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For every sufficiently large integer \\(n\\), we construct a codimension-\\(n\\) Lipschitz manifold of non-radial initial data whose corresponding solutions blow up in finite time and whose rescaled profiles converge to the prescribed self-similar profile \\(\\Phi_n\\) of the homogeneous equation.\n  The main novelty is to show that the finite-codimensional stability mechanism for self-similar blow-up, developed in the w"},"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":"2607.11165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T07:01:52Z","cross_cats_sorted":[],"title_canon_sha256":"51a1ea190e27d560ce9136d37ddc76be3d5d1cbdd30055ec82e7a5e7267e266a","abstract_canon_sha256":"f93da3ebbf86754b567be50aabd570c777289346fc38133a23a9e37aaccc1968"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:22:19.848874Z","signature_b64":"KQmnw3zMcTFi6+g0q5Su181U7AbyeUomZ07M5vWR6sdQ+hu2p5UDusmwAV+e56MxvP0xHQL0FJhkPePXVP6aCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b8f80d32484cc0156d777caa41e51f9f427afdd858593ecef8c52750363be65","last_reissued_at":"2026-07-14T01:22:19.848046Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:22:19.848046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite time blow-up for an inhomogeneous parabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kaiqiang Zhang","submitted_at":"2026-07-13T07:01:52Z","abstract_excerpt":"We consider the inhomogeneous nonlinear heat equation \\[ \\partial_t u-\\Delta u=|u|^{p-1}u+f(x),\\qquad x\\in\\mathbb{R}^3,\\quad p>5, \\] where \\(f\\in L^\\infty\\cap C^{0,1}(\\mathbb{R}^3)\\). For every sufficiently large integer \\(n\\), we construct a codimension-\\(n\\) Lipschitz manifold of non-radial initial data whose corresponding solutions blow up in finite time and whose rescaled profiles converge to the prescribed self-similar profile \\(\\Phi_n\\) of the homogeneous equation.\n  The main novelty is to show that the finite-codimensional stability mechanism for self-similar blow-up, developed in the w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11165","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.11165/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.11165","created_at":"2026-07-14T01:22:19.848472+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.11165v1","created_at":"2026-07-14T01:22:19.848472+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11165","created_at":"2026-07-14T01:22:19.848472+00:00"},{"alias_kind":"pith_short_12","alias_value":"POHYBUZEQTGA","created_at":"2026-07-14T01:22:19.848472+00:00"},{"alias_kind":"pith_short_16","alias_value":"POHYBUZEQTGACVWX","created_at":"2026-07-14T01:22:19.848472+00:00"},{"alias_kind":"pith_short_8","alias_value":"POHYBUZE","created_at":"2026-07-14T01:22:19.848472+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/POHYBUZEQTGACVWXO7FKIHSR7H","json":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H.json","graph_json":"https://pith.science/api/pith-number/POHYBUZEQTGACVWXO7FKIHSR7H/graph.json","events_json":"https://pith.science/api/pith-number/POHYBUZEQTGACVWXO7FKIHSR7H/events.json","paper":"https://pith.science/paper/POHYBUZE"},"agent_actions":{"view_html":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H","download_json":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H.json","view_paper":"https://pith.science/paper/POHYBUZE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.11165&json=true","fetch_graph":"https://pith.science/api/pith-number/POHYBUZEQTGACVWXO7FKIHSR7H/graph.json","fetch_events":"https://pith.science/api/pith-number/POHYBUZEQTGACVWXO7FKIHSR7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H/action/storage_attestation","attest_author":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H/action/author_attestation","sign_citation":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H/action/citation_signature","submit_replication":"https://pith.science/pith/POHYBUZEQTGACVWXO7FKIHSR7H/action/replication_record"}},"created_at":"2026-07-14T01:22:19.848472+00:00","updated_at":"2026-07-14T01:22:19.848472+00:00"}