{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DUGAMGFF76HQPPXIKWZ7ADY7GG","short_pith_number":"pith:DUGAMGFF","canonical_record":{"source":{"id":"1606.04600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-06-15T00:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"f2713a27649ebb1454293b6f1f83a6db06c37b9d0089472f2c2845f07cf05b48","abstract_canon_sha256":"ce103fbfad36ee315b35535cd8c4982454977be27f0e78df4ee021e40d378d50"},"schema_version":"1.0"},"canonical_sha256":"1d0c0618a5ff8f07bee855b3f00f1f319106ae710a8b836115ba15522071db5f","source":{"kind":"arxiv","id":"1606.04600","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04600","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04600v1","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04600","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"pith_short_12","alias_value":"DUGAMGFF76HQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DUGAMGFF76HQPPXI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DUGAMGFF","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DUGAMGFF76HQPPXIKWZ7ADY7GG","target":"record","payload":{"canonical_record":{"source":{"id":"1606.04600","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-06-15T00:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"f2713a27649ebb1454293b6f1f83a6db06c37b9d0089472f2c2845f07cf05b48","abstract_canon_sha256":"ce103fbfad36ee315b35535cd8c4982454977be27f0e78df4ee021e40d378d50"},"schema_version":"1.0"},"canonical_sha256":"1d0c0618a5ff8f07bee855b3f00f1f319106ae710a8b836115ba15522071db5f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.634081Z","signature_b64":"FnbXDEHVyaypZzwma3VMG1vs8x42+6jHoQ/dZOfRrZP9DhDnp+4Rb1OIbX3i6sKZWBAMIX9iyTkG8a7vkxJ6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d0c0618a5ff8f07bee855b3f00f1f319106ae710a8b836115ba15522071db5f","last_reissued_at":"2026-05-18T01:07:50.633692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.633692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.04600","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":"2026-05-18T01:07:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6iurTIA/ORUhVgpPPn8EBbCeotvmugFmcCpYojvkme8zLPV1jo9cRKA7uYzmfKqF05GFsI3dXu3ED1izYMQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:27.130385Z"},"content_sha256":"a1ee87b8273c25b418a7704c2cb374925b004c11790ee45e6f78bbd723ee3404","schema_version":"1.0","event_id":"sha256:a1ee87b8273c25b418a7704c2cb374925b004c11790ee45e6f78bbd723ee3404"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DUGAMGFF76HQPPXIKWZ7ADY7GG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic solutions in an SIRWS model with immune boosting and cross-immunity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Barry D. Hughes, Federico Frascoli, James M. McCaw, Tiffany Leung","submitted_at":"2016-06-15T00:48:48Z","abstract_excerpt":"Incidence of whooping cough, an infection caused by Bordetella pertussis and Bordetella parapertussis, has been on the rise since the 1980s in many countries. Immunological interactions, such as immune boosting and cross-immunity between pathogens, have been hypothesised to be important drivers of epidemiological dynamics. We present a two-pathogen model of transmission which examines how immune boosting and cross-immunity can influence the timing and severity of epidemics. We use a combination of numerical simulations and bifurcation techniques to study the dynamical properties of the system,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04600","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":"2026-05-18T01:07:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OV0CMG7KEf1189yV14o5nEDu8f5Mg0WoRq89Nv1sklnOeDYltmHPUT/OV6VB3+hhWm7XWs5crQ5E4WSoGSr6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:27.130729Z"},"content_sha256":"12070af6c4928b6081f56b9224fbfa4702afab59d1140c3879ee37194e8d7e60","schema_version":"1.0","event_id":"sha256:12070af6c4928b6081f56b9224fbfa4702afab59d1140c3879ee37194e8d7e60"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/bundle.json","state_url":"https://pith.science/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/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":"2026-05-28T23:12:27Z","links":{"resolver":"https://pith.science/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG","bundle":"https://pith.science/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/bundle.json","state":"https://pith.science/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DUGAMGFF76HQPPXIKWZ7ADY7GG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DUGAMGFF76HQPPXIKWZ7ADY7GG","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":"ce103fbfad36ee315b35535cd8c4982454977be27f0e78df4ee021e40d378d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-06-15T00:48:48Z","title_canon_sha256":"f2713a27649ebb1454293b6f1f83a6db06c37b9d0089472f2c2845f07cf05b48"},"schema_version":"1.0","source":{"id":"1606.04600","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04600","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04600v1","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04600","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"pith_short_12","alias_value":"DUGAMGFF76HQ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DUGAMGFF76HQPPXI","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DUGAMGFF","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:12070af6c4928b6081f56b9224fbfa4702afab59d1140c3879ee37194e8d7e60","target":"graph","created_at":"2026-05-18T01:07:50Z","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":"Incidence of whooping cough, an infection caused by Bordetella pertussis and Bordetella parapertussis, has been on the rise since the 1980s in many countries. Immunological interactions, such as immune boosting and cross-immunity between pathogens, have been hypothesised to be important drivers of epidemiological dynamics. We present a two-pathogen model of transmission which examines how immune boosting and cross-immunity can influence the timing and severity of epidemics. We use a combination of numerical simulations and bifurcation techniques to study the dynamical properties of the system,","authors_text":"Barry D. Hughes, Federico Frascoli, James M. McCaw, Tiffany Leung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-06-15T00:48:48Z","title":"Periodic solutions in an SIRWS model with immune boosting and cross-immunity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04600","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:a1ee87b8273c25b418a7704c2cb374925b004c11790ee45e6f78bbd723ee3404","target":"record","created_at":"2026-05-18T01:07:50Z","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":"ce103fbfad36ee315b35535cd8c4982454977be27f0e78df4ee021e40d378d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-06-15T00:48:48Z","title_canon_sha256":"f2713a27649ebb1454293b6f1f83a6db06c37b9d0089472f2c2845f07cf05b48"},"schema_version":"1.0","source":{"id":"1606.04600","kind":"arxiv","version":1}},"canonical_sha256":"1d0c0618a5ff8f07bee855b3f00f1f319106ae710a8b836115ba15522071db5f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d0c0618a5ff8f07bee855b3f00f1f319106ae710a8b836115ba15522071db5f","first_computed_at":"2026-05-18T01:07:50.633692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:50.633692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FnbXDEHVyaypZzwma3VMG1vs8x42+6jHoQ/dZOfRrZP9DhDnp+4Rb1OIbX3i6sKZWBAMIX9iyTkG8a7vkxJ6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:50.634081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04600","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1ee87b8273c25b418a7704c2cb374925b004c11790ee45e6f78bbd723ee3404","sha256:12070af6c4928b6081f56b9224fbfa4702afab59d1140c3879ee37194e8d7e60"],"state_sha256":"e12d93e85935a80e533cce79bc17f29338cfb6df0825e4baf8e32158d5b8b947"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PXLr/BzBg5wuWI1CbcNGm+cH1fXifluDszTa7I8o7uluFl7fJ75VNPLh2Jc/n6Xt7c1pXN2lBaqDS3KgHDFiBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:12:27.132563Z","bundle_sha256":"cca402bf016e1370b7a0c48765f1baa42404c64cc52deb8e5c76d87a7e749a69"}}