{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3F554WTFY4K72JLXEDR6JYH2GD","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":"d11ebeb12605003521f2bdbd6d6a33e2cecb8b554f6443bf3e6edceab36b2b6a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-07T22:52:49Z","title_canon_sha256":"39b6c26b8525454046a7c1ffcf161fd4a2192abe1a80fa986382cf0e1c1c2652"},"schema_version":"1.0","source":{"id":"1112.1724","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1724","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1724v1","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1724","created_at":"2026-05-17T23:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"3F554WTFY4K7","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3F554WTFY4K72JLX","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3F554WTF","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:4ad31a5757e78a2aa2d4f627a53207eb41707afbc10d3ee0f0814c8c99c0a11e","target":"graph","created_at":"2026-05-17T23:50:43Z","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 introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we es","authors_text":"Angel Calsina, Jozsef Z. Farkas","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-07T22:52:49Z","title":"Steady states in a structured epidemic model with Wentzell boundary condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1724","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":"sha256:26d646fbc66af376a022a639002e4e67f4a1a1537e551449896c99fddaf30526","target":"record","created_at":"2026-05-17T23:50:43Z","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":"d11ebeb12605003521f2bdbd6d6a33e2cecb8b554f6443bf3e6edceab36b2b6a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-07T22:52:49Z","title_canon_sha256":"39b6c26b8525454046a7c1ffcf161fd4a2192abe1a80fa986382cf0e1c1c2652"},"schema_version":"1.0","source":{"id":"1112.1724","kind":"arxiv","version":1}},"canonical_sha256":"d97bde5a65c715fd257720e3e4e0fa30cf6a9ff12d5c58e5953650c26f398f4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d97bde5a65c715fd257720e3e4e0fa30cf6a9ff12d5c58e5953650c26f398f4e","first_computed_at":"2026-05-17T23:50:43.089817Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:43.089817Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fRr2aZWqTksqrPuZra3GZKVQzijXfqt9C0J4W3kTWzVFdK26ZGNCN1LfENFh3C8/vzuMjaLaLFAn0v6fowH4BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:43.090601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1724","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26d646fbc66af376a022a639002e4e67f4a1a1537e551449896c99fddaf30526","sha256:4ad31a5757e78a2aa2d4f627a53207eb41707afbc10d3ee0f0814c8c99c0a11e"],"state_sha256":"3bdfb70e01490682471db78e6e78300d08a6a4006d51bf2b997e8ca2cf23ed35"}