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Here, $f$ is a continuous function with $f(0)=f(1)=0$, and such that~$|f(u)|\\le K|u(1-u)|^\\gamma$ with~$\\gamma\\ge 1/2$, and $\\dot{W}(t,x)$ is a space-time Gaussian white noise. We assume that the initial condition $u_0(x)$ satisfies $0\\le u_0(x)\\le 1$ for all $x\\in\\Rm$, $u_0(x)=1$ for~$x<L_0$ and $ u_0(x)=0$ for~$x>R_0$. We show that when $\\s"},"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":"1903.03645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-08T19:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"b6053f563c7913ab83ca504c51cea0cf2ddb356775e4689b0398013c038d920d","abstract_canon_sha256":"b30b2ab1be690c22a40546c168c1ea7b1a39f39d70081d1f83d2840a34cc1c07"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:41.402553Z","signature_b64":"GqjaRiOaPPbS9cG3eRjHcWRd8znLJyjqwUeXgu7OwXFheVeQiWJYoq+nI+9X3Iyg/Hbs+LQ/GlsgKqOlDzbJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"354dc8a2a58de364e4f3c6b3fd5a436320492b33c3a759139acddb152c069e3a","last_reissued_at":"2026-05-17T23:51:41.402019Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:41.402019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The speed of a random front for stochastic reaction-diffusion equations with strong noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carl Mueller, Lenya Ryzhik, Leonid Mytnik","submitted_at":"2019-03-08T19:45:54Z","abstract_excerpt":"We study the asymptotic speed of a random front for solutions $u_t(x)$ to stochastic reaction-diffusion equations of the form \\[ \\partial_tu=\\farc{1}{2}\\partial_x^2u+f(u)+\\sigma\\sqrt{u(1-u)}\\dot{W}(t,x),~t\\ge 0,~x\\in\\Rm, \\] arising in population genetics. Here, $f$ is a continuous function with $f(0)=f(1)=0$, and such that~$|f(u)|\\le K|u(1-u)|^\\gamma$ with~$\\gamma\\ge 1/2$, and $\\dot{W}(t,x)$ is a space-time Gaussian white noise. We assume that the initial condition $u_0(x)$ satisfies $0\\le u_0(x)\\le 1$ for all $x\\in\\Rm$, $u_0(x)=1$ for~$x<L_0$ and $ u_0(x)=0$ for~$x>R_0$. We show that when $\\s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.03645","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":"1903.03645","created_at":"2026-05-17T23:51:41.402099+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.03645v1","created_at":"2026-05-17T23:51:41.402099+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.03645","created_at":"2026-05-17T23:51:41.402099+00:00"},{"alias_kind":"pith_short_12","alias_value":"GVG4RIVFRXRW","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GVG4RIVFRXRWJZHT","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GVG4RIVF","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.14914","citing_title":"FKPP fronts in quenched random media","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM","json":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM.json","graph_json":"https://pith.science/api/pith-number/GVG4RIVFRXRWJZHTY2Z72WSDMM/graph.json","events_json":"https://pith.science/api/pith-number/GVG4RIVFRXRWJZHTY2Z72WSDMM/events.json","paper":"https://pith.science/paper/GVG4RIVF"},"agent_actions":{"view_html":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM","download_json":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM.json","view_paper":"https://pith.science/paper/GVG4RIVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.03645&json=true","fetch_graph":"https://pith.science/api/pith-number/GVG4RIVFRXRWJZHTY2Z72WSDMM/graph.json","fetch_events":"https://pith.science/api/pith-number/GVG4RIVFRXRWJZHTY2Z72WSDMM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM/action/storage_attestation","attest_author":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM/action/author_attestation","sign_citation":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM/action/citation_signature","submit_replication":"https://pith.science/pith/GVG4RIVFRXRWJZHTY2Z72WSDMM/action/replication_record"}},"created_at":"2026-05-17T23:51:41.402099+00:00","updated_at":"2026-05-17T23:51:41.402099+00:00"}