $j$ each strain dies out and the infection-free equilibrium is globally asymptotically stable; whereas for $R_{01} \\equiv \\mathrm{max}_j\\, R_{0j} > 1$ the endemic equilibrium point $\\bar{P}^1$, at which only the fittest strain (i.e. strain 1) remains in circulation, become","authors_text":"Daniel G. Cocks, Emma S. McBryde, Michael T. Meehan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-19T02:03:50Z","title":"Global stability of the multi-strain Kermack-McKendrick (renewal) epidemic model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06984","kind":"arxiv","version":2},"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":"sha256:2450d34ddcec9959a31782b20dd27be4e155eef12343ee5e81304891f6889bb1","target":"record","created_at":"2026-05-17T23:41:47Z","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":"40eb7491fed31dce4a718675b7725b364192b84d15f1282adca7b2ed26648136","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2017-10-19T02:03:50Z","title_canon_sha256":"00009c9cd0b8624a571fc073bec36c8f6381dabe66943b4f76a42a8e55e3fa76"},"schema_version":"1.0","source":{"id":"1710.06984","kind":"arxiv","version":2}},"canonical_sha256":"ddf3fea2770f012df4a9c781c133698ee36397a6434aec2c6c64cca52b96af1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddf3fea2770f012df4a9c781c133698ee36397a6434aec2c6c64cca52b96af1f","first_computed_at":"2026-05-17T23:41:47.072928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:47.072928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QRfKXNjoykRuWnPrZM+dM1LJM+rkMrukhq4XewNJrBhaucKf+/C5LWzzh3WD9MfNX6hrjpDoXrVfhs9t3mGBCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:47.073661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2450d34ddcec9959a31782b20dd27be4e155eef12343ee5e81304891f6889bb1","sha256:0a5b5987893c95a45f95793c1db8f736d466767d65aa68672c35df1a25d10c94"],"state_sha256":"ecfd97e308126e57de59324b52271bfd925ed5927ab90faae4eb8071d662cc66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NngrQ48Rj1/ohPyuHAd9yuZPUkoa0cRlljvwP3FDf+xRfb10JkUCCwAyOSdEbIYU5u8ctfd2zwfJpqMODVIAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:56:55.737013Z","bundle_sha256":"fb201dde8601266abe94feea9a10e2aacb8fb76488332cd5b7d5be525de14504"}}