{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RRM65BTO3J5TS33EIDPZAFW7TQ","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":"2faa13fa215bf80501f132443f7cab7eab3741d89085066f3dfa1d2d062b1cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-06T06:31:58Z","title_canon_sha256":"e27697e08ba7b57e079a94fe04266cd7d584d439a7c0a3f2bcce6857fc5bc461"},"schema_version":"1.0","source":{"id":"1307.1754","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1754","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1754v4","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1754","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"RRM65BTO3J5T","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RRM65BTO3J5TS33E","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RRM65BTO","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:f90fb7189e0f5d5c3162c3731f318c2d991deb221ce7bbd1d2d7c6485589670b","target":"graph","created_at":"2026-05-18T02:49:46Z","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 propose two nonlinear models for the control of anthracnose disease. The first is an ordinary differential equation (ODE) model which represents the within-host evolution of the disease. The second includes spatial diffusion of the disease in a bounded domain. We demonstrate the well-posedness of those models by verifying the existence of solutions for given initial conditions and positive invariance of the positive cone. By considering a quadratic cost functional and applying a maximum principle, we construct a feedback optimal control for the ODE model which is evaluated thr","authors_text":"Christopher Thron, David B\\'ekoll\\'e, David Fotsa, Elvis Houpa, Michel Ndoumb\\'e","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-06T06:31:58Z","title":"Mathematical modelling and optimal control of anthracnose"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1754","kind":"arxiv","version":4},"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:c89517366f173fa396c799946a9adce7c535035e6727a437ab0c0ae620e949f5","target":"record","created_at":"2026-05-18T02:49:46Z","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":"2faa13fa215bf80501f132443f7cab7eab3741d89085066f3dfa1d2d062b1cbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-07-06T06:31:58Z","title_canon_sha256":"e27697e08ba7b57e079a94fe04266cd7d584d439a7c0a3f2bcce6857fc5bc461"},"schema_version":"1.0","source":{"id":"1307.1754","kind":"arxiv","version":4}},"canonical_sha256":"8c59ee866eda7b396f6440df9016df9c0ee2fe54fb4b8f633750348144b5fbd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c59ee866eda7b396f6440df9016df9c0ee2fe54fb4b8f633750348144b5fbd8","first_computed_at":"2026-05-18T02:49:46.004455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:46.004455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S3g/R8itarQvxKhJGCjJTbFQP027b5nUP+t/+E6/vowlra7SxAV7JSuRupjmn67vayHPimiQxSjieCi660GDBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:46.004826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1754","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c89517366f173fa396c799946a9adce7c535035e6727a437ab0c0ae620e949f5","sha256:f90fb7189e0f5d5c3162c3731f318c2d991deb221ce7bbd1d2d7c6485589670b"],"state_sha256":"6cf139887413742928987985134d49abd8d684c8e54eb6054675ddb2e244fcbb"}