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We prove that there exists an integer $k_0$ such that for any integer $k\\geq k_0$ there exist initial data $u_0$ and smooth parameter functions $\\xi(t)\\to q$, $0<\\mu(t)\\to 0$ as $t\\to +\\infty$ such that the solution $u_q$ of the critical nonlinear heat equation \\begin{equation*} \\begin{cases} u_t = \\Delta u + |u|^{\\frac{4}{n-2}}u\\text{ in } \\Omega\\times (0, \\infty),\\\\ u = 0\\text{ on } \\"},"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":"1811.00039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-31T18:05:09Z","cross_cats_sorted":[],"title_canon_sha256":"7f9c068eca33513a8b3c4eeab373a91a0cb991017cfa3a9676adb23446ae3ddf","abstract_canon_sha256":"b26265a279c902e9cf58fac4b0a10a679aab7cd06ccc0baf32daaf894bc07fd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.416667Z","signature_b64":"8KlW8hLFGuVYo4lNdrM+BW754OYo/eUNRif2do+h8FZS7qaU4ob7wCDgF1v54d8nKdiDP2qq/DyHdqKF2sJKBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cd85bd469fccc9eb23c02e8bd465f51c050e0db1cfbe73c88bc07d472bcee14","last_reissued_at":"2026-05-18T00:01:48.416154Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.416154Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign-changing blowing-up solutions for the critical nonlinear heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Manuel del Pino, Monica Musso, Youquan Zheng","submitted_at":"2018-10-31T18:05:09Z","abstract_excerpt":"Let $\\Omega$ be a smooth bounded domain in $\\mathbb{R}^n$ and denote the regular part of the Green's function on $\\Omega$ with Dirichlet boundary condition as $H(x,y)$. 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