{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:ML5B6RCNTWXJQ7765ZLPBXK3J4","short_pith_number":"pith:ML5B6RCN","schema_version":"1.0","canonical_sha256":"62fa1f444d9dae987ffeee56f0dd5b4f34b88b68cf62447ddfb1b5467505fcd5","source":{"kind":"arxiv","id":"1104.3686","version":2},"attestation_state":"computed","paper":{"title":"Propagation phenomena for time heterogeneous KPP reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin, Luca Rossi","submitted_at":"2011-04-19T09:50:24Z","abstract_excerpt":"We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation $\\partial_t u -\\Delta u = f(t,u)$, $x\\in R^N$, $t\\in\\R$, where f=f(t,u) is a KPP monostable nonlinearity which depends in a general way on t. A typical f which satisfies our hypotheses is f(t,u)=m(t) u(1-u), with m bounded and having positive infimum. We first prove the existence of generalized transition waves (recently defined by Berestycki and Hamel, Shen) for a given class of speeds. As an application of this result, we obtain the existence of random transition waves when f is a random stat"},"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":"1104.3686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-19T09:50:24Z","cross_cats_sorted":[],"title_canon_sha256":"fb0d0c58fb13753a935a8ba7aa5f1057c1b55215d4a5ead382a976c580a42d69","abstract_canon_sha256":"1be5937059a2d6a36b4b1190aa9e9642c866e326ca3b1ec2a4bf91a30d0bdef0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:12.742862Z","signature_b64":"ZP31Kxq5p5VaYMU6B8yMDA6nIWid97J3HS2EQn9BlSbKuRD/PFQW71D6OkC+VVF+5sEqw5P2ou+H6sjBqjawCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62fa1f444d9dae987ffeee56f0dd5b4f34b88b68cf62447ddfb1b5467505fcd5","last_reissued_at":"2026-05-18T04:23:12.742354Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:12.742354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Propagation phenomena for time heterogeneous KPP reaction-diffusion equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gr\\'egoire Nadin, Luca Rossi","submitted_at":"2011-04-19T09:50:24Z","abstract_excerpt":"We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation $\\partial_t u -\\Delta u = f(t,u)$, $x\\in R^N$, $t\\in\\R$, where f=f(t,u) is a KPP monostable nonlinearity which depends in a general way on t. A typical f which satisfies our hypotheses is f(t,u)=m(t) u(1-u), with m bounded and having positive infimum. We first prove the existence of generalized transition waves (recently defined by Berestycki and Hamel, Shen) for a given class of speeds. As an application of this result, we obtain the existence of random transition waves when f is a random stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3686","kind":"arxiv","version":2},"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":"1104.3686","created_at":"2026-05-18T04:23:12.742429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.3686v2","created_at":"2026-05-18T04:23:12.742429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3686","created_at":"2026-05-18T04:23:12.742429+00:00"},{"alias_kind":"pith_short_12","alias_value":"ML5B6RCNTWXJ","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"ML5B6RCNTWXJQ776","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"ML5B6RCN","created_at":"2026-05-18T12:26:34.985390+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/ML5B6RCNTWXJQ7765ZLPBXK3J4","json":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4.json","graph_json":"https://pith.science/api/pith-number/ML5B6RCNTWXJQ7765ZLPBXK3J4/graph.json","events_json":"https://pith.science/api/pith-number/ML5B6RCNTWXJQ7765ZLPBXK3J4/events.json","paper":"https://pith.science/paper/ML5B6RCN"},"agent_actions":{"view_html":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4","download_json":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4.json","view_paper":"https://pith.science/paper/ML5B6RCN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.3686&json=true","fetch_graph":"https://pith.science/api/pith-number/ML5B6RCNTWXJQ7765ZLPBXK3J4/graph.json","fetch_events":"https://pith.science/api/pith-number/ML5B6RCNTWXJQ7765ZLPBXK3J4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4/action/storage_attestation","attest_author":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4/action/author_attestation","sign_citation":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4/action/citation_signature","submit_replication":"https://pith.science/pith/ML5B6RCNTWXJQ7765ZLPBXK3J4/action/replication_record"}},"created_at":"2026-05-18T04:23:12.742429+00:00","updated_at":"2026-05-18T04:23:12.742429+00:00"}