{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:HN4UJ75KKEVU4OXNTRLSO46JXV","short_pith_number":"pith:HN4UJ75K","schema_version":"1.0","canonical_sha256":"3b7944ffaa512b4e3aed9c572773c9bd492f87dd4d7e0837d1432846c1273aaa","source":{"kind":"arxiv","id":"1111.5161","version":1},"attestation_state":"computed","paper":{"title":"Pushed traveling fronts in monostable equations with monotone delayed reaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk","submitted_at":"2011-11-22T11:24:44Z","abstract_excerpt":"We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \\Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \\R_+ \\to \\R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \\leq g'(0)x,$ $x \\geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish "},"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":"1111.5161","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-22T11:24:44Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"fa631b01979332bcf6c8c290cebd7026aee6ee974f4cb1bb61b20d294a2b8954","abstract_canon_sha256":"59e3b69b873c791e05cab0ce7bf0c15bebeb2ddebd8c4855c10239cc5faa8f8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:17.169543Z","signature_b64":"uxX2WuPJIfs/njAE9zPCh6yEslVqw+7BKcwBeJgEHhM4ZSoCJh088yTo+7x7InYZCUxbjeUMCGXXkGqFPW8pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b7944ffaa512b4e3aed9c572773c9bd492f87dd4d7e0837d1432846c1273aaa","last_reissued_at":"2026-05-18T03:32:17.168929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:17.168929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pushed traveling fronts in monostable equations with monotone delayed reaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Elena Trofimchuk, Manuel Pinto, Sergei Trofimchuk","submitted_at":"2011-11-22T11:24:44Z","abstract_excerpt":"We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \\Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \\R_+ \\to \\R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \\leq g'(0)x,$ $x \\geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5161","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":"1111.5161","created_at":"2026-05-18T03:32:17.169011+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.5161v1","created_at":"2026-05-18T03:32:17.169011+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5161","created_at":"2026-05-18T03:32:17.169011+00:00"},{"alias_kind":"pith_short_12","alias_value":"HN4UJ75KKEVU","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HN4UJ75KKEVU4OXN","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HN4UJ75K","created_at":"2026-05-18T12:26:30.835961+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/HN4UJ75KKEVU4OXNTRLSO46JXV","json":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV.json","graph_json":"https://pith.science/api/pith-number/HN4UJ75KKEVU4OXNTRLSO46JXV/graph.json","events_json":"https://pith.science/api/pith-number/HN4UJ75KKEVU4OXNTRLSO46JXV/events.json","paper":"https://pith.science/paper/HN4UJ75K"},"agent_actions":{"view_html":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV","download_json":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV.json","view_paper":"https://pith.science/paper/HN4UJ75K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.5161&json=true","fetch_graph":"https://pith.science/api/pith-number/HN4UJ75KKEVU4OXNTRLSO46JXV/graph.json","fetch_events":"https://pith.science/api/pith-number/HN4UJ75KKEVU4OXNTRLSO46JXV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV/action/storage_attestation","attest_author":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV/action/author_attestation","sign_citation":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV/action/citation_signature","submit_replication":"https://pith.science/pith/HN4UJ75KKEVU4OXNTRLSO46JXV/action/replication_record"}},"created_at":"2026-05-18T03:32:17.169011+00:00","updated_at":"2026-05-18T03:32:17.169011+00:00"}