{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SW6LWXWNJYGFIFTIQCMANK5WCH","short_pith_number":"pith:SW6LWXWN","schema_version":"1.0","canonical_sha256":"95bcbb5ecd4e0c541668809806abb611c6ff1539e1c0f1b374e461195e3f20ec","source":{"kind":"arxiv","id":"1408.6326","version":1},"attestation_state":"computed","paper":{"title":"The spreading fronts of an infective environment in a man-environment-man epidemic model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inkyung Ahn, Zhigui Lin","submitted_at":"2014-08-27T06:38:39Z","abstract_excerpt":"A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model.\n  The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally transmitted disease. The basic reproduction number $R^F_0(t)$ for the free boundary problem is introduced, and the behavior of positive solutions to the reaction-diffusion system is discussed. Sufficient conditions for the bacteria to vanish or spread are given. We show that, if $R_0\\leq 1$, the bacteria always vanish, and if $R^F_0(t_0)\\geq 1$ for some $t_"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.6326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-27T06:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"18d3d017a8ebfaa5ac1fd4d88cefade1cd141098e4a05663c4ea7762f2aaeaa9","abstract_canon_sha256":"21e101c45512a25d20343cd4faffa510deb04779a055a14f4891132d87d96ec4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.746790Z","signature_b64":"Q8iea0aCxaDf3M/XxjlFQfUCfXMu+LAZUfKK4JcklIpmQIPemuJ52eoAmO6L2h/1qdRaH7W7VGzKnCQeUOo2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95bcbb5ecd4e0c541668809806abb611c6ff1539e1c0f1b374e461195e3f20ec","last_reissued_at":"2026-05-18T02:44:07.746227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.746227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The spreading fronts of an infective environment in a man-environment-man epidemic model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inkyung Ahn, Zhigui Lin","submitted_at":"2014-08-27T06:38:39Z","abstract_excerpt":"A reaction-diffusion model is investigated to understand infective environments in a man-environment-man epidemic model.\n  The free boundary is introduced to describe the expanding front of an infective environment induced by fecally-orally transmitted disease. The basic reproduction number $R^F_0(t)$ for the free boundary problem is introduced, and the behavior of positive solutions to the reaction-diffusion system is discussed. Sufficient conditions for the bacteria to vanish or spread are given. We show that, if $R_0\\leq 1$, the bacteria always vanish, and if $R^F_0(t_0)\\geq 1$ for some $t_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6326","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.6326","created_at":"2026-05-18T02:44:07.746306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.6326v1","created_at":"2026-05-18T02:44:07.746306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6326","created_at":"2026-05-18T02:44:07.746306+00:00"},{"alias_kind":"pith_short_12","alias_value":"SW6LWXWNJYGF","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SW6LWXWNJYGFIFTI","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SW6LWXWN","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH","json":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH.json","graph_json":"https://pith.science/api/pith-number/SW6LWXWNJYGFIFTIQCMANK5WCH/graph.json","events_json":"https://pith.science/api/pith-number/SW6LWXWNJYGFIFTIQCMANK5WCH/events.json","paper":"https://pith.science/paper/SW6LWXWN"},"agent_actions":{"view_html":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH","download_json":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH.json","view_paper":"https://pith.science/paper/SW6LWXWN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.6326&json=true","fetch_graph":"https://pith.science/api/pith-number/SW6LWXWNJYGFIFTIQCMANK5WCH/graph.json","fetch_events":"https://pith.science/api/pith-number/SW6LWXWNJYGFIFTIQCMANK5WCH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH/action/storage_attestation","attest_author":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH/action/author_attestation","sign_citation":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH/action/citation_signature","submit_replication":"https://pith.science/pith/SW6LWXWNJYGFIFTIQCMANK5WCH/action/replication_record"}},"created_at":"2026-05-18T02:44:07.746306+00:00","updated_at":"2026-05-18T02:44:07.746306+00:00"}