{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:G6U7VO44CNMMGT6LSRSRWCJYJM","short_pith_number":"pith:G6U7VO44","canonical_record":{"source":{"id":"1311.3209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-13T16:58:34Z","cross_cats_sorted":["math.DS","q-bio.PE"],"title_canon_sha256":"d249c8d8cadceacf9bb7164a54ed44923d3af18b2c3acbe232741accaa296088","abstract_canon_sha256":"35bbf9242a64b87cbfec5b6ced217d3e5c2c6b1e2f40804a846cc8d83afc61cd"},"schema_version":"1.0"},"canonical_sha256":"37a9fabb9c1358c34fcb94651b09384b0a2420a43b85394a6a9bdf971ddb5dfb","source":{"kind":"arxiv","id":"1311.3209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3209","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3209v1","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3209","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"G6U7VO44CNMM","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G6U7VO44CNMMGT6L","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G6U7VO44","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:G6U7VO44CNMMGT6LSRSRWCJYJM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-13T16:58:34Z","cross_cats_sorted":["math.DS","q-bio.PE"],"title_canon_sha256":"d249c8d8cadceacf9bb7164a54ed44923d3af18b2c3acbe232741accaa296088","abstract_canon_sha256":"35bbf9242a64b87cbfec5b6ced217d3e5c2c6b1e2f40804a846cc8d83afc61cd"},"schema_version":"1.0"},"canonical_sha256":"37a9fabb9c1358c34fcb94651b09384b0a2420a43b85394a6a9bdf971ddb5dfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:12.694755Z","signature_b64":"u43RX0MhUzrobFmr4ghO12lcL8RpNqtvA2cdSKOM/kobICILBEm3ZYgTkn9TmYNT1CEqWhmrNX6O+7yEJXhRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37a9fabb9c1358c34fcb94651b09384b0a2420a43b85394a6a9bdf971ddb5dfb","last_reissued_at":"2026-05-18T03:07:12.694060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:12.694060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3209","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":"2026-05-18T03:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wu5VtqaAP0R4eOn9Wdnj2fYW+gld2oBLZ/g4yoqAnERGhSVIqv3Q4Qqu6Uf+6LiuQQ3KeSLK3svI7XgdrrMAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:42.176883Z"},"content_sha256":"ab4b2a59e2292807bb22057545a9eed859f9d1b58b7088f577a5c499dc18ea2d","schema_version":"1.0","event_id":"sha256:ab4b2a59e2292807bb22057545a9eed859f9d1b58b7088f577a5c499dc18ea2d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:G6U7VO44CNMMGT6LSRSRWCJYJM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a malaria model with mosquito host choice and bed-net control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","q-bio.PE"],"primary_cat":"math.CA","authors_text":"Bruno Buonomo","submitted_at":"2013-11-13T16:58:34Z","abstract_excerpt":"A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The occurrence of a backward bifurcation at R_0=1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3209","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":"2026-05-18T03:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KNfjE+6DHRP0C52IaGK5hwEV4FI+2QJ9ZPfiuZz8P6tcuFuuxqiIDTaIZ4UjrHcOx1YGsrf3z5LJ67HYVW8SDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:46:42.177605Z"},"content_sha256":"d7c721e714db5cd1fc7c60309b050d20d0242922c7d14cb815f69d0fc7ba9f52","schema_version":"1.0","event_id":"sha256:d7c721e714db5cd1fc7c60309b050d20d0242922c7d14cb815f69d0fc7ba9f52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/bundle.json","state_url":"https://pith.science/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/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":"2026-06-09T07:46:42Z","links":{"resolver":"https://pith.science/pith/G6U7VO44CNMMGT6LSRSRWCJYJM","bundle":"https://pith.science/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/bundle.json","state":"https://pith.science/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G6U7VO44CNMMGT6LSRSRWCJYJM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:G6U7VO44CNMMGT6LSRSRWCJYJM","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":"35bbf9242a64b87cbfec5b6ced217d3e5c2c6b1e2f40804a846cc8d83afc61cd","cross_cats_sorted":["math.DS","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-13T16:58:34Z","title_canon_sha256":"d249c8d8cadceacf9bb7164a54ed44923d3af18b2c3acbe232741accaa296088"},"schema_version":"1.0","source":{"id":"1311.3209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3209","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3209v1","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3209","created_at":"2026-05-18T03:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"G6U7VO44CNMM","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"G6U7VO44CNMMGT6L","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"G6U7VO44","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:d7c721e714db5cd1fc7c60309b050d20d0242922c7d14cb815f69d0fc7ba9f52","target":"graph","created_at":"2026-05-18T03:07:12Z","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":"A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The occurrence of a backward bifurcation at R_0=1 is shown to be possible, which implies that multiple endemic equilibria co-exist with a stable disease-free equilibrium when the basic reproduction number is less than unity. This phenomenon is found to be caused by disease-induced human mortality. The global asymptotic stability of the endemic equilibrium for R_","authors_text":"Bruno Buonomo","cross_cats":["math.DS","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-13T16:58:34Z","title":"Analysis of a malaria model with mosquito host choice and bed-net control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3209","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:ab4b2a59e2292807bb22057545a9eed859f9d1b58b7088f577a5c499dc18ea2d","target":"record","created_at":"2026-05-18T03:07:12Z","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":"35bbf9242a64b87cbfec5b6ced217d3e5c2c6b1e2f40804a846cc8d83afc61cd","cross_cats_sorted":["math.DS","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-13T16:58:34Z","title_canon_sha256":"d249c8d8cadceacf9bb7164a54ed44923d3af18b2c3acbe232741accaa296088"},"schema_version":"1.0","source":{"id":"1311.3209","kind":"arxiv","version":1}},"canonical_sha256":"37a9fabb9c1358c34fcb94651b09384b0a2420a43b85394a6a9bdf971ddb5dfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37a9fabb9c1358c34fcb94651b09384b0a2420a43b85394a6a9bdf971ddb5dfb","first_computed_at":"2026-05-18T03:07:12.694060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:12.694060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u43RX0MhUzrobFmr4ghO12lcL8RpNqtvA2cdSKOM/kobICILBEm3ZYgTkn9TmYNT1CEqWhmrNX6O+7yEJXhRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:12.694755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab4b2a59e2292807bb22057545a9eed859f9d1b58b7088f577a5c499dc18ea2d","sha256:d7c721e714db5cd1fc7c60309b050d20d0242922c7d14cb815f69d0fc7ba9f52"],"state_sha256":"d51f50303a3e368e6768cced4bdbd9f75b3a16786db8948ddeaef402ab05a6f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdb4GtIJkrDliVFzDVqxQMgjCjk9GecfqqYocxKHnHHVNK+fiAGVv98NmZjhxgS59YQ6jlMkI8thK2T1ycKUCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:46:42.181235Z","bundle_sha256":"c4bc4ab8e2a226242fe1b15072413f0f641217e42e0d4613f7c01f0e3f2d5d0e"}}