{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:STJO5DUBMBANOJLMUWACEHKTQG","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":"06490a7fc8ff15935703de44928d1585f612e3c8a21643b710f033c25a278f1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-02T08:01:20Z","title_canon_sha256":"9ff301620685d32f6eb38834b0593f365b274a48a59cbe99cbd5f9fe56c5a3f5"},"schema_version":"1.0","source":{"id":"1809.00308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00308","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00308v1","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00308","created_at":"2026-05-18T00:06:35Z"},{"alias_kind":"pith_short_12","alias_value":"STJO5DUBMBAN","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"STJO5DUBMBANOJLM","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"STJO5DUB","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:8a79f4f1a7f08f8a3bb54397766a2e53d10c014040f0d2eba604a48b9c296203","target":"graph","created_at":"2026-05-18T00:06:35Z","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 study the entire solutions of the Fisher-KPP equation $u_t=u_{xx}+f(u)$ on the half line $[0,\\infty)$ with Dirichlet boundary condition at $x=0$. (1). For any $c\\geq 2\\sqrt{f'(0)}$, we show the existence of an entire solution $\\mathcal{U}^c(x,t)$ which connects the traveling wave solution $\\phi^c(x+ct)$ at $t=-\\infty$ and the unique positive stationary solution $V(x)$ at $t=+\\infty$; (2). We also construct an entire solution $\\mathcal{U}(x,t)$ which connects the solution of $\\eta_t =f(\\eta)$ at $t=-\\infty$ and $V(x)$ at $t=+\\infty$.","authors_text":"Bendong Lou, Junfan Lu, Yoshihisa Morita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-02T08:01:20Z","title":"Entire Solutions of the Fisher-KPP Equation on the Half Line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00308","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":"sha256:97f95750c418cac7e5547bad7dc050060047fab0674edc7eee038880ef2fae4e","target":"record","created_at":"2026-05-18T00:06:35Z","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":"06490a7fc8ff15935703de44928d1585f612e3c8a21643b710f033c25a278f1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-02T08:01:20Z","title_canon_sha256":"9ff301620685d32f6eb38834b0593f365b274a48a59cbe99cbd5f9fe56c5a3f5"},"schema_version":"1.0","source":{"id":"1809.00308","kind":"arxiv","version":1}},"canonical_sha256":"94d2ee8e816040d7256ca580221d538187bebec5fa22efc799893b01cbddc19f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94d2ee8e816040d7256ca580221d538187bebec5fa22efc799893b01cbddc19f","first_computed_at":"2026-05-18T00:06:35.536725Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:35.536725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LMh2+itPhrfbVkTK527DHaU9BaNelikv+huzHr15N7cdUgOtEIFqxuQK3qAorNSJzavedbPi4e+oR0UNQfLsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:35.537234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97f95750c418cac7e5547bad7dc050060047fab0674edc7eee038880ef2fae4e","sha256:8a79f4f1a7f08f8a3bb54397766a2e53d10c014040f0d2eba604a48b9c296203"],"state_sha256":"893400aa18a0dab93479a0cc0824edcc275ec2068c4b3ae007a5254d953a4c73"}