{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XRTTGHHUML4GV4AOQ2NLEGTU7U","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":"d6c2b7bd2874e8c1febc4e8e05d089f63b309807111bfe1befac9c2232cfb88f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-27T02:34:48Z","title_canon_sha256":"1df11102892eaa69a45d9d48a232be3c1bb1ac98789a6e03aa8400d6b41de573"},"schema_version":"1.0","source":{"id":"1706.08652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08652","created_at":"2026-05-18T00:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08652v1","created_at":"2026-05-18T00:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08652","created_at":"2026-05-18T00:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"XRTTGHHUML4G","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XRTTGHHUML4GV4AO","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XRTTGHHU","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:5196e87798af96230a7d1d42dc8d7a1ca7c5696e04d3fe8cb26918ca43fbf2bf","target":"graph","created_at":"2026-05-18T00:41:31Z","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 reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous environment. The threshold $R^D_0$ for the model with Dirichlet boundary condition is defined and the threshold $R^F_0(t)$ for the free boundary problem is introduced, and the long-time behavior of positive solutions to the reaction-diffusion-advection system is discussed. Sufficient conditions for the mosquitoes to be eradicated or to spread are given. We show","authors_text":"Jing Ge, Mengyun Zhang, Zhigui Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-27T02:34:48Z","title":"The invasive dynamics of Aedes aegypti mosquito in a heterogenous environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08652","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:b1208e43c944f448a8580fc6bd16c124d65a333f8111f37cace7dbfa37be543e","target":"record","created_at":"2026-05-18T00:41:31Z","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":"d6c2b7bd2874e8c1febc4e8e05d089f63b309807111bfe1befac9c2232cfb88f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-27T02:34:48Z","title_canon_sha256":"1df11102892eaa69a45d9d48a232be3c1bb1ac98789a6e03aa8400d6b41de573"},"schema_version":"1.0","source":{"id":"1706.08652","kind":"arxiv","version":1}},"canonical_sha256":"bc67331cf462f86af00e869ab21a74fd162c60693de36de2f02697033abad958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc67331cf462f86af00e869ab21a74fd162c60693de36de2f02697033abad958","first_computed_at":"2026-05-18T00:41:31.453779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:31.453779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqqjjziRKB3mOEgUkF1XhSO4ZeBrAiZp6CRdZFRXoRv69OXA1Qbh8B/SHjmeUIi2bo2/2mEthWw/rxHRoi8QCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:31.454279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1208e43c944f448a8580fc6bd16c124d65a333f8111f37cace7dbfa37be543e","sha256:5196e87798af96230a7d1d42dc8d7a1ca7c5696e04d3fe8cb26918ca43fbf2bf"],"state_sha256":"eecd843a6a6b50caf5b893cd7040138e22560a67ea18739e7104457082d130e1"}