{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WGKG5B7ABWUKAYTJRGTEI6KYUT","short_pith_number":"pith:WGKG5B7A","canonical_record":{"source":{"id":"1706.04563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-14T16:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"85608ba00944f3cc3691f08645b61cc04816b0ef685d33d38c49b16c4be552f1","abstract_canon_sha256":"2a185491870731256fdce5e9df5a73c924822ee1f007806d7187935aeb9bc7a1"},"schema_version":"1.0"},"canonical_sha256":"b1946e87e00da8a0626989a6447958a4e2bb9710bc8c6d9c696b33b6edbbb6cf","source":{"kind":"arxiv","id":"1706.04563","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04563","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04563v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04563","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"WGKG5B7ABWUK","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WGKG5B7ABWUKAYTJ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WGKG5B7A","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WGKG5B7ABWUKAYTJRGTEI6KYUT","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-14T16:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"85608ba00944f3cc3691f08645b61cc04816b0ef685d33d38c49b16c4be552f1","abstract_canon_sha256":"2a185491870731256fdce5e9df5a73c924822ee1f007806d7187935aeb9bc7a1"},"schema_version":"1.0"},"canonical_sha256":"b1946e87e00da8a0626989a6447958a4e2bb9710bc8c6d9c696b33b6edbbb6cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:22.313096Z","signature_b64":"ELm5dIhF317flXA5pUPTMF/gS0kxrj6iUn/L1LnCk7779tuo+kg1ykQ8rCBaqvz3qtVxIl2gHI8PrB0poUWUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1946e87e00da8a0626989a6447958a4e2bb9710bc8c6d9c696b33b6edbbb6cf","last_reissued_at":"2026-05-18T00:42:22.312435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:22.312435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04563","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BilPecnojifzwVm4WEGd7YB/5s7Rr3gMn9F0R321K0ODsUr/r6tnrdP/AC7fogd/zU6dZMfOw3FdLMUhlcJoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:39:32.301268Z"},"content_sha256":"b94d7124bfdc5a4a1f0439fa36e0b53ff31841ed804f0cf8ab6738cdf13f2b60","schema_version":"1.0","event_id":"sha256:b94d7124bfdc5a4a1f0439fa36e0b53ff31841ed804f0cf8ab6738cdf13f2b60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WGKG5B7ABWUKAYTJRGTEI6KYUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Vector-Host Epidemic Model with Spatial Structure and Age of Infection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Glenn F. Webb, Jeffrey J. Morgan, William E. Fitzgibbon, Yixiang Wu","submitted_at":"2017-06-14T16:10:40Z","abstract_excerpt":"In this paper we study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of the host population incorporated to account for incubation periods. The disease is transmitted between vector and host populations in crisscross fashion. The existence of solutions of the model is studied by operator semigroup methods, and the asymptotic behavior of the solution is investigated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04563","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CE84ouo9HtK689/xiGiSBTWcgDPVGwU7CTLZXvejjq75BkqI7asjO7qUDk1nOd9wPnvl22DY5Dq5pAqjIQQICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:39:32.301624Z"},"content_sha256":"b0da4d8cf9cfcf0e465c02ec7e73d648c947e9d044d3f8c840353d395664059a","schema_version":"1.0","event_id":"sha256:b0da4d8cf9cfcf0e465c02ec7e73d648c947e9d044d3f8c840353d395664059a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/bundle.json","state_url":"https://pith.science/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/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":"2026-06-01T11:39:32Z","links":{"resolver":"https://pith.science/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT","bundle":"https://pith.science/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/bundle.json","state":"https://pith.science/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGKG5B7ABWUKAYTJRGTEI6KYUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WGKG5B7ABWUKAYTJRGTEI6KYUT","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":"2a185491870731256fdce5e9df5a73c924822ee1f007806d7187935aeb9bc7a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-14T16:10:40Z","title_canon_sha256":"85608ba00944f3cc3691f08645b61cc04816b0ef685d33d38c49b16c4be552f1"},"schema_version":"1.0","source":{"id":"1706.04563","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04563","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04563v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04563","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"WGKG5B7ABWUK","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WGKG5B7ABWUKAYTJ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WGKG5B7A","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:b0da4d8cf9cfcf0e465c02ec7e73d648c947e9d044d3f8c840353d395664059a","target":"graph","created_at":"2026-05-18T00:42:22Z","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 study a diffusive age structured epidemic model with disease transmission between vector and host populations. The dynamics of the populations are described by reaction-diffusion equations, with infection age structure of the host population incorporated to account for incubation periods. The disease is transmitted between vector and host populations in crisscross fashion. The existence of solutions of the model is studied by operator semigroup methods, and the asymptotic behavior of the solution is investigated.","authors_text":"Glenn F. Webb, Jeffrey J. Morgan, William E. Fitzgibbon, Yixiang Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-14T16:10:40Z","title":"A Vector-Host Epidemic Model with Spatial Structure and Age of Infection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04563","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:b94d7124bfdc5a4a1f0439fa36e0b53ff31841ed804f0cf8ab6738cdf13f2b60","target":"record","created_at":"2026-05-18T00:42:22Z","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":"2a185491870731256fdce5e9df5a73c924822ee1f007806d7187935aeb9bc7a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-14T16:10:40Z","title_canon_sha256":"85608ba00944f3cc3691f08645b61cc04816b0ef685d33d38c49b16c4be552f1"},"schema_version":"1.0","source":{"id":"1706.04563","kind":"arxiv","version":1}},"canonical_sha256":"b1946e87e00da8a0626989a6447958a4e2bb9710bc8c6d9c696b33b6edbbb6cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1946e87e00da8a0626989a6447958a4e2bb9710bc8c6d9c696b33b6edbbb6cf","first_computed_at":"2026-05-18T00:42:22.312435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:22.312435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ELm5dIhF317flXA5pUPTMF/gS0kxrj6iUn/L1LnCk7779tuo+kg1ykQ8rCBaqvz3qtVxIl2gHI8PrB0poUWUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:22.313096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04563","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b94d7124bfdc5a4a1f0439fa36e0b53ff31841ed804f0cf8ab6738cdf13f2b60","sha256:b0da4d8cf9cfcf0e465c02ec7e73d648c947e9d044d3f8c840353d395664059a"],"state_sha256":"5ca98e8fe03dc88041540e893ccc100a99ce5e247b5cbd9af8564d388b0df40f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ceypl35oIRQGCTv05aqGOltH5pxHhrVtvVbOnHB09yuIyIAagoxxbzR9uU6YTimC9uDqR1aPC2crKTZPaT4OAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:39:32.303536Z","bundle_sha256":"00641b0832c88be193e321e0d89491965693b339c17895fff02225a4ecfdad36"}}