{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TIK6J7UHQL66O4SNYNL3HJ2CUV","short_pith_number":"pith:TIK6J7UH","canonical_record":{"source":{"id":"1310.8360","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T01:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"6c4c0c9874d1022c17df47a748ab41dbd88e7882647fb782ffc65e093265fd8a","abstract_canon_sha256":"22065962c90cce8c9d30d6bcdfbec6fdcb40be2e8d5dd2bf882a181111f36785"},"schema_version":"1.0"},"canonical_sha256":"9a15e4fe8782fde7724dc357b3a742a5771006fc507023e52b7902b9b3397de1","source":{"kind":"arxiv","id":"1310.8360","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8360","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8360v4","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8360","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"TIK6J7UHQL66","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TIK6J7UHQL66O4SN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TIK6J7UH","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TIK6J7UHQL66O4SNYNL3HJ2CUV","target":"record","payload":{"canonical_record":{"source":{"id":"1310.8360","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T01:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"6c4c0c9874d1022c17df47a748ab41dbd88e7882647fb782ffc65e093265fd8a","abstract_canon_sha256":"22065962c90cce8c9d30d6bcdfbec6fdcb40be2e8d5dd2bf882a181111f36785"},"schema_version":"1.0"},"canonical_sha256":"9a15e4fe8782fde7724dc357b3a742a5771006fc507023e52b7902b9b3397de1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:48.613406Z","signature_b64":"/tP6Pqs0ns/RNIC1EDm1wa9/o7x/tqBYFl/QWHrLz1KCg3p52QcUYO3bFt5CB3tVkZ1hS7uFDFEzPpCNknahCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a15e4fe8782fde7724dc357b3a742a5771006fc507023e52b7902b9b3397de1","last_reissued_at":"2026-05-18T02:03:48.612753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:48.612753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.8360","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:03:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpG6JZUU4bwBbp+uv0zwDm8lvqM0LUDXh7n37yzp3NTGAhw6WwULH0CpPZ0L9ZxSyJ3RbgqSCAdUuosMhCluDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:18:20.800379Z"},"content_sha256":"c9523083d7e5a2577c84c5c60801bd7da80f6a420c3c4fad82c136e56b7fdb3e","schema_version":"1.0","event_id":"sha256:c9523083d7e5a2577c84c5c60801bd7da80f6a420c3c4fad82c136e56b7fdb3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TIK6J7UHQL66O4SNYNL3HJ2CUV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A SIS reaction-diffusion-advection model in a low-risk and high-risk domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Huaiping Zhu, Jing Ge, Kwang Ik Kim, Zhigui Lin","submitted_at":"2013-10-31T01:48:51Z","abstract_excerpt":"A simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary is introduced to model the contact transmission at the spreading front of the disease. The behavior of positive solutions to a reaction-diffusion-advection system are discussed. The basic reproduction number $R_0^F(t)$ associated with the diseases in the spatial setting is introduced for this diffusive SIS model with the free boundary, we prove that fast diff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8360","kind":"arxiv","version":4},"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":"2026-05-18T02:03:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"893lRdtr2ZmiE3a6xt/kTeYlFsjggVa9G5X97l4H3OY1Rj9pHMnfgr9etd5SO7ETcKDzTQFMf5sz0/JLkchhCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:18:20.800730Z"},"content_sha256":"8f3ea89b9dba4903b2b0b50c39b50f0b569868f13671814511fe10f5295218e3","schema_version":"1.0","event_id":"sha256:8f3ea89b9dba4903b2b0b50c39b50f0b569868f13671814511fe10f5295218e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/bundle.json","state_url":"https://pith.science/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/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":"2026-05-31T08:18:20Z","links":{"resolver":"https://pith.science/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV","bundle":"https://pith.science/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/bundle.json","state":"https://pith.science/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIK6J7UHQL66O4SNYNL3HJ2CUV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TIK6J7UHQL66O4SNYNL3HJ2CUV","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":"22065962c90cce8c9d30d6bcdfbec6fdcb40be2e8d5dd2bf882a181111f36785","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T01:48:51Z","title_canon_sha256":"6c4c0c9874d1022c17df47a748ab41dbd88e7882647fb782ffc65e093265fd8a"},"schema_version":"1.0","source":{"id":"1310.8360","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8360","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8360v4","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8360","created_at":"2026-05-18T02:03:48Z"},{"alias_kind":"pith_short_12","alias_value":"TIK6J7UHQL66","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TIK6J7UHQL66O4SN","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TIK6J7UH","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:8f3ea89b9dba4903b2b0b50c39b50f0b569868f13671814511fe10f5295218e3","target":"graph","created_at":"2026-05-18T02:03:48Z","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 simplified SIS reaction-diffusion-advection model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The free boundary is introduced to model the contact transmission at the spreading front of the disease. The behavior of positive solutions to a reaction-diffusion-advection system are discussed. The basic reproduction number $R_0^F(t)$ associated with the diseases in the spatial setting is introduced for this diffusive SIS model with the free boundary, we prove that fast diff","authors_text":"Huaiping Zhu, Jing Ge, Kwang Ik Kim, Zhigui Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T01:48:51Z","title":"A SIS reaction-diffusion-advection model in a low-risk and high-risk domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8360","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:c9523083d7e5a2577c84c5c60801bd7da80f6a420c3c4fad82c136e56b7fdb3e","target":"record","created_at":"2026-05-18T02:03:48Z","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":"22065962c90cce8c9d30d6bcdfbec6fdcb40be2e8d5dd2bf882a181111f36785","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-31T01:48:51Z","title_canon_sha256":"6c4c0c9874d1022c17df47a748ab41dbd88e7882647fb782ffc65e093265fd8a"},"schema_version":"1.0","source":{"id":"1310.8360","kind":"arxiv","version":4}},"canonical_sha256":"9a15e4fe8782fde7724dc357b3a742a5771006fc507023e52b7902b9b3397de1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a15e4fe8782fde7724dc357b3a742a5771006fc507023e52b7902b9b3397de1","first_computed_at":"2026-05-18T02:03:48.612753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:48.612753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/tP6Pqs0ns/RNIC1EDm1wa9/o7x/tqBYFl/QWHrLz1KCg3p52QcUYO3bFt5CB3tVkZ1hS7uFDFEzPpCNknahCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:48.613406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8360","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9523083d7e5a2577c84c5c60801bd7da80f6a420c3c4fad82c136e56b7fdb3e","sha256:8f3ea89b9dba4903b2b0b50c39b50f0b569868f13671814511fe10f5295218e3"],"state_sha256":"274fb4a9c44422c3cf7455cba1b1f89bf3a49a1d7cd87cdcd87ab67a2e35a3b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvSTObck28dCwW9IvL3XL16Xnuo2Z5zhejVhqDnezw2j0QdoO4P3I7RBOLiwoXVSP1alviAmIz5w3rXYsNHeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:18:20.802654Z","bundle_sha256":"8ef3bb5b43ea7a2454d8e643e46a3465c3519f3b69bd256d4ca2b727fcf2f119"}}