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The relation between diffusion and taxis sensitivity is critical since the ratio $u(u+1)^m/(u+1)^{m-1}$ grows like $u^{2/n}$ for large $u$ with $n = \\dim((0, 1)) = 1$. Nonetheless, we show that there is no critical mass ph"},"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":"2606.18006","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-16T14:52:21Z","cross_cats_sorted":[],"title_canon_sha256":"76b779794e28cb182dee5c52da2dfd6db8131c413b4cd6ebf06d7ea6e1b39f4a","abstract_canon_sha256":"ce6ffbbdac483a02d5b60d0426fd36c5ca717bed96ee166b741293d6a585773e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:45.696137Z","signature_b64":"C9Xy6EI+EGI6v3oCftfotG5Q0mmWsq0CGDYPyP33OjURKNZ9RwXzkRCxcUbOckn+gfe4OWgy27nBGTqf9ttfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d74aace6ae90b0f0ddb0590390bc6e584fc089e78b421e43c28cb56bcd362970","last_reissued_at":"2026-06-19T16:10:45.695788Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:45.695788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Absence of critical mass phenomena in one-dimensional critical quasilinear Keller-Segel systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mario Fuest, Xinru Cao","submitted_at":"2026-06-16T14:52:21Z","abstract_excerpt":"We consider the Neumann initial boundary value problem associated to the chemotaxis system \\begin{align}\\label{prob:abstract}\\tag{$\\star$} \\begin{cases} u_t = \\big((u+1)^{m-1} u_x - u(u+1)^m v_x\\big)_x & \\text{in $(0, 1) \\times (0, \\infty)$}, \\\\ v_t = v_{xx} - v + u, &\\text{in $(0, 1) \\times (0, \\infty)$}, \\end{cases} \\end{align} where $m \\in \\mathbb R$ is a given parameter. The relation between diffusion and taxis sensitivity is critical since the ratio $u(u+1)^m/(u+1)^{m-1}$ grows like $u^{2/n}$ for large $u$ with $n = \\dim((0, 1)) = 1$. 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